JP2013044901A - Quantum state generating method, quantum state generating device, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To generate a plurality of quantum bits in desired entanglement states while suppressing influence of loss, using a probabilistic gate.SOLUTION: A method includes performing X measurement of one quantum bit contained in a first quantum bit set consisting of three or more quantum bits in an entanglement state, to generate a second quantum bit set in a quantum state: |η>|Φ>|Φ>|η>+|η>|Φ>|Φ>|η>. To the quantum state and a quantum state of a third quantum bit set: |η>|Φ>|η>+|η>|Φ>|η>, a quantum operation is applied represented by the relation: γ<Φ|<Φ|+γ<Φ|<Φ|, to generate a fourth quantum bit set in a quantum state: |η>|Φ>|η>+|η>|Φ>|η>, which is in an entanglement state.

Description

  The present invention relates to a quantum computation technique, and more particularly to a technique for generating an entanglement state qubit.

  In recent years, quantum information processing has been proposed that enables processing that has been impossible until now by using quantum mechanics. For example, in the one-way quantum calculation disclosed in Non-Patent Document 1 and the like, a plurality of qubits are changed to an entanglement state called a cluster state having a quantum mechanical correlation, and then measurement and control for a single qubit are performed. Quantum computation is performed by doing.

  In order to realize one-way quantum computation, it is necessary to implement a realistic device and deal with loss and error, and various methods for realizing one-way quantum computation have been proposed so far. (See, for example, Non-Patent Document 2-11).

  In addition, it is known that linear optical quantum calculations using single photon generators, linear optical elements, photon detectors, etc. cannot be implemented in principle by deterministic gates, but only by stochastic gates. However, non-patent literature 3 shows that quantum computation is possible. Note that “deterministic gate” means a gate whose output is uniquely specified with respect to the input, and “stochastic gate” means a gate whose output is specified stochastically with respect to the input. .

Robert Raussendorf and Hans J. Briegel, “A One-Way Quantum Computer,” Phys. Rev. Lett. 86, 5188-5191 (2001). Daniel E. Browne and Terry Rudolph, “Resource-Efficient Linear Optical Quantum Computation,” Phys. Rev. Lett. 95, 010501 (2005). E Knill, R Laflamme, and Gj Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46-52 (2001). Michael Varnava, Daniel Browne, and Terry Rudolph, “Loss Tolerance in One-Way Quantum Computation via Counterfactual Error Correction,” Physical Review Letters 97, (2006). Michael Varnava, Daniel E. Browne, and Terry Rudolph, “How good must single photon sources and detectors be for efficient linear optical quantum computation?” Phys. Rev. Lett. 100, 060502 (2008). C M Dawson, H L Haselgrove, and M A Nielsen, “Noise Thresholds for Optical Quantum Computers,” Phys. Rev. Lett. 96020501, (2006). Sean Barrett and Thomas Stace, “Fault Tolerant Quantum Computation with Very High Threshold for Loss Errors,” Phys. Rev. Lett. 105, 200502 (2010). R. Raussendorf, J. Harrington, and K. Goyal, “A fault-tolerant one-way quantum computer,” Annals Of Physics 321, 2242-2270 (2005). R Raussendorf and J Harrington, “Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions,” Phys. Rev. Lett. 98, 190504 (2007). Keisuke Fujii and Yuuki Tokunaga, “Fault-Tolerant Topological One-Way Quantum Computation with Probabilistic Two-Qubit Gates,” Phys. Rev. Lett. 105, 250503 (2010). Ying Li, Sean Barrett, Thomas Stace, and Simon Benjamin, “Fault Tolerant Quantum Computation with Nondeterministic Gates,” Physical Review Letters 105, 1-4 (2010).

  As described above, in the one-way quantum calculation, it is necessary to generate a plurality of qubits in a desired cluster state in order to perform the quantum calculation. However, a specific method for efficiently generating a plurality of qubits in a desired entanglement state using a stochastic gate and suppressing the influence of loss is not known. This is not only a problem when performing one-way quantum computation, but is a problem common when generating a plurality of qubits in a desired entanglement state.

  The present invention has been made in view of these points, and provides a technique for generating a plurality of qubits in a desired entanglement state using a stochastic gate while suppressing the influence of loss. Objective.

In the present invention, β ₀₁ , β ₀₂ , β ₀₃ , β ₀₄ represent complex numbers, | η ₁ >, | η ₂ >, | η ₃ >, | η ₄ > each represent an arbitrary quantum state, When each of Φ ₁ >, | Φ ₂ >, | Φ ₃ >, | Φ ₄ > represents a quantum state of one qubit, and | H>, | V> represents a quantum state of a calculation base (Β ₀₁ | η ₁ > | Φ ₁ > + β ₀₂ | η ₂ > | Φ ₂ >) | H> (β ₀₃ | Φ ₃ > | η ₃ > + β ₀₄ | Φ ₄ > | η ₄ >) + (Β ₀₁ | η ₁ > | Φ ₁ > −β ₀₂ | η ₂ > | Φ ₂ >) | V> (β ₀₃ | Φ ₃ > | η ₃ > −β ₀₄ | Φ ₄ > | η ₄ >) A single qubit in a superposed state of quantum states | H> and | V> included in a first qubit set composed of three or more qubits in the entanglement state in the quantum state X And measuring the X-measured one qubit to the first qubit set A second qubit set which is a complementary set removed from the first qubit is generated, and the specific quanta included in the second qubit set in the adjacent entanglement state with the one qubit measured in X When the bit quantum state is overlapped with | Φ ₁ > | Φ ₃ > and | Φ ₂ > | Φ ₄ >, and the quantum states of the second qubit set are represented by β ₁₃ and β ₂₄ as complex numbers Β ₁₃ | η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + β ₂₄ | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ >, and α ₅ and α ₆ represent complex numbers. , | Η ₅₁ >, | η ₅₂ >, | η ₆₁ >, and | η ₆₂ > represent arbitrary quantum states, and the superposition state of the quantum state | Φ ₅ > and the quantum state | Φ ₆ > third qubit collection quantum state of alpha ₅ consisting of three or more qubits in the entangled state containing one qubit is a | eta _{51 | Φ 5> | η 52>} + α 6 | η 61> | Φ 6> | η 62> or _{α 5 | Φ 5> | η} 52> + α 6 | Φ 6> | and eta _62>, wherein the second qubit quantum state beta ₁₃ set _{| η 1> | Φ 1>} | Φ 3> | η 3> + β 24 | η 2> | Φ 2> | Φ 4> | to the _{η 4>, γ 1, γ} 2 Is a complex number, a quantum operation represented by γ ₁ <Φ ₃ | <Φ ₅ | + γ ₂ <Φ ₄ | <Φ ₆ | is performed, and a quantum state | Φ ₃ > and a quantum state | Φ ₄ > And a complementary set obtained by removing one qubit from the second set of qubits and a superposed state of the quantum state | Φ ₅ > and the quantum state | Φ ₆ >. Generating a fourth qubit set that is a union of a qubit and a complementary set obtained by removing the qubit from the third qubit set, wherein α ₇ and α ₈ represent complex numbers, | Η ₇₁ >, | η ₇₂ >, | η ₈₁ >, | η _{8 When} each of ₂ > represents an arbitrary quantum state, α ₇ | η ₇₁ > | Φ ₁ > | η ₇₂ > + α ₈ | η ₈₁ > | Φ ₂ > | η ₈₂ >.

  In the present invention, a plurality of qubits in an entanglement state can be generated using a stochastic gate while suppressing the influence of loss.

FIG. 1 is a block diagram illustrating a functional configuration of the quantum state generation device according to the embodiment. FIG. 2 is a diagram illustrating the initial state generation unit of the first embodiment. FIG. 3A is a diagram illustrating the X measurement unit of the embodiment. FIG. 3B is a diagram illustrating the Z measurement unit of the embodiment. FIG. 4 is a diagram illustrating the integrated gate unit of the embodiment. FIG. 5 is a diagram for explaining the quantum state generation method of the embodiment. 6A-6C are diagrams for explaining an example of a quantum state generation method. 7A and 7B are diagrams for explaining an example of a quantum state generation method. 8A and 8B are diagrams for explaining an example of a quantum state generation method. 9A to 9C are diagrams for explaining an example of the quantum state generation method. 10A and 10B are diagrams for explaining an example of a quantum state generation method. FIG. 11 is a diagram for explaining an example of a quantum state generation method. FIG. 12 is a diagram for explaining an example of the quantum state generation method. FIG. 13 is a diagram for explaining an example of the quantum state generation method. FIG. 14 is a diagram for explaining an example of the quantum state generation method. FIG. 15 is a diagram for explaining an example of the quantum state generation method. FIG. 16 is a diagram illustrating photons in a three-dimensional cluster state. FIG. 17 is a diagram illustrating an initial state generation unit according to the second embodiment.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
[Definition]
Symbols and terms used in the embodiment are defined.
A qubit is a basic unit in quantum information processing. Specific examples of qubits include photon polarization and atomic nuclear spin. A qubit takes a superposition state of quantum states of calculation bases (orthogonal bases) corresponding to binary values of classical bits. The superposition state means that a plurality of quantum states exist simultaneously in terms of quantum mechanics. When the qubit is a photon polarization, the computational basis is the direction of polarization of the photons orthogonal to each other. For example, the polarization direction (0 ° polarization direction / horizontal polarization direction (corresponding to “first polarization direction”)) along a specific straight line orthogonal to the traveling direction of the photon, and orthogonal to the traveling direction of the photon and the horizontal polarization direction The calculation direction is the polarization direction (90 ° polarization direction / vertical polarization direction (corresponding to “second polarization direction”)).

A quantum state is expressed using a ket vector | Φ>, and a dual bra vector corresponding to the quantum state is expressed as <Φ |. The photon measurement by the detector is represented by a bra vector <σ |. When the quantum state of the calculation base is | H> and | V>, the quantum state φ of one qubit can be expressed by a linear combination of | H> and | V> as follows.
φ = c ₁ | H> + c ₂ | V> (| c ₁ | ² + | c ₂ | ² = 1) ... (1)
Where c ₁ , c ₂ Is a coefficient (referred to as “amplitude”) of each quantum state represented by a complex number, and indicates the probability that the square value of the absolute value takes the corresponding quantum state.
<Γ | δ> represents an inner product of | γ> and | δ>. (X) represents a tensor product, | γ> (x) | δ> represents a tensor product of | γ> and | δ>, and sometimes | γ> (x) | δ> represents | γ> | δ > Is simply displayed. A quantum state of a plurality of qubits that cannot be expressed by | γ> (×) | δ> using any | γ> and | δ> is called an entanglement state. An entanglement state obtained by a control unitary operation (control NOT operation, control Z operation, etc.) on a pair of qubits is called an adjacent entanglement state, and a pair of qubits in an adjacent entanglement state is adjacent to an adjacent qubit (adjacent quantum). Bit).

  Shrinkage means that a superposition state of a plurality of quantum states becomes a superposition state of a smaller number of quantum states or any one quantum state.

量子状態が｜Φ＞の量子ビットをＺ測定した結果、｜Ｈ＞が観測される確率は｜＜Ｈ｜Φ＞｜²であり、｜Ｖ＞が観測される確率は｜＜Ｖ｜Φ＞｜²である。 The Z measurement is a measurement based on two quantum states having amplitudes of the eigenvectors (1, 0) and (0, 1) of the matrix Z representing the Pauli Z operation, that is, | H> and | V>. Means to do. The matrix Z is as follows.

As a result of Z measurement of a qubit having a quantum state of | Φ>, the probability that | H> is observed is | <H | Φ> | ² , and the probability that | V> is observed is | <V | Φ>. | ² .

なお、行列Ｘは以下のようになる。

量子状態が｜Φ＞の量子ビットをＸ測定した結果、｜＋＞が観測される確率は｜＜＋｜Φ＞｜²であり、｜−＞が観測される確率は｜＜−｜Φ＞｜²である。 The X measurement is the following two values with the amplitudes of the eigenvectors (1 / √2, 1 / √2) and (1 / √2, −1 / √2) of the following matrix X representing the Pauli X operation. That is, the measurement is performed based on the quantum state of the above, that is, | +> and | −>.

The matrix X is as follows.

As a result of X measurement of a qubit having a quantum state of | Φ>, the probability that | +> is observed is | <+ | Φ> | ² and the probability that | −> is observed is | <− | Φ>. | ² .

すなわちＧＨＺ状態の３個の量子ビットは、当該３個の量子ビットそれぞれの量子状態がすべて｜Ｈ＞である量子状態とすべて｜Ｖ＞である量子状態との重ね合わせ状態にあるか、又は、この重ね合わせ状態に対してさらに量子ビットに個別なユニタリ変換操作を施して得られる量子状態にある。 The GHZ state is an entanglement state of three qubits expressed as follows, and an individual (local) unitary transformation operation (unitary) for each qubit with respect to a qubit in the entanglement state. This means a quantum state obtained by applying a quantum operation represented by transformation.

That is, the three qubits in the GHZ state are in a superposed state of a quantum state in which all the quantum states of the three qubits are | H> and a quantum state in which all are | V>, or This superposition state is a quantum state obtained by further performing individual unitary transformation operations on the qubits.

A cluster state is a kind of entanglement state, and means a state in which each pair of qubits (a pair of logically adjacent qubits) included in a plurality of qubits is in an adjacent cluster state. An adjacent cluster state is a quantum obtained by performing a control Pauli Z operation CZ on a quantum state | +> | +> of a pair of qubits (two qubits) whose quantum state is | +>. And a quantum state obtained by performing control Pauli Z operation CZ on a quantum state of a pair of qubits in an adjacent cluster state and a quantum state of a pair of qubits in an adjacent cluster state It means a quantum state obtained by performing an individual unitary transformation operation for each qubit. The control Pauli Z operation is expressed by the following matrix CZ.

In other words, the control Pauli Z operation is performed by changing | H> | H> to | H> | H>, | H> | V> to | H> | V>, and | V> | H> to | V> | H> is an operation of changing | V> | V> to − | V> | V>. In other words Additionally, pairs of qubits Q _A, control Pauli Z operations on the quantum state of the Q _B is the quantum state of the qubit Q _A is | Pauli Z operations for quantum state of qubit Q _B when V> alms, quantum state of qubit Q _a is | are those that do not operate the quantum state of qubit Q _B when H>. The Pauli Z operation sets | H> to | H> and | V> to-| V>. However, the following is satisfied.

Note that the three qubits in the GHZ state are in the cluster state. Each of the quantum state | +> a is three qubit _{Q A, Q B,} the quantum state of the _{Q C | +> | +>} | +> can be expressed as follows. In order to simplify the description, the amplitude is omitted from the following expressions (5) to (7).
| +> | +> | +>
= | H + V> | H + V> | H + V>
= | H> | H> | H> + | H> | H> | V> + | H> | V> | H> + | H> | V> | V> + | V> | H> | H> + | V> | H> | V> + | V> | V> | H> + | V> | V> | V> (5)
Qubit Q _A, versus the qubit Q _B of Q _B, when subjected to control Pauli Z operation on each pair of Q _C, as follows.
| H> | H> | H> + | H> | H> | V> + | H> | V> | H>-| H> | V> | V> + | V> | H> | H> + | V> | H> | V> − | V> | V> | H> + | V> | V> | V>
= (| H> + | V>) | H> (| H> + | V>) + (| H> − | V>) | V> (| H> − | V>)
= | +> | H> | +> + |-> | V>|-> ... (6)
Further subjected to Hadamard gate operation sigma _H is a unitary transformation operations per qubit in the qubit Q _A and Q _C quantum state represented by the formula (6), in other words, three of the formula (6) qubit _Q a _of, Q B, subjected to the operation of _{σ H (×) I (×} ) σ H relative to _{Q C.} Then, qubit _{Q A,} Q B, the quantum state of the _{Q C} is as follows. However, I indicates that no quantum operation is performed on one qubit (no operation).
| H> | H> | H> + | V> | V> | V> = | GHZ> (7)
This shows that the three qubits in the GHZ state are in the cluster state. The Hadamard gate operation is expressed as follows.

  The three-dimensional cluster state means a state in which each of six or more qubits included in a set of a plurality of qubits is in an adjacent cluster state with any four qubits included in the set. An example of a qubit set in a three-dimensional cluster state includes qubits Q (n) (n = 0, ..., 17), and qubits Q (1) are qubits Q (7), Q (8 ), Q (9), Q (10) and adjacent cluster states, and qubit Q (2) is adjacent to qubits Q (8), Q (11), Q (12), Q (15) The qubit Q (3) is in the adjacent cluster state with the qubits Q (15), Q (16), Q (17), Q (18), and the qubit Q (4) is the qubit Q (10 ), Q (13), Q (14), Q (17) and adjacent cluster states, and qubit Q (5) is qubit Q (9), Q (12), Q (13), Q (16 ) And an adjacent cluster state, and qubit Q (6) is adjacent to qubits Q (7), Q (11), Q (14), and Q (18) (see FIG. 16). .

  When a photon is incident on an optical element (polarizing beam splitter, polarization rotation element, polarizing plate, detector, etc.), it means that the quantum state of the photon is input to the optical element. That a photon is emitted from an optical element means that the quantum state of the photon is output from the optical element. Here, the quantum state of a photon is a concept including not only a single quantum state of a photon but also a superposed state. In other words, when a photon is incident on an optical element, it means that the wave function of the photon is input to the optical element, and when a photon is emitted from the optical element, it means that the wave function of the photon is output from the optical element. To do.

〔principle〕
Next, the principle of the embodiment will be described.
In the embodiment, the desired entanglement state is generated while suppressing the influence of the loss by the measurement step and the connection step realized by the stochastic gate.

In the measurement step, ψ = (β ₀₁ | η ₁ > | Φ ₁ > + β ₀₂ | η ₂ > | Φ ₂ >) | H> (β ₀₃ | Φ ₃ > | η ₃ > + β ₀₄ | Φ ₄ > | η ₄ >) + (β ₀₁ | η ₁ > | Φ ₁ > −β ₀₂ | η ₂ > | Φ ₂ >) | V> (β ₀₃ | Φ ₃ > | η ₃ > −β ₀₄ | Φ ₄ > | one superposed state of quantum states | H> and | V> included in the first qubit set of three or more qubits in the entanglement state in the quantum state η ₄ >) X measurement is performed on the qubit, and a second qubit set that is a complementary set obtained by removing the one qubit measured in X from the first qubit set is generated, and the one qubit measured in X is Superimposing | Φ ₁ > | Φ ₃ > and | Φ ₂ > | Φ ₄ > for the quantum states of two specific qubits included in the second set of qubits that are in adjacent entanglement states The quantum state of the second qubit set is β ₁₃ | η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + β ₂₄ | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ > To. However, β ₀₁ , β ₀₂ , β ₀₃ , β ₀₄ , β ₁₃ , β ₂₄ represent complex numbers, and | η ₁ >, | η ₂ >, | η ₃ >, | η ₄ > are arbitrary quantum states. Each of | Φ ₁ >, | Φ ₂ >, | Φ ₃ >, | Φ ₄ > represents the quantum state of one qubit, and | H>, | V> represents the quantum of the computation basis. Represents a state. “Arbitrary quantum state” means any quantum state of one or a plurality of qubits, or a state where no qubit exists.

In the connecting step, a third qubit set consisting of three or more qubits in an entanglement state including one qubit that is superposed with the quantum state | Φ ₅ > and the quantum state | Φ ₆ > Quantum state α ₅ | η ₅₁ > | Φ ₅ > | η ₅₂ > + α ₆ | η ₆₁ > | Φ ₆ > | η ₆₂ > or α ₅ | Φ ₅ > | η ₅₂ > + α ₆ | Φ ₆ > | η ₆₂ > And the quantum state β ₁₃ | η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + β ₂₄ | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ > of the second qubit set On the other hand, a quantum operation represented by γ ₁ <Φ ₃ | <Φ ₅ | + γ ₂ <Φ ₄ | <Φ ₆ | is performed, and the quantum state | Φ ₃ > and the quantum state | Φ ₄ > are superposed. The third quanta is obtained by superimposing the complementary set obtained by removing one qubit from the second qubit set and the quantum state | Φ ₅ > and the quantum state | Φ ₆ >. Remove from bit set To produce a fourth qubit set the union of the complement, the fourth qubit collection quantum state of the _{α 7 | η 71> | Φ} 1> | η 72> + α 8 | η 81> | Φ ₂ > | η ₈₂ >. However, α ₅ , α ₆ , α ₇ , α ₈ , γ ₁ , γ ₂ represent complex numbers, and | η ₅₁ >, | η ₅₂ >, | η ₆₁ >, | η ₆₂ >, | η ₇₁ >, | Each of η ₇₂ >, | η ₈₁ >, and | η ₈₂ > represents a quantum state. When i = j, <Φ _i | Φ _j > ≠ 0 is satisfied, and when i ≠ j, <Φ _i | Φ _j > = 0 is satisfied. For example, <Φ _i | Φ _j > = ε is satisfied when i = j, and <Φ _i | Φ _j > = 0 is satisfied when i ≠ j. ε is a constant, for example, ε = 1.

In the measurement step, when X of one qubit that is superposed with | H> and | V> included in the first qubit set is X-measured, one of the calculation bases | H> or | V> Is observed. In this X measurement, the above quantum state ψ is changed to (β ₀₁ | η ₁ > | Φ ₁ > + β ₀₂ | η ₂ > | Φ ₂ >) | H + V> (β ₀₃ | Φ ₃ > | η ₃ > + β ₀₄ | Φ ₄ > | η ₄ >) + (α ₀ (β ₀₁ | η ₁ > | Φ ₁ > −β ₀₂ | η ₂ > | Φ ₂ >) | HV> (β ₀₃ | Φ ₃ > | η ₃ > −β ₀₄ | Φ ₄ > | η ₄ >), and this corresponds to measuring the quantum state of one qubit with the basis | H> or | V>.
Here, assuming that the calculation basis | H> is observed, the quantum state of the complementary set obtained by excluding one qubit of X measurement from the first qubit set is as follows.
β ₀₁ β ₀₃ | η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + β ₀₂ β ₀₄ | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ >
_{= Β 13 | η 1> |} Φ 1> | Φ 3> | η 3> + β 24 | η 2> | Φ 2> | Φ 4> | η 4> ... (8)
On the other hand, if the calculation basis | V> is observed, the quantum state of the complementary set obtained by removing one measured qubit from the first qubit set is as follows.
β ₀₁ | η ₁ > | Φ ₁ > β ₀₄ | Φ ₄ > | η ₄ > + β ₀₂ | η ₂ > | Φ ₂ > β ₀₃ | Φ ₃ > | η ₃ >
_{= Β 14 | η 1> |} Φ 1> | Φ 4> | η 4> + β 23 | η 2> | Φ 2> | Φ 3> | η 3> ... (9)

When the calculation basis | H> is observed, the quantum state of the equation (8) is the quantum state of the final second qubit set as it is. On the other hand, when the calculation basis | V> is observed, a unitary transformation operation for each qubit is further performed on the quantum state of Equation (9), and the quantum state of the final second qubit set (Equation (8) quantum state). This unitary transformation operation is performed on the qubits in the superposition state of | Φ ₃ > and | Φ ₄ > in the quantum state of Equation (9). Therefore, when this unitary transformation operation is performed in an actual physical system, there is a possibility that qubits in the superposed state of | Φ ₃ > and | Φ ₄ > in this quantum state may be lost. For example, in the case of an optical system in which the polarization of a photon is a qubit, this unitary conversion operation is equivalent to passing a photon that is in a superposed state of | Φ ₃ > and | Φ ₄ > by entering the wave plate. This wave plate may cause loss of photons. However, in the next concatenation step, γ ₁ <Φ ₃ | <Φ ₅ | + γ ₂ <Φ ₄ for a qubit that is in a superposed state of | Φ ₃ > and | Φ ₄ > may be lost. A quantum operation represented by | <Φ ₆ | is performed. When i = j, <Φ _i | Φ _j > ≠ 0 and when i ≠ j, <Φ _i | Φ _j > = 0, so that the superposition of | Φ ₃ > and | Φ ₄ > The qubits in the state are excluded by this quantum operation, and the fourth qubit set in the entanglement state is generated. That is, <Φ _i | Φ _j > ≠ 0 when i = j, and <Φ _i | Φ _j > = 0 when i ≠ j, so that (α ₅ | η ₅₁ > | _{Φ 5> | η 52> +} α 6 | η 61> | Φ 6> | η 62>) (β 13 | η 1> | Φ 1> | Φ 3> | η 3> + β 24 | η 2> | Φ ₂ > | Φ ₄ > | η ₄ >) (γ ₁ <Φ ₃ | <Φ ₅ | + γ ₂ <Φ ₄ | <Φ ₆ |), or (α ₅ | Φ ₅ > | η ₅₂ > + α ₆ | Φ ₆ > | η ₆₂ >) (β ₁₃ | Φ ₁ > | Φ ₃ > | η ₃ > + β ₂₄ | Φ ₂ > | Φ ₄ > | η ₄ >) (γ ₁ <Φ ₃ | <Φ ₅ | + γ ₂ <Φ ₄ | <Φ ₆ |) The quantum state obtained by the operation of α ₇ | η ₇ > | Φ ₁ > | η ₅₂ > + α ₈ | η ₈ > | Φ ₂ > | η ₆₂ > The qubits in the superposition state of | Φ ₃ > and | Φ ₄ > that are in the entanglement state and can be lost as described above are derived from the qubit set in this entanglement state. Excluded.
As described above, by eliminating the qubits in the overlapping state of | Φ ₃ > and | Φ ₄ > that can be lost, the fourth qubit set in the entanglement state is generated while suppressing the influence of the loss. Is done.

  In the measurement step, only when the result obtained by X measurement of one qubit in which the quantum states | H> and | V> are superposed is a calculation basis | H>, Two qubit sets may be generated. Since such a second qubit set is in the quantum state of Equation (8), the subsequent linking step can be executed without performing the unitary transformation operation that may cause a loss. This also makes it possible to generate the fourth qubit set in the entanglement state while suppressing the influence of loss.

  Also, when a measurement result of the calculation basis | H> or | V> is obtained as a result of X measurement of one qubit in which the quantum states | H> and | V> are superposed in the measurement step In the measurement step, the second qubit set may be generated. That is, in the case of the above X measurement, one of the calculation bases | H> or | V> is surely observed, but in the measurement in the actual physical system, the observation result depends on the performance of the detector. It may not be obtained. In such a case, it is unclear whether the quantum state after X measurement is in the formulas (8) and (9), and it becomes impossible to finally generate a qubit in a desired entanglement state. In such a case, it is desirable not to generate the second qubit set.

Further, even if X measurement is performed on one qubit in which the quantum states | H> and | V> are superposed in the measurement step, the measurement result of the calculation basis | H> or | V> cannot be obtained. In this case, at least one qubit in the superposition state of the quantum states | Φ ₃ > and | Φ ₄ > among the qubits included in the first qubit set is represented by the base | Φ ₃ >, | Φ ₄ > A set of qubits whose quantum states are contracted to | η ₃ > or | η ₄ >, or their children (for example, Z measurement when measuring with calculation bases | H>, | V>) A set of qubits obtained by performing a unitary transformation operation for each qubit on a set of qubits whose state has shrunk to | η ₃ > or | η ₄ > is set as a new first qubit set. A three-qubit set may be used.
The quantum state when Φ ₃ is observed by this measurement is one of the following.
| Η ₁ > | Φ ₁ > | η ₃ > ... (10)
| Η ₂ > | Φ ₂ > | η ₃ > ... (11)
On the other hand, the quantum state when Φ ₄ is observed is one of the following.
| Η ₂ > | Φ ₂ > | η ₄ > ... (12)
| Η ₁ > | Φ ₁ > | η ₄ > ... (13)
That is, whether the quantum state of a plurality or single qubits in a superposition state of quantum states | η ₃ > and | η ₄ > was contracted to | η ₃ > due to the measurement result of Φ ₃ or Φ ₄ It can be known whether or not it has shrunk to | η ₄ >. Therefore, among the set of qubits in the quantum state of equations (10) to (13), one qubit in a superposed state of | Φ ₁ > and | Φ ₂ > is further Z-measured | A set of qubits contracted to η ₃ > or | η ₄ > is obtained, and a set of qubits contracted to | η ₃ > or | η ₄ >, or the child state is | η ₃ > or | η ₄ A set of qubits obtained by subjecting a set of qubits contracted to> to a unitary transformation operation for each qubit can be used to generate a desired entangled state.

Further, the qubit is a photon, the qubit set is a photon set, the quantum state is the polarization direction of the photon, the quantum state | H> is the first polarization direction, and the quantum state | V> is the second polarization. Each of | Φ ₁ >, | Φ ₃ >, | Φ ₅ > is a first polarization direction, and each of | Φ ₂ >, | Φ ₄ >, | Φ ₆ > is a second polarization direction. In some cases, the connecting step is performed using, for example, the following integrated gate unit. The integrated gate unit includes a polarization beam splitter including first and second incident units and first and second emission units, and first and second polarization rotation elements that emit by changing the polarization direction of incident qubits by 45 °. , First and second polarizing plates that pass qubits whose polarization direction is the first polarization direction and block qubits whose polarization direction is the second polarization direction orthogonal to the first polarization direction, and first and second detection Including The first emitting part emits a qubit in the first polarization direction incident on the first incident part and a qubit in the second polarization direction incident on the second incident part, and the second emitting part enters the first incident part. A qubit in the second polarization direction and a qubit in the first polarization direction incident on the second incident portion are emitted, and the qubit emitted from the first emission portion is incident on the first polarization rotation element, and the second The qubit emitted from the second emitting part is incident on the polarization rotator, the qubit emitted from the first polarization rotator is incident on the first polarizer, and the second polarization rotator is incident on the second polarizer. The qubits emitted from the laser beam enter, the qubits transmitted through the first polarizing plate enter the first detector, and the qubits transmitted through the second polarizing plate enter the second detector. In the connection step of this example, the first incident part of the integrated gate part is a superposed state of the quantum state | Φ ₃ > and the quantum state | Φ ₄ > contained in two specific qubits. Qubits are made incident, and one qubit in a superposition state of quantum states | Φ ₅ > and quantum states | Φ ₆ > included in the third qubit set is input to the second incident portion. It is made to enter, and it is determined whether the qubit is detected by both the first and second detectors. The complementary set obtained by removing the qubits incident on the first incident part from the second qubit set when it is determined that both qubits are detected by both the first and second detectors, A sum set of the third qubit set and the complementary set excluding the qubits incident on the second incident portion when it is determined that both qubits are detected is defined as a fourth qubit set.

  In the processing using such an integrated gate unit, when it is determined that either of the first and second detectors does not detect a qubit, the entanglement state is adjacent to the qubit incident on the first incident unit. The first adjacent qubit that is the qubit and the second adjacent qubit that is the qubit in the adjacent entanglement state are Z-measured, and the qubit incident on the second incident unit is in the adjacent entanglement state. Z measurement is performed on the third adjacent qubit that is the qubit and the fourth adjacent qubit that is the qubit in the adjacent entanglement state, and the qubit that is incident on the first incident unit, the first adjacent qubit, A subset of the first complementary set obtained by removing two adjacent qubits from the second qubit set, a qubit incident on the second incident portion, a third adjacent qubit, and a fourth A subset of the second complement obtained by removing the tangent qubit from the third qubit set, a set of qubits obtained by performing a unitary transformation operation for each qubit on the subset of the first complement, and As a new first qubit set or a new third qubit set, at least a part of the set of qubits obtained by performing a unitary transformation operation for each qubit on a subset of the second complementary set Also good. Thereby, it is possible to reuse the qubit in which the processing of the integrated gate unit has failed.

Preferably, the superposition state of | η ₁ > and | η ₂ > is an entanglement state, the superposition state of | η ₃ > and | η ₄ > is an entanglement state, and | η ₅₁ > and | η ₆₁ > overlap state is entanglement state, | η ₅₂ > and | η ₆₂ > overlap state is entanglement state, and | η ₇₂ > and | η ₈₂ > overlap state is entanglement state It is. In this case, a plurality of qubits in a desired entanglement state can be generated by repeatedly executing the measurement step and the connection step as described above. In this case, for example, by measuring any specific qubit included in the fifth qubit set including a plurality of entangled qubits, the specific qubit is obtained from the fifth qubit set. A removal step for generating the excluded sixth qubit set may be performed. The fourth qubit set or the sixth qubit set is a new first qubit set or a new third qubit set until the fourth qubit set or the sixth qubit set becomes a desired qubit set. A process in which the measurement step and the connection step are executed again, a process in which the fourth qubit set obtained in any of the connection steps is set as the fifth qubit set, and a removal step is executed, and a sixth quantum At least a part of the process in which the bit set is set as a new fifth qubit set and the removal step is executed again may be repeatedly executed. Examples of measurements performed in the removal step are X measurement and Z measurement.

  The example of the plurality of qubits in the entanglement state described above is a plurality of qubits in the cluster state, and the example of the pair of qubits in the adjacent entanglement state is the adjacent cluster state. Thereby, a plurality of qubits in a desired cluster state can be generated. This also makes it possible to generate qubits in a three-dimensional cluster state using a stochastic gate. The method of Non-Patent Document 7 is a method of generating a qubit in a three-dimensional cluster state using a deterministic gate and performing one-way quantum calculation using the qubit. The method of Non-Patent Document 7 does not have means for suppressing the influence of loss that occurs when generating a qubit in a three-dimensional cluster state. In the system of this embodiment, a stochastic gate that can be realized by an optical quantum computer or the like can be used to generate a qubit in a three-dimensional cluster state while suppressing the effect of loss in the generation process. The quantum bits in the three-dimensional cluster state generated as described above can also be applied to the one-way quantum calculation in Non-Patent Document 7. Thereby, the one-way quantum computation method of Non-Patent Document 7 can be expanded and improved.

[First Embodiment]
Next, a first embodiment of the present invention will be described. In the first embodiment, the qubit is a photon, the quantum state is the polarization direction of the photon, the quantum state | H> is the horizontal polarization direction, the quantum state | V> is the vertical polarization direction V, and | H> , | V> is a calculation basis, | Φ ₁ >, | Φ ₃ >, | Φ ₅ > are | H>, and | Φ ₂ >, | Φ ₄ >, | Φ ₆ > are | V>, β ₀₁ = β ₀₂ = β ₀₃ = β ₀₄ = β ₁₃ = β ₁₄ = β ₂₃ = β ₂₄ = α ₅ = α ₆ = α ₇ = α ₈ = γ ₁ = γ ₂ = 1 / √2. In this embodiment, the superposition state of | η ₁ > and | η ₂ > is an entanglement state, the superposition state of | η ₃ > and | η ₄ > is an entanglement state, and | η ₅₁ > The superposition state of | η ₆₁ > is the entanglement state, the superposition state of | η ₅₂ > and | η ₆₂ > is the entanglement state, and the superposition state of | η ₇₂ > and | η ₈₂ > is the entanglement state. Is in a state of Furthermore, it is a quantum state of the first qubit set, and a quantum state of the fourth qubit set is a cluster state. Further, from the definition of the cluster state, | η ₄ > = (σ _z · I ······ I) | η ₃ > is satisfied. However, σ _z represents a Pauli Z operation for one qubit. Further, it is assumed that <Φ _i | Φ _j > = 1 is satisfied when i = j, and <Φ _i | Φ _j > = 0 is satisfied when i ≠ j. However, these do not limit the present invention. For simplification of description, the amplitude is omitted from the notation of the quantum state of this embodiment.

<Overall configuration>
As illustrated in FIG. 1, the quantum state generation device 1 of the first embodiment includes an initial state generation unit 11, a measurement unit 12, a connection unit 13, reuse units 14 and 15, a deletion unit 16, a control unit 17, and A quantum memory 18 is included.

<Initial state generation unit 11>
As illustrated in FIG. 2, the initial state generation unit 11 of this embodiment includes a photon generation unit 111a-111f, a polarization beam splitter 112a-112e, a polarization rotation element 113ac, 113ad, 113bc, 113bd, 113cc, 113cd, 113dd, 113ec. 113ed, polarizing plates 114dd, 114ec, 114ed, and detectors 115dd, 115ec, 115ed.

[Photon generators 111a-111f]
Each of the photon generators 111a to 111f includes a single photon generator and is a device that generates and emits a single photon having a 45 ° polarization direction (quantum state | +>). The single photon generator may generate and emit a single photon having a quantum state | +>, or may generate and emit a single photon having a polarization direction other than | +>. Also good. When the single photon generator generates a single photon having a polarization direction other than | +>, a quantum state | +> is further generated using a wave plate or the like.
Examples of single photon generators are devices that emit single photons by controlling the spontaneous emission of photons from single atoms or artificial single atoms (quantum dots, center of nitrogen vacancies in diamond, etc.), parametric Down conversion (PDC) (eg, “PG Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, AV Sergienko, and Y. Shih,“ New high-intensity source of polarization-entangled photon pairs, ”Phys. Rev. Lett., 75: 4337-4341, 1995. (Reference 1), “PG Kwiat, E. Waks, AG White, I. Appelbaum, and PH Eberhard,“ Ultrabright source of polarization-entangled photons, ”Phys. Rev. A, 60: R773-R776, 1999. (Ref. 2) etc.)), a device that emits a single photon, a device that emits weak coherent light (laser light), etc. (for example, “GS Buller and RJ Collins, “Single-photon generation and detection,” Measurement Science and Technology 21, 012002 (2010). (Ref. 3) ”etc.)

[Polarized beam splitter 112a-112e]
Each of the polarization beam splitters 112a to 112e transmits the photon straight when the polarization direction of the incident photon is 0 ° (H: horizontal polarization direction), and the polarization direction of the photon is 90 ° (V: vertical). It is an optical element that reflects the photon in the case of (polarization direction).

[Polarization rotator]
Each of the polarization rotation elements 113ac, 113ad, 113bc, 113bd, 113cc, 113cd, 113dd, 113ec, and 113ed is an optical element that emits light by changing the polarization direction of incident photons by 45 °. Specific examples of the polarization rotation elements 113a to 113c use the electro-optic effect of a crystal such as a half-wave plate and an electro-optic effect modulator (for example, a Faraday rotator or LiNbO 3) that rotate the polarization direction of incident photons by 45 °. Modulator, etc.), acoustic elements, liquid crystal elements, and the like.

[Polarizing plates 114dd, 114ec, 114ed]
Each of the polarizing plates 114dd, 114ec, and 114ed passes a photon having a polarization direction of 0 ° (H: horizontal polarization direction) and blocks or reflects a photon having a polarization direction of 90 ° (V: vertical polarization direction). It is an optical element. Polarizing beam splitters that reflect incident photons having a polarization direction of 90 ° may be used as the polarizing plates 114dd, 114ec, and 114ed.

[Detectors 115dd, 115ec, 115ed]
Each of the detectors 115dd, 115ec, and 115ed is a photon detector that can be used in the photon counting region and can identify the number of detected photons. Specific examples of the detectors 115dd, 115ec, and 115ed are superconducting transition end sensors and the like (see Reference 3 and the like).

[Configuration]
As illustrated in FIG. 2, the photon generators 111a to 111f and the polarization beam splitters 112a to 112c are configured such that the single photons emitted from the photon generators 111a to 111f are converted into the incident part aa and the polarization beam splitter of the polarization beam splitter 112a. 112b, the incident part ab of the polarizing beam splitter 112a, the incident part ca of the polarizing beam splitter 112c, the incident part bb of the polarizing beam splitter 112b, and the incident part cb of the polarizing beam splitter 112c, respectively. Is done. However, in the polarization beam splitter 112a-112c, a photon is incident on the incident part aa and the incident part ab simultaneously, a photon is incident on the incident part ba and the incident part bb simultaneously, and a photon is incident on the incident part ca and the incident part cb simultaneously. To be arranged. The polarization beam splitter 112a emits a photon whose polarization direction is incident on the incident part aa from the emitting part ac and emits a photon whose polarization direction is incident on the incident part aa is the emitting part ad. The photon having the polarization direction H incident on the incident part ab is emitted from the output part ad, and the photon having the polarization direction incident on the incident part ab is emitted from the output part ac. Configured to do. The polarization beam splitter 112b emits a photon whose polarization direction is incident on the incident portion ba from the emission portion bc, and a photon whose polarization direction is incident on the incidence portion ba is the emission portion bd. The photon having the polarization direction H incident on the incident part bb is emitted from the exit part bd and the photon having the polarization direction V incident on the incident part bb is emitted from the exit part bc. Configured to do. The polarization beam splitter 112c emits a photon whose polarization direction is incident on the incident part ca from the emission part cc, and a photon whose polarization direction is incident on the incident part ca is the emission part cd. The photon having the polarization direction H incident on the incident part cb is emitted from the emission part cd, and the photon having the polarization direction V incident on the incident part cb is emitted from the output part cc. Configured to do.

  Each of the polarization rotation elements 113ac and 113ad is disposed at a position where the photons emitted from the emission portions ac and ad of the polarization beam splitter 112a are incident, and each of the polarization rotation elements 113bc and 113bd is emitted from the polarization beam splitter 112b. The photons emitted from the parts bc and bd are arranged at the positions where they are incident, and the polarization rotation elements 113cc and 113cd are arranged at the positions where the photons emitted from the emission parts cc and cd of the polarization beam splitter 112c are incident, respectively. Is done.

  The polarization beam splitter 112d is disposed at a position where the photon emitted from the polarization rotation element 113ac enters the incident part da and the photon emitted from the polarization rotation element 113bd enters the incident part db. The polarization beam splitter 112d emits a photon whose polarization direction is incident on the incident portion da from the output portion dc, and a photon whose polarization direction is incident on the incident portion da is the output portion dd. The photon having the polarization direction H incident on the incident part db is emitted from the exit part dd, and the photon having the polarization direction V incident on the incident part db is emitted from the exit part dc. To do. The polarization beam splitter 112e is disposed at a position where the photons emitted from the emission part dc of the polarization beam splitter 112d enter the incidence part ea, and the photons emitted from the polarization rotation element 113cd enter the incidence part eb. The polarization beam splitter 112e emits a photon whose polarization direction is incident on the incident part ea from the emission part ec, and a photon whose polarization direction is incident on the incident part ea is an emission part ed. The photon having the polarization direction H incident on the incident part eb is emitted from the exit part ed, and the photon having the polarization direction incident on the incident part eb is emitted from the exit part ec. To do. The polarization beam splitters 112d and 112e are arranged such that photons are incident on the incident part da and the incident part db simultaneously, and photons are incident on the incident part ea and the incident part eb simultaneously.

  The polarization rotation element 113dd is disposed at a position where the photon emitted from the emission part dd of the polarization beam splitter 112d is incident, and the polarizing plate 114dd is disposed at a position where the photon emitted from the polarization rotation element 113dd is incident and detected. The unit 115dd is arranged at a position where the photons emitted from the polarizing plate 114dd enter. The polarization rotation element 113ed is disposed at a position where a photon emitted from the emission part ed of the polarization beam splitter 112e is incident, and the polarizing plate 114ed is disposed at a position where a photon emitted from the polarization rotation element 113ed is incident and detected. The unit 115ed is disposed at a position where the photons emitted from the polarizing plate 114ed are incident. The polarization rotation element 113ec is disposed at a position where the photon emitted from the emission part ec of the polarization beam splitter 112e is incident, and the polarizing plate 114ec is disposed at a position where the photon emitted from the polarization rotation element 113ec is incident and detected. The container 115ec is disposed at a position where the photons emitted from the polarizing plate 114ec enter.

<Measurement unit 12>
The measurement unit 12 includes an X measurement unit 121, a determination unit 122, and a unitary conversion unit 123.
[X measurement unit 121]
The X measurement unit 121 is an optical element that performs measurement using the Pauli X operation as an observable, and performs X measurement on the quantum state of incident photons.
As illustrated in FIG. 3A, the X measurement unit 121 includes a polarization rotation element 121a, a polarization beam splitter 121b, and detectors 121c and 121d. The configuration of the polarization rotation element 121a is the same as that of the polarization rotation element 113ac described above, the configuration of the polarization beam splitter 121b is the same as that of the polarization beam splitter 112a-112e, and the detectors 121c and 121d are photomultiplier tubes. It is a detector capable of detection in the photon counting region, such as a streak camera, a photodiode, an avalanche photodiode, or a superconducting transition edge sensor. In the polarization rotation element 121a, the polarization beam splitter 121b, and the detectors 121c and 121d, the photons incident on the X measurement unit 121 are incident on the polarization rotation element 121a, and the photons emitted from the polarization rotation element 121a are converted into the polarization beam splitter 121b. When the incident photon is transmitted through the polarization beam splitter 121b, the photon is incident on the detector 121c, and when the incident photon is reflected by the polarization beam splitter 121b, the photon is detected. It arrange | positions in the position which injects into the device 121d.

A quantum state of a cluster state photon set including three or more photons can be expressed as follows.
(| Η ₁ > | H> + | η ₂ > | V>) | H> (| H> | η ₃ > + | V> | η ₄ >) + (| η ₁ > | H> − | η ₂ > | V>) | V> (| H> | η ₃ > − | V> | η ₄ >)
Assuming that one photon in a superposition state of | H> and | V> in this quantum state is X-measured and a calculation base | H> is observed, one X-measured qubit is converted into a first qubit. The quantum state of the complementary set removed from the qubit set is as follows (see equation (8)).
β ₁₃ | η ₁ > | H> | H> | η ₃ > + β ₂₄ | η ₂ > | V> | V> | η ₄ >
On the other hand, if the calculation basis | V> is observed, the quantum state of the complementary set obtained by removing one measured qubit from the first qubit set is as follows (see Expression (9)).
| Η ₁ > | H> | V> | η ₄ > + | η ₂ > | V> | H> | η ₃ >
In this way, adjacent quantum bits (a pair of quantum bits) whose quantum state is | H> | H> + | V> | V> or | H> | V> + | V> | H> A quantum state of a set of qubits in which the qubit is in a cluster state with another qubit other than the adjacent qubit is referred to as a “redundant cluster state”.

[Determining unit 122]
The determination unit 122 is a processing unit that receives a measurement result from the X measurement unit 121 and performs a determination process according to the input measurement result. The determination unit 122 may be configured by an integrated circuit, for example, or may be configured by reading a predetermined program into a classical computer or a quantum computer.

[Unitary Converter 123]
The unitary conversion unit 123 is a processing unit that performs a unitary conversion device for each qubit based on the determination processing in the determination unit 122. The unitary conversion unit 123 includes, for example, a (1/2, 1/4) wave plate, an acoustic element, a polarization rotation element such as an element made of liquid crystal, and an electro-optic effect modulator that can control the polarization angle and phase of transmitted light by a control voltage. (For example, a Faraday rotator, a modulator using the electro-optic effect of a crystal such as LiNbO ₃ ), a control unit configured by reading a predetermined program into an integrated circuit, a classical computer, or a quantum computer.

<Connecting part 13>
The connection part 13 performs the connection step mentioned above. The connection unit 13 includes a mixed gate measurement unit (FG) 131 and a determination unit 132.
[Mixed gate measurement unit 131]
As illustrated in FIG. 4, the mixed gate measuring unit 131 (corresponding to “integrated gate part”) includes incident parts a and b (corresponding to “first and second incident parts”) and output parts c and d (“first” part). Polarizing beam splitter 131a including the first and second light emitting portions), and polarization rotating elements 131b and 131c (first and second light emitting devices 131b and 131c) that emit light by changing the polarization direction of incident photons (corresponding to “qubits”) by 45 °. And a photon whose polarization direction is a horizontal polarization direction (corresponding to “first polarization direction”) and whose polarization direction is a vertical polarization direction (corresponding to “second polarization direction”). It includes polarizing plates 131d and 131e (corresponding to “first and second polarizing plates”) and detectors 131f and 131g (corresponding to “first and second detectors”) that block certain photons. The configuration of the polarization beam splitter 131a is the same as that of the polarization beam splitters 112a to 112e described above, the configuration of the polarization rotation elements 131b and 131c is the same as that of the polarization rotation element 113ac described above, and the configuration of the polarizing plates 131d and 131e. The configuration of the detectors 131f and 131g is the same as that of the detectors 115dd, 115ec, and 115ed.
The exit part c of the polarization beam splitter 131a emits a photon having a vertical polarization direction incident on the incident part a and a photon having a vertical polarization direction incident on the incident part b, and the exit part d has a vertical polarization direction incident on the incident part a. The photons in the horizontal polarization direction that have entered the photons and the incident part b are emitted. The photon emitted from the emission part c is incident on the polarization rotation element 131b, and the photon emitted from the emission part d is incident on the polarization rotation element 131c. The photon emitted from the polarization rotating element 131b is incident on the polarizing plate 131d, the photon emitted from the polarization rotating element 131c is incident on the polarizing plate 131e, and the photon transmitted through the polarizing plate 131d is transmitted to the detector 131f. The photons that have entered and passed through the polarizing plate 131e enter the detector 131g.

The second photon set of the quantum state | η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ > at the incident part a of the polarizing beam splitter 131a ( Among the photons included in the “second qubit set”), one photon that is in a superposed state of the quantum state | Φ ₃ > and the quantum state | Φ ₄ > is incident, and is incident on the incident portion b. Among the photons included in the third photon set (corresponding to the “third qubit set”) of the quantum state | η ₅₁ > | Φ ₅ > | η ₅₂ > + | η ₆₁ > | Φ ₆ > | η ₆₂ > When a single qubit in which the quantum state | Φ ₅ > and the quantum state | Φ ₆ > are overlapped is incident and a photon is detected by both the detectors 131 f and 131 g, the mixed gate measurement unit 131. Performs quantum operations on these quantum states represented by <Φ ₃ | <Φ ₅ | + <Φ ₄ | <Φ ₆ | The state | η ₇ > | Φ ₁ > | η ₅₂ > + | η ₈ > | Φ ₂ > | η ₆₂ > is generated. The reason for this will be described below.

In this embodiment, each of | Φ ₃ > and | Φ ₅ > is | H>, and each of | Φ ₄ > and | Φ ₆ > is | V>, so that a photon is incident on the polarization beam splitter 131a. The quantum state of the second and third photon sets before is expressed as follows.
_{(| Η 1> | Φ 1} > | H> a | η 3> + | η 2> | Φ 2> | V> a | η 4>) (| η 51> | H> b | η 52> + | η ₆₁ > | V> _b | η ₆₂ >)
_{= | Η 1> | Φ 1} > | H> a | η 3> | η 51> | H> b | η 52> + | η 1> | Φ 1> | H> a | η 3> | η 61> _{| V> b | η 62>} + | η 2> | Φ 2> | V> a | η 4> | η 51> | H> b | η 52> + | η 2> | Φ 2> | V> a | Η ₄ > | η ₆₁ > | V> _b | η ₆₂ > ... (14)
However, | Φ> _a represents the quantum state of a photon incident on the incident part a, and | Φ> _b represents the quantum state of a photon incident on the incident part b.

The quantum state after the photon is emitted from the emission parts c and d of the polarization beam splitter 131a is as follows.
| Η ₁ > | Φ ₁ > | H> _c | η ₃ > | η ₅₁ > | H> _d | η ₅₂ > + | η ₁ > | Φ ₁ > | H> _c | η ₃ > | η ₆₁ > | _{V> c | η 62> +} | η 2> | Φ 2> | V> d | η 4> | η 51> | H> d | η 52> + | η 2> | Φ 2> | V> d | η ₄ > | η ₆₁ > | V> _c | η ₆₂ > ... (15)
However, | Φ> _c represents a quantum state of a photon emitted from the emitting unit c, and | Φ> _d represents a quantum state of a photon emitted from the emitting unit d.

The quantum states after the photons emitted from the emission parts c and d pass through the polarization rotation elements 131b and 131c are as follows.
| Η ₁ > | Φ ₁ > | H + V> _c | η ₃ > | η ₅₁ > | H + V> _d | η ₅₂ > + | η ₁ > | Φ ₁ > | H + V> _c | η ₃ > | η ₆₁ > | _{H-V> c | η 62} > + | η 2> | Φ 2> | H-V> d | η 4> | η 51> | H + V> d | η 52> + | η 2> | Φ 2> | _{H-V> d | η 4} > | η 61> | H-V> c | η 62> ... (16)

The quantum states after the photons that have passed through the polarization rotation elements 131b and 131c have passed through the polarizing plates 131d and 131e are as follows.
| Η ₁ > | Φ ₁ > | H> _c | η ₃ > | η ₅₁ > | H> _d | η ₅₂ > + | η ₁ > | Φ ₁ > | H> _c | η ₃ > | η ₆₁ > | _{H> c | η 62> +} | η 2> | Φ 2> | H> d | η 4> | η 51> | H> d | η 52> + | η 2> | Φ 2> | H> d | η ₄ > | η ₆₁ > | H> _c | η ₆₂ > ... (17)

Thereafter, if one photon is detected at each of the detectors 131f and 131g, the quantum state of Expression (17) contracts as follows.
| Η ₁ > | Φ ₁ > | η ₃ > | η ₅₁ > | η ₅₂ > + | η ₂ > | Φ ₂ > | η ₄ > | η ₆₁ > | η ₆₂ >
... (18)
From the above, | η ₁ > = | η ₇₁ >, | η ₂ > = | η ₈₁ >, | η ₇₂ > = | η ₃ > | η ₅₁ > | η ₅₂ >, | η ₈₂ > = | η ₄ > If | η ₆₁ > | η ₆₂ >, it will be understood that the following quantum operation was performed when one photon was detected at each of the detectors 131f and 131g.
(| Η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ >) (| η ₅₁ > | Φ ₅ > | η ₅₂ > + | η ₆₁ > | Φ ₆ > | η ₆₂ >) (<Φ ₃ | <Φ ₅ | + <Φ ₄ | <Φ ₆ |)
= | Η ₇₁ > | Φ ₁ > | η ₇₂ > + | η ₈₁ > | Φ ₂ > | η ₈₂ >
In this respect, | η ₅₁ > | Φ ₅ > | η ₅₂ > + | η ₆₁ > | Φ ₆ > | η ₆₂ > has been replaced by | Φ ₅ > | η ₅₂ > + | Φ ₆ > | η ₆₂ > Even in this case, it can be similarly understood if | η ₇₂ > = | η ₃ > | η ₅₂ >, | η ₈₂ > = | η ₄ > | η ₆₂ >.
The superposition state of | η ₇₁ > | Φ ₁ > and | η ₈₁ > | Φ ₂ > is a cluster state, and the superposition state of | Φ ₁ > | η ₇₂ > and | Φ ₂ > | η ₈₂ > is a cluster state. Since it is in a state, the quantum state of | η ₇₁ > | Φ ₁ > | η ₇₂ > + | η ₈₁ > | Φ ₂ > | η ₈₂ > is also a cluster state.

[Determining unit 132]
The determination unit 132 is a processing unit that receives a measurement result from the mixed gate measurement unit 131 and performs a determination process according to the input measurement result. The determination unit 132 may be configured by an integrated circuit, for example, or may be configured by reading a predetermined program into a classical computer or a quantum computer.

<Reuse unit 14>
Even when the measurement unit 12 performs X measurement on one photon that is made to be in a superposition state of the quantum states | H> and | V>, the reuse unit 14 does not obtain the measurement result of the calculation basis | H> or | V>. If not obtained, at least one photon included in the first photon set (corresponding to the “first qubit set”) was in a superposition state of quantum states | Φ ₃ > and | Φ ₄ > [Phi _3>, | | basal photons measured by [Phi _4>, whereby the quantum states | eta _3> or | eta ₄ a set of photons contracted>, third or the first photon set new Let it be a photon set. In this embodiment, since | Φ ₃ > = | H> and | Φ ₄ > = | V>, the reuse unit 14 performs Z measurement.
The reuse unit 14 of this embodiment includes a Z measurement unit 141, a determination unit 142, and a unitary conversion unit 143.

[Z measurement unit 141]
The Z measurement unit 141 is an optical element that performs measurement using the Pauli Z operation as an observable, and performs Z measurement on the quantum state of incident photons.
As illustrated in FIG. 3B, the Z measurement unit 141 includes a polarization beam splitter 141b and detectors 141c and 141d. The configuration of the polarization beam splitter 141b is the same as that of the polarization beam splitters 112a to 112e described above, and the detectors 141c and 141d are the same as the detectors 121c and 121d described above. In the polarization beam splitter 141b and the detectors 141c and 141d, when the photon incident on the Z measurement unit 141 is incident on the polarization beam splitter 141b and the incident photon passes through the polarization beam splitter 141b, the photon is When the incident photon is incident on the detector 141c and reflected by the polarization beam splitter 141b, the photon is disposed at a position where the photon is incident on the detector 141d.

A quantum state of a cluster state photon set including three or more photons can be expressed as follows.
(| Η ₁ > | H> + | η ₂ > | V>) | H> (| H> | η ₃ > + | V> | η ₄ >) + (| η ₁ > | H> − | η ₂ > | V>) | V> (| H> | η ₃ > − | V> | η ₄ >)
Assuming that one photon in a superposition state of | H> and | V> in this quantum state is Z-measured and a calculation basis | H> is observed, one Z-measured qubit is expressed as the first qubit. The quantum state of the complementary set removed from the qubit set is as follows.
(| Η ₁ > | H> + | η ₂ > | V>) (| H> | η ₃ > + | V> | η ₄ >)
On the other hand, if the calculation basis | V> is observed, the quantum state of the complementary set obtained by removing one qubit measured in Z from the first qubit set is as follows.
(| Η ₁ > | H> − | η ₂ > | V>) (| H> | η ₃ > − | V> | η ₄ >)
In this way, no matter what observation result is obtained, the cluster state is canceled at the photon portion measured by Z, and (| η ₁ > | H> + | η ₂ > | V>) and (| H> Tensor product of | η ₃ > + | V> | η ₄ >), or (| η ₁ > | H> − | η ₂ > | V>) and (| H> | η ₃ > − | V> | It becomes a state represented by a tensor product with η ₄ >).

[Determining unit 142]
The determination unit 142 is a processing unit that receives a measurement result from the measurement unit 12 or the Z measurement unit 141 and performs a determination process according to the input measurement result. The determination unit 142 may be configured by, for example, an integrated circuit, or may be configured by reading a predetermined program into a classical computer or a quantum computer.

[Unitary Conversion Unit 143]
The unitary conversion unit 143 is a processing unit that performs a unitary conversion device for each photon based on the determination processing in the determination unit 142. The unitary conversion unit 143 includes, for example, a (1/2, 1/4) wave plate, an acoustic element, a polarization rotation element such as an element made of liquid crystal, and an electro-optic effect modulator that can control the polarization angle and phase of transmitted light by a control voltage. The control unit is configured by reading a predetermined program into an integrated circuit, a classical computer, or a quantum computer.

<Reuse unit 15>
The reuse unit 15 receives the determination result from the determination unit 132 of the connection unit 13. When it is determined that the photon is not detected by any of the detectors 131f and 131g of the mixed gate measurement unit 131 (FIG. 4), the reuse unit 15 uses the photon incident on the incident unit a of the polarization beam splitter 131a. A first adjacent photon (corresponding to “first adjacent qubit”) that is a photon that is in an adjacent cluster state (corresponding to “adjacent entanglement state”) and a second adjacent photon that is a photon that is in an adjacent cluster state (second Z corresponding to the adjacent qubit) is measured, and the third adjacent photon (corresponding to the third adjacent qubit) that is in the adjacent cluster state with the photon incident on the incident portion b is in the adjacent cluster state. The fourth adjacent photon (corresponding to the fourth adjacent qubit), which is a photon, is Z-measured. As a result, a subset of the complement obtained by removing the photon, the first adjacent photon, and the second adjacent photon incident on the incident part a from the second photon set, and the photon incident on the incident part b and the third adjacent part At least a part of the subset of the complementary set obtained by removing the photon and the fourth adjacent photon from the third photon set is set as a new first photon set or a new third photon set.
The reuse unit 15 includes a Z measurement unit 151, a determination unit 152, and a unitary conversion unit 153.

[Z measurement unit 151]
The Z measurement unit 151 is an optical element that performs measurement using a Pauli Z operation as an observable, and performs Z measurement on the quantum state of an incident photon.
As illustrated in FIG. 3B, the Z measurement unit 151 includes a polarization beam splitter 151b and detectors 151c and 151d. The configuration of the polarization beam splitter 151b is the same as that of the polarization beam splitters 112a to 112e described above, and the detectors 151c and 151d are the same as the detectors 121c and 121d described above. The polarization beam splitter 151b and the detectors 151c and 151d are configured such that when a photon incident on the Z measurement unit 151 is incident on the polarization beam splitter 151b and the incident photon passes through the polarization beam splitter 151b, the photon is When the incident photon is incident on the detector 151c and reflected by the polarization beam splitter 151b, the photon is disposed at a position where it enters the detector 151d.

[Determining unit 152]
The determination unit 152 is a processing unit that receives a measurement result from the connecting unit 13 or the Z measurement unit 151 and performs a determination process according to the input measurement result. The determination unit 152 may be configured by, for example, an integrated circuit, or may be configured by reading a predetermined program into a classical computer or a quantum computer.

[Unitary Conversion Unit 153]
The unitary conversion unit 153 is a processing unit that performs a unitary conversion device for each photon based on the determination processing in the determination unit 152. The unitary conversion unit 153 is configured in the same manner as the unitary conversion unit 143.

<Delete unit 16>
The deletion unit 16 includes an X measurement unit 161, a Z measurement unit 162, a determination unit 163, and a unitary conversion unit 164.
[X measurement unit 161]
The X measurement unit 161 is an optical element that performs measurement using the Pauli X operation as an observable, and performs X measurement on the quantum state of incident photons.
As illustrated in FIG. 3A, the X measurement unit 161 includes a polarization rotation element 161a, a polarization beam splitter 161b, and detectors 161c and 161d. The configuration of the polarization rotation element 161a is the same as the polarization rotation element 113ac described above, the configuration of the polarization beam splitter 161b is the same as that of the polarization beam splitter 112a-112e, and the configuration of the detectors 161c and 161d is the detection described above. The same as the devices 121c and 121d. In the polarization rotation element 161a, the polarization beam splitter 161b, and the detectors 161c and 161d, the photons incident on the X measurement unit 161 are incident on the polarization rotation element 161a, and the photons emitted from the polarization rotation element 161a are converted into the polarization beam splitter 161b. When the incident photon is transmitted through the polarization beam splitter 161b, the photon is incident on the detector 161c, and when the incident photon is reflected by the polarization beam splitter 161b, the photon is detected. It arrange | positions in the position which injects into the device 161d.
[Z measurement unit 162]
The Z measurement unit 162 is an optical element that performs measurement using the Pauli Z operation as an observable, and performs Z measurement on the quantum state of incident photons.
As illustrated in FIG. 3B, the Z measurement unit 162 includes a polarization beam splitter 162b and detectors 162c and 162d. The configuration of the polarization beam splitter 162b is the same as that of the polarization beam splitters 112a to 112e described above, and the detectors 162c and 162d are the same as the detectors 121c and 121d described above. The polarization beam splitter 162b and the detectors 162c and 162d are configured such that when the photon incident on the Z measurement unit 162 is incident on the polarization beam splitter 162b and the incident photon passes through the polarization beam splitter 162b, the photon is When the incident photon is incident on the detector 162c and reflected by the polarization beam splitter 162b, the photon is disposed at a position where it enters the detector 162d.

[Determining unit 163]
The determination unit 163 is a processing unit that receives measurement results from the X measurement unit 161 and the Z measurement unit 162 and performs a determination process according to the input measurement results. The determination unit 163 may be configured by an integrated circuit, for example, or may be configured by reading a predetermined program into a classical computer or a quantum computer.

[Unitary Conversion Unit 164]
The unitary conversion unit 164 is a processing unit that performs a unitary conversion device for each photon based on the determination processing in the determination unit 163. The unitary conversion unit 164 is configured in the same manner as the unitary conversion unit 143.

<Control unit 17>
The control unit 17 controls the entire quantum state generation device 1. The control unit 17 may be configured by an integrated circuit including a storage unit, or may be configured by reading a predetermined program into a classical computer or a quantum computer including a storage unit.

<Quantum memory 18>
The quantum memory 18 is a device that stores a quantum state. Although not described below, the quantum state obtained by the processing of each unit is recorded in the quantum memory 18 as necessary, and is read from the quantum memory 18 when necessary in each unit. Examples of the quantum memory 18 include a device that stores the quantum state of a photon by using an optical fiber, a device that stores a quantum state by using a delay caused by a waveguide, a device that stores a quantum state by a resonator, electromagnetic induction transparency, and photon. Devices such as echoes can be used to store quantum states at the energy level of atoms (eg, “AI Lvovsky, BC Sanders, and W. Tittel,“ Optical quantum memory, ”Nature Photonics, vol. 3, 2009 , pp. 706-714.).

<Quantum state generation method>
In the present embodiment, the quantum state generation device 1 performs processing according to FIG. 5 to generate a set of cluster-state photons. In the example of the present embodiment, steps S102, S103, S105, and S106 exemplified below correspond to the “measurement step”, steps S107 and S108 correspond to the “connection step”, and step S104 is the “first reuse step”. Step S109 corresponds to a “second reuse step”, and step S111 corresponds to a “deletion step”. Hereinafter, the quantum state generation method of this embodiment will be described with reference to FIG.

In step S101, the initial state generation unit 11 (FIG. 2) generates a set of three photons in a cluster state and sets it as a second photon set (corresponding to a “second qubit set”) (step S101). S101-1), ψ = (| η ₁ > | Φ ₁ > + | η ₂ > | Φ ₂ >) | H> (| Φ ₃ > | η ₃ > + | Φ ₄ > | η ₄ >) + ( | Η ₁ > | Φ ₁ > −β ₀₂ | η ₂ > | Φ ₂ >) | V> (| Φ ₃ > | η ₃ > − | Φ ₄ > | η ₄ >) X measurement of one photon in a superposed state of quantum states | H> and | V> included in a first photon set of three or more photons (corresponding to “first qubit set”) (Step S101-2).

  Whether step S101-1 is executed or step S101-2 is executed depends on whether the first photon set already exists, what cluster state photon set is finally generated, and the like. Dependent. As an example, when the first photon set does not exist, Step S101-1 is executed, and when the first photon set exists, Step S101-2 is executed. At this time, the first photon set may be obtained by performing a unitary transformation operation for each photon on the existing photon set. Alternatively, even if the first photon set already exists, step S101-1 may be executed when a new first photon set needs to be generated.

  When step S101-1 is executed, under the control of the control unit 17, the photon generation units 111a to 111f of the initial state generation unit 11 (FIG. 2) each have one single photon in the quantum state | +>. Generate and emit. The control unit 17 determines whether one photon is observed at each of the detectors 115dd, 115ec, and 115ed. The process of generating, emitting, observing, and determining the single photons of the quantum state | +> is repeated until one photon is observed at each of the detectors 115dd, 115ec, and 115ed. When one photon is observed at each of the detectors 115dd, 115ec, and 115ed, a total of three photons 1001, 1002, and 1003 respectively emitted from the polarization rotation elements 113ad, 113bc, and 113cc of the initial state generation unit 11 are observed. Is in the GHZ state (see, for example, Non-Patent Document 5) and is in the cluster state as described above. The three photons thus generated or three photons subjected to unitary conversion operation for each photon are set as the second photon set, and the process proceeds to step S107 (step S102).

  When Step S101-2 is executed, the quantum state | H> and | V> included in the first photon set consisting of three or more photons in the cluster state of the quantum state ψ is set to be a superposed state 1 X photons are measured. That is, under the control of the control unit 17, this one photon is incident on the polarization rotation element 121a of the X measurement unit 121 (FIG. 3A) of the measurement unit 12, and is measured by the detectors 121c and 121d. In this case (step S102), the determination unit 122 of the measurement unit 12 then determines whether a photon is observed by the detector 121c or 121d (whether a measurement result of calculation basis | H> or | V> is obtained). (Step S103).

When no photon is observed in any detector 121c or 121d (failure), the Z determination unit 141 of the reuse unit 14 determines the quantum state | Φ ₃ before the X measurement among the photons included in the first photon set. Z measurement is performed on one photon that is in a superposed state of> = | H> and | Φ ₄ > = | V>. That is, under the control of the control unit 17, this one photon is incident on the polarization beam splitter 141b of the Z measurement unit 141 (FIG. 3B) of the reuse unit 14, and is measured by the detectors 141c and 141d. The determination unit 142 determines whether photons are observed by the detector 141c or 141d.
If the photon at the detector 141c or 141d is observed, whereby the quantum states | eta _3> or | photon collection of contracted to eta _4>, or, the quantum state | eta _3> or | in eta _4> Of the photon sets obtained by subjecting the contracted photon set to unitary conversion operation for each photon by the unitary conversion unit 143, a photon set that can be the first photon set or the third photon set is a new first photon set. Or the third photon set, and the process returns to step S101. If there is nothing that can be the first photon set or the third photon set, the process returns to step S101 without generating a new first photon set or third photon set.
When no photon is observed in any of the detectors 141c and 141d, the Z measurement unit 141 performs Z measurement for each photon in the adjacent cluster state with the Z measurement photon before the Z measurement. 142 repeats the process of determining whether or not a photon is observed by the detector 141c or 141d until it is determined that each Zn-measured photon is observed by the detector 141c or 141d. When the photons measured with Z are observed by the detector 141c or 141d, among the photons included in the first photon set, a set of photons in a cluster state not measured for X or Z, or a set of the photons Among the photon sets obtained by performing the unitary conversion operation for each photon in the unitary conversion unit 143, a photon set that can be the first photon set or the third photon set is set as a new first photon set. The photon set is selected, and the process returns to step S101. If there is nothing that can be the first photon set or the third photon set, the process returns to step S101 without generating a new first photon set or third photon set (step S104).

On the other hand, when it is determined in step S103 that the photon is observed by the detector 121c or 121d (success), the determination unit 122 determines whether the photon is observed by the detector 121c (whether the calculation basis | H> is observed). Then, it is determined whether the photon is observed by the detector 121d (whether the calculation basis | V> is observed) (step S105). When it is determined that the photon is observed by the detector 121c (calculation basis | H> is observed), the quantum state of the complementary set obtained by removing one photon measured from the first photon set is X. | Η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ > Therefore, the complementary set is directly used as the second photon set, and the process proceeds to step S107. On the other hand, when it is determined that the photon is observed by the detector 121d (calculation basis | V> is observed), the quantum of the complementary set obtained by removing one photon measured from the first photon set. The state is contracted to | η ₁ > | Φ ₁ > | Φ ₄ > | η ₄ > + | η ₂ > | Φ ₂ > | Φ ₃ > | η ₃ >. Therefore, the unitary conversion unit 123 performs unitary conversion operation for each photon on this quantum state, and | η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + | η ₂ > | Φ ₂ > | Φ _The complement set having the quantum state of ₄ > | η ₄ > is set as the second photon set (step S106), and the process proceeds to step S107.

In step S107, the coupling unit 13 includes a third photon set including three or more photons in a cluster state including one photon in which the quantum state | Φ ₅ > and the quantum state | Φ ₆ > are overlapped. Quantum state α ₅ | η ₅₁ > | Φ ₅ > | η ₅₂ > + α ₆ | η ₆₁ > | Φ ₆ > | η ₆₂ > or α ₅ | Φ ₅ > | η ₅₂ > + α ₆ | Φ ₆ > | η ₆₂ > And the quantum state β ₁₃ | η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + β ₂₄ | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ > On the other hand, a quantum operation represented by γ ₁ <Φ ₃ | <Φ ₅ | + γ ₂ <Φ ₄ | <Φ ₆ | is performed. The third photon set may be generated by the initial state generation unit 11 as in step S101-1, or generated by the process of step S104 described above or the process of step S109 described later. It may be obtained by the process of step S107 performed in the past, or may be provided separately. By this quantum operation, the coupling unit 13 causes the complementary set obtained by removing one photon, which is a superposition state of the quantum state | Φ ₃ > and the quantum state | Φ ₄ >, from the second photon set, and the quantum state | The quantum state of the fourth photon set, which is the union of one photon, which is a superposition of Φ ₅ > and the quantum state | Φ ₆ >, from the third photon set is represented by | η ₇₁ > | Φ ₁ > | η ₇₂ > + | η ₈₁ > | Φ ₂ > | η ₈₂ >.

In step S107 of the present embodiment, the overlapping state of quantum states | Φ ₃ > and | Φ ₄ > included in the second photon set is incident on the incident portion a of the polarization beam splitter 131a of the mixed gate measurement unit 131 (FIG. 4). One photon is made to enter, and one photon in which the quantum states | Φ ₅ > and | Φ ₆ > included in the third photon set are superimposed on the incident part b of the polarization beam splitter 131a. Is incident. These photons are simultaneously incident on the incident part a and the incident part b (step S107). The determination unit 132 determines whether a photon is detected by both the detectors 131f and 131g (step S108).

When no photon is observed in any of the detectors 121c or 121d (failure), the Z measurement unit 151 of the reuse unit 15 is in an adjacent cluster state with the photons incident on the incident unit a of the polarization beam splitter 131a. The first adjacent photon that is a photon and the second adjacent photon that is in the adjacent cluster state are Z-measured, and the photon that is in the adjacent cluster state with the photon incident on the incident portion b of the polarization beam splitter 131a. The third adjacent photon and the fourth adjacent photon which is a photon in the adjacent cluster state are measured with Z. Then, a unitary calculation operation for each photon is performed as necessary to generate a new first qubit set or a new third qubit set.
That is, under the control of the control unit 17, the second adjacent photon is incident on the polarization beam splitter 151b of the Z measurement unit 151 (FIG. 3B) of the reuse unit 15, and is measured by the detectors 151c and 151d. The determination unit 152 determines whether or not photons are observed by the detector 151c or 151d. When a photon is observed by the detector 141c or 141d, a photon incident on the incident part a of the polarization beam splitter 131a, a first adjacent photon, and a second adjacent photon are excluded from the second photon set. Among photons obtained by performing unitary transformation operation for each photon in the unitary transformation unit 153 with respect to the subset and the subset of the first complementary set, those that can be the first photon set or the third photon set , A new first photon set or a new third photon set.
Similarly, the fourth adjacent photon is incident on the polarization beam splitter 151b of the Z measurement unit 151 (FIG. 3B) of the reuse unit 15, and is measured by the detectors 151c and 151d. The determination unit 152 determines whether or not photons are observed by the detector 151c or 151d. When a photon is observed by the detector 141c or 141d, a subset of the second complement obtained by removing the photon, the third adjacent photon, and the fourth adjacent photon incident on the incident part b from the third photon set, and Among the photon sets obtained by performing unitary conversion operation for each photon by the unitary conversion unit 153 with respect to the subset of the second complementary set, those that can be the first photon set or the third photon set are the new first set. Either a photon set or a new third photon set.
On the other hand, if no photons are observed in any of the detectors 151c and 151d in these Z measurements, the Z measurement unit 151 sets each photon in the adjacent cluster state to each of the photons measured in Z before the Z measurement. The measurement and the determination unit 152 repeats the process of determining whether or not a photon is observed by the detector 151c or 151d until it is determined that each photon measured by Z is observed by the detector 151c or 151d. If the Z-measured photon is observed by the detector 151c or 151d, the third complement obtained by excluding the photon thus measured from the first complement or the second complement described above, or the third complement Whether a photon set obtained by performing a unitary conversion operation for each photon on the complement set by the unitary conversion unit 143 can be a first photon set or a third photon set is a new first photon set Let it be the third photon set.
If there is nothing that can be the first photon set or the third photon set, no new first photon set or third photon set is generated.
After the above process (step S109), the process returns to step S101.

On the other hand, if it is determined in step S108 that photons are detected by both detectors 131f and 131g (success), the photon incident on the incident part a is removed from the second photon set, and the incident part b A sum set with a complementary set obtained by removing the incident photons from the third photon set is defined as a fourth photon set. As described above, the quantum state of the fourth photon set is | η ₇₁ > | Φ ₁ > | η ₇₂ > + | η ₈₁ > | Φ ₂ > | η ₈₂ >. Next, when any photon included in the fourth photon set is excluded from the set in order to generate desired cluster information, the process proceeds to step S111. Otherwise, the process proceeds to step S112.

  In step S111, the deletion unit 16 measures any specific photon included in the fifth photon set (corresponding to the “fifth qubit set”) including a plurality of photons in a cluster state, whereby the fifth photon is measured. A sixth photon set (corresponding to a “sixth qubit set”) obtained by removing the specific photon from the set is generated. The initial value of the fifth photon set in step S111 is the fourth photon set. When removing a plurality of photons, the sixth photon set is changed to a new fifth photon set, and the same process is repeated.

  When the cluster state between the photons to be measured and the photons in the adjacent cluster state is maintained after the measurement, the X measurement unit 161 performs the X measurement. When the cluster state between the photons to be measured and the photons in the adjacent cluster state is eliminated after the measurement, the Z measurement unit 162 performs Z measurement. Whether to perform X measurement or Z measurement depends on the quantum state required after the measurement. The details of the X measurement by the X measurement unit 161 are as follows. The polarization rotation element 121a, the polarization beam splitter 121b, and the detectors 121c and 121d are replaced with the polarization rotation element 161a, the polarization beam splitter 161b, and the detectors 161c and 161d. This is the same as the X measurement by the X measurement unit 121 described above except that the photon is replaced. The details of the Z measurement by the Z measurement unit 162 are as described above except that the polarization beam splitter 141b and the detectors 141c and 141d are replaced with the polarization beam splitter 162b and the detectors 162c and 162d, and the photons to be measured are replaced. This is the same as the Z measurement by the unit 141.

When X measurement is performed by the X measurement unit 161, the determination unit 163 determines whether a photon is observed by the detector 161c or 161d. When a photon is observed by the detector 161c or 161d, a sixth photon set is generated by removing the X-measured photon from the fifth photon set. After the X measurement, a unit in which the unitary conversion operation for each photon is performed in the unitary conversion unit 164 may be set as the sixth photon set. When the Z measurement is performed by the Z measurement unit 162, the determination unit 163 determines whether a photon is observed by the detector 162c or 162d. When a photon is observed by the detector 162c or 162d, a sixth photon set is generated by removing the Z-measured photon from the fifth photon set. After the Z measurement, a unit where the unitary conversion unit 164 performs a unitary conversion operation for each photon may be the sixth photon set.
On the other hand, if no photon is observed in any of the detectors 161c and 161d during X measurement, or if no photon is observed in any of the detectors 162c and 162d during Z measurement, the Z measurement unit 162 performs the X measurement or The Z-measured photon and each photon in an adjacent cluster state are Z-measured, and the determination unit 163 detects whether the photon is observed by the detector 161c or 161d. Repeat until it is determined that the signal is observed by the device 161c or 161d. In the case where the Z-measured photon is observed by the detector 161c or 161d, a complement set obtained by removing the X-measured or Z-measured photon from the fifth photon set, or a unitary conversion unit 164 for the complement set. A unit in which a unitary conversion operation is performed for each photon is taken as a sixth photon set.
If a desired sixth photon set is obtained by the above processing, the process proceeds to step S112.

  The processing in step S112 differs depending on whether the fourth photon set or the sixth photon set is a desired quantum state to be finally generated (step S112). If the fourth photon set or the sixth photon set is not the desired quantum state to be finally generated, the fourth photon set or the sixth photon set, or the fourth photon set or the sixth photon set On the other hand, the photon set obtained by performing the unitary conversion operation for each photon is set as a new first qubit set or a new third qubit set, and the process proceeds to step S101. On the other hand, when the fourth photon set or the sixth photon set is a desired quantum state to be finally generated, the fourth photon set or the sixth photon set which is the desired quantum state is the quantum state generation device. 1 (step S113).

<Example of quantum state generation method>
Next, an actual example of the quantum state generation method is shown.
In the example of FIGS. 6A and 6B, step S101-2 is performed on the first photon set 1010 in the cluster state, and the photons 1012 in the adjacent cluster state with the photons 1013 and 1011 are X-measured (step S102).

When the X measurement is successful (step S103) and the photon is observed (| H> is observed) by the detector 121c (step S105), the photons 1013 and 1011 are | H> | H> and | V> | V>. And photons 1023 and 1021 in a superposed state, and a second photon set 1020 having a quantum state of | η ₁ > | H> | H> + | η ₂ > | V> | V> is obtained (FIG. 6A). ).

When the X measurement is successful (step S103) and the photon is observed (| V> is observed) by the detector 121d (| V> is observed) (step S105), the photons 1013 and 1011 are | H> | V> and | V> | H>. The photons 1023 and 1021X are superimposed on each other, and a photon set 1020R having a quantum state of | η ₁ > | H> | V> + | η ₂ > | V> | H> is obtained (FIG. 6B). The unitary conversion unit 123 performs a Pauli X operation on the photon 1021X of the photon set 1020R, the photon 1021X becomes a photon 1021, and the quantum state is | η ₁ > | H> | H> + | η ₂ > | V> | V A second photon set 1020 is obtained (FIG. 6C). In this case, a loss may occur in the photon 1021 subjected to the Pauli X operation.

If the X measurement fails (step S103), whether the second photon set 1020 of the quantum state | η ₁ > | H> | H> + | η ₂ > | V> | V> is obtained or the quantum state | It is unclear whether a photon set 1020R of η ₁ > | H> | V> + | η ₂ > | V> | H> is obtained (FIG. 7A). In this case, the Z measurement unit 141 of the reuse unit 14 measures the photon 1023, and the photon set 1020A from which the photon 1022 and the photon 1021 or 1021X whose quantum state is unknown is removed is obtained by successful Z measurement. (Step S104). The photon set 1020A can be reused as the first and third photon sets (FIG. 7B).

As illustrated in FIG. 8A, the photons 1021 of the second photon set 1020 obtained as shown in FIG. 6A or FIG. Measurement is performed by the mixed gate measurement unit 131 (step S107). If this measurement is successful, a fourth photon set 1040 having a quantum state of | η ₇₁ > | H> | η ₇₂ > + | η ₈₁ > | V> | η ₈₂ > is obtained (step S108). Note that it is possible to specify whether or not the photon 1021 has been lost by the measurement by the mixed gate measurement unit 131. That is, if the photon 1021 is lost, it is determined as “failure” in step S108, and even if the photon 1021 is lost, the influence does not reach the fourth photon set 1040.

  When the measurement by the mixed gate measurement unit 131 fails, a photon set 1040A obtained by removing the photon 1021 from the second photon set 1020 and a photon set 1040B obtained by removing the photon 1031 from the third photon set 1030 are obtained. In this case, the photon 1024 and 1033 are Z-measured by the Z measurement unit 151 of the reuse unit 15, and if they are successful, the first complement set obtained by removing the photons 1023 and 1024 from the photon set 1040A, and the photon set A second complement set obtained by removing photons 1032 and 1033 from 1040B is obtained (step S109). The first and second complement sets and the set obtained by subjecting those photons to unitary transformation can be reused as the first and third photon sets (FIG. 8B).

  In the example of FIGS. 9A and 9B, step S101-2 is performed on the first photon set 1110 in the cluster state including the photons 1111-1115, and the photons 1113 in the adjacent cluster state with the photons 1112 and 1114 are X-measured. (Step S102).

When the X measurement is successful (step S103) and the photon is observed (| H> is observed) by the detector 121c (step S105), the photons 1112 and 1114 are | H> | H> and | V> | V>. Photons 1122 and 1124 superimposed on each other, and the second photon whose quantum state is | η ₁ > | H> | H> | η ₃ > + | η ₂ > | V> | V> | η ₄ > A set 1120 is obtained (FIG. 9A).

If the X measurement is successful (step S103) and the photon is observed (| V> is observed) by the detector 121d (step S105), the photons 1112 and 1114 are | H> | V> and | V> | H>. The photons 1122 and 1124X are superposed with each other, and the photon 1115 becomes the photon 1125Z of the quantum state obtained by subjecting the quantum state to the Pauli Z operation, and the quantum state becomes | η ₁ > | H> | V> | η ₄ A photon set 1120R satisfying> + | η ₂ > | V> | H> | η ₃ > is obtained (FIG. 9B). The unitary conversion unit 123 performs a Pauli X operation on the photon 1124X of the photon set 1120R, performs a Pauli Z operation on the photon 1125X of the photon set 1120R, and the quantum state is | η ₁ > | H> | H> | η _A second photon set 1120 satisfying ₃ > + | η ₂ > | V> | V> | η ₄ > is obtained (FIG. 9C). In this case, a loss may occur in the photon 1124 subjected to the Pauli X operation and the photon 1125 subjected to the Pauli Z operation.

If the X measurement fails (step S103), a second photon set 1120 of quantum state | η ₁ > | H> | H> | η ₃ > + | η ₂ > | V> | V> | η ₄ > is obtained. Whether the photon set 1120R of the quantum state | η ₁ > | H> | V> | η ₄ > + | η ₂ > | V> | H> | η ₃ > is obtained. (FIG. 10A). In this case, the Z measurement unit 141 of the reuse unit 14 performs Z measurement on the photon 1122 and the photon 1124 or 1124X, and the Z measurement is successful, thereby specifying whether the photon is the photon 1125 or the photon 1125Z ( In the definition of cluster state), the entanglement state is lost between the photon 1121 and the photon 1125 or 1125X. That is, when the result of Z measurement of photon 1124 or 1124X is | H> (when it is photon 1124), it is found that the photon logically adjacent to it is photon 1125, and photon 1121 is A cluster-state photon set 1120A including a cluster state and a cluster-state photon set 1120B including a photon 1125 are obtained. If the result of Z measurement of photon 1124 or 1124X is | V> (in the case of photon 1124X), it is found that the photon logically adjacent to it is photon 1125Z, and a cluster including photon 1121 A photon set 1120A in the state and a photon set 1120C in the cluster state including the photon 1125Z are obtained. The photon sets 1120A and 1120B, the photon set 1120C, and sets obtained by performing unitary transformation operations on these photons can be reused as the first and third photon sets (FIG. 10B).

As illustrated in FIG. 11, the photons 1124 of the second photon set 1120 and the photons 1133 of the third photon set 1130 in a cluster state including the photons 1131-1135 and the like obtained as shown in FIG. 9A or 9C are: Measurement is performed by the mixed gate measurement unit 131 (step S107). If this measurement is successful, the fourth photon set of quantum states | η ₇₁ > | H> | η ₇₂ > + | η ₈₁ > | V> | η ₈₂ > in a cluster state including photons 1141-1149 and the like 1140 is obtained (step S108). As described above, even if the photon 1124 is lost, the influence does not reach the fourth photon set 1140.

  When the measurement by the mixed gate measurement unit 131 fails, the entanglement state is lost between the photons 1122 and 1125 in the second photon set 1120, and between the photons 1132 and 1134 in the third photon set 1130. Is no longer entangled. As a result, a cluster state photon set 1140A including photons 1121 and 1122, a cluster state photon set 1140B including photons 1125 and 1126, a cluster state photon set 1140C including photons 1131 and 1132, and photons 1134 and 1135 are obtained. A clustered photon set 1140D is obtained. In this case, the Z measurement unit 151 of the reuse unit 15 performs Z measurement on the photons 1121, 1131, 1126, and 1135, and if they succeed, the complement set obtained by removing the photons 1121 and 1122 from the photon set 1140A, A complement set obtained by removing photons 1125 and 1126 from the photon set 1140B, a complement set obtained by removing photons 1131 and 1132 from the photon set 1140C, and a complement set obtained by removing photons 1134 and 1135 from the photon set 1140D are obtained (step S109). . These complementary sets and sets obtained by subjecting those photons to unitary transformation can be reused as the first and third photon sets. Since the photon 1125 is excluded by the measurement by the Z measuring unit 151, even if the photon 1125 is lost (FIG. 9C), the influence does not reach the reused first and third photon sets.

  Similarly, as illustrated in FIG. 12, the first photon set 1210 is X-measured to form the second photon set, and one photon of the second photon set and one photon of the third photon set 1230 Thus, measurement is performed by the mixing gate measurement unit 131. If the measurement by the mixed gate measurement unit 131 fails, some photons in the photon sets 1240A and 1240B at that time are measured and removed by the Z measurement unit 151 of the reuse unit 15 as described above, and the cluster State photon sets 1260A, 1260B are obtained. Photon sets 1260A and 1260B and sets obtained by subjecting these photons to unitary transformation operations can be reused as the first and third photon sets.

If the measurement by the mixed gate measurement unit 131 is successful, a fourth photon set 1240 is obtained, and the X measurement unit 161 of the deletion unit 16 performs X measurement. If the measurement is successful, unnecessary photons are removed, and the cluster state The sixth photon set 1260 is obtained. Here, in order for the sixth photon set 1260 to be in a cluster state, the number of X measurements in the X measurement unit 161 needs to be an even number. Therefore, as in the photon collections 1210 and 1230 illustrated in FIG. 12, the cluster state with respect to the “photons in the adjacent cluster state with four or more photons” and the “photons in the adjacent cluster state with four or more photons”. A photon set including an even number of photons in the first photon set 1210 is referred to as “photons in four or more photons and adjacent cluster states” and “photons in four or more photons and adjacent cluster states”. On the other hand, a photon set including an odd number of photons in a cluster state is referred to as a third photon set 1230, and is changed to a cluster state with respect to “four photons and photons in an adjacent cluster state” included in the first photon set 1210. It is in a cluster state with respect to a part of an even number of photons and “photons in four or more photons and adjacent cluster states” included in the third photon set 1230 Against a portion of the several number of photons, the measurement in the X measurement and step S107 in step S101 it is desirable that made. As a result, like the photon set 1240, the number of unnecessary photons to be deleted becomes an even number, and the sixth photon set 1260 can be in a cluster state. In the example of FIG. 12, four unnecessary photons are removed from the fourth photon set 1240 by four X measurements, and a sixth photon set 1260 in a cluster state is obtained (step S111). As illustrated in FIG. 12, the sixth photon set 1260 thus generated includes four photons and photons in adjacent cluster states. Accordingly, unnecessary photons can be deleted by Z measurement, and the above-described processing can be repeated to generate a photon set in a three-dimensional cluster state as illustrated in FIG.
When X measurement fails in the X measurement unit 161, Z measurement is performed in the Z measurement unit 162, and if they succeed, cluster photons 1260A and 1260B are obtained. Photon sets 1260A and 1260B and sets obtained by subjecting these photons to unitary transformation operations can be reused as the first and third photon sets.

  In the example of FIG. 13, there may be a case where the measurement result is not obtained even though the photons 1414 of the photon set 1310 in the cluster state including the photons 1311 to 1317 are Z-measured. In this case, whether the photons 1313 and 1315 that were in a close cluster state with the photon 1414 before the Z measurement are photons 1313 and 1315 after the Z measurement, or obtained by performing Hadamard transformation on the photons 1313 and 1315, respectively. It is unclear whether the photons 1313H and 1315H are in a quantum state. Thus, in such a case, photons 1313 or 1313H and photons 1315 or 1315H are Z-measured and, if they are successful, these photons are removed.

  In the example of FIGS. 14 and 15, one photon of the first photon set 1610 is X-measured, and one photon of the second photon set 1610 ′ obtained thereby and one photon of the third photon set 1630 are obtained. Measurement by the mixed gate measurement unit 131 is performed on the photons. If the measurement by the mixed gate measurement unit 131 fails, some photons in the photon sets 1640A and 1640B at that time are measured and removed by the Z measurement unit 151 of the reuse unit 15 as described above, and the cluster State photon sets 1660A, 1660B are obtained. The photon sets 1660A and 1660B and sets obtained by subjecting those photons to unitary transformation can be reused as the first and third photon sets.

  When the measurement by the mixed gate measurement unit 131 is successful, a fourth photon set 1640 is obtained, and the X measurement unit 161 of the deletion unit 16 performs X measurement. If the measurement is successful, unnecessary photons are removed, and the cluster state The sixth photon set 1660 is obtained. Here, in order for the sixth photon set 1660 to be in a cluster state, the number of X measurements in the X measurement unit 161 needs to be an even number. Therefore, as in the photon collections 1610 and 1630 illustrated in FIG. 14, the cluster state with respect to “photons in adjacent cluster state with four or more photons” and “photons in adjacent cluster state with four or more photons”. A photon set including an even number of photons in the first photon set 1610 is referred to as “photons in four or more photons and adjacent cluster states” and “photons in four or more photons and adjacent cluster states”. On the other hand, a photon set including an odd number of photons in a cluster state is referred to as a third photon set 1630, and a cluster state with respect to “four or more photons and a photon in an adjacent cluster state” included in the first photon set 1610. Are in a cluster state with respect to a part of the even number of photons and “photons in four or more photons and adjacent cluster states” included in the third photon set 1630. Against a portion of the photons of the odd number that, it is desirable that the measurement of the X measurement and step S107 in step S101 is made. Thereby, like the photon set 1640, the number of unnecessary photons to be deleted becomes an even number, and the sixth photon set 1660 can be in a cluster state. In the example of FIG. 15, four unnecessary photons are removed from the sixth photon set 1640 by four X measurements, and a sixth photon set 1660 in a cluster state is obtained (step S111). As illustrated in FIG. 12, the sixth photon set 1260 thus generated includes four photons and photons in adjacent cluster states. Accordingly, unnecessary photons can be deleted by Z measurement, and the above-described processing can be repeated to generate a photon set in a three-dimensional cluster state as illustrated in FIG.

[Second Embodiment]
The second embodiment is a modification of the first embodiment, and only the configuration of the initial state generation unit is different from the first embodiment. Below, it demonstrates focusing on the difference of an initial state production | generation part.

ＥＰＲ光子対は、パラメトリック下方変換によって得られることが知られている（例えば、「Paul G. Kwiat, Klaus Mattle, Harald Weinfurter, and Anton Zeilinge, “New High-Intensity Source of Polarization-Entangled Photon Pairs,”Phys. Rev. Lett. 4337 (1995).」「Paul G. Kwiat, Edo Waks, Andrew G. White, Ian Appelbaum, and Philippe H. Eberhard, “Ultra-bright source of polarization-entangled photons,” Phys. Rev. A 60, R773-R776 (1999).」等参照）。 As illustrated in FIG. 1, the quantum state generation device 2 of the second embodiment is obtained by replacing the initial state generation unit 11 of the quantum state generation device 1 of the first embodiment with an initial state generation unit 21.
As illustrated in FIG. 17, the initial state generation unit 21 of the present embodiment includes an EPR state generation unit 212a to 212c, polarization beam splitters 112d and 112e, polarization rotation elements 113ac, 113ad, 113bc, 113bd, 113cc, 113cd, 113dd, 113ec, 113ed, polarizing plates 114dd, 114ec, 114ed, and detectors 115dd, 115ec, 115ed. Each of the EPR state generation units 212a to 212c generates and outputs one photon pair (EPR photon pair) called an EPR state shown below.

EPR photon pairs are known to be obtained by parametric downconversion (eg, “Paul G. Kwiat, Klaus Mattle, Harald Weinfurter, and Anton Zeilinge,“ New High-Intensity Source of Polarization-Entangled Photon Pairs, ” Rev. Lett. 4337 (1995). ”“ Paul G. Kwiat, Edo Waks, Andrew G. White, Ian Appelbaum, and Philippe H. Eberhard, “Ultra-bright source of polarization-entangled photons,” Phys. Rev. A 60, R773-R776 (1999).

  One photon of the EPR photon pair generated by the EPR state generation unit 212a is a photon 1001, and the other photon is incident on the incident part da of the polarization beam splitter 112d. One photon of the EPR photon pair generated by the EPR state generation unit 212b is a photon 1002, and the other photon is incident on the incident part db of the polarization beam splitter 112d. One photon of the EPR photon pair generated by the EPR state generation unit 212c is a photon 1003, and the other photon is incident on the incident part eb of the polarization beam splitter 112e.

  The control unit 17 determines whether one photon is observed at each of the detectors 115dd, 115ec, and 115ed. The generation / emission, observation, and determination processing of these EPR photon pairs is repeated until one photon is observed at each of the detectors 115dd, 115ec, and 115ed. When one photon is observed at each of the detectors 115dd, 115ec, and 115ed, a total of three photons 1001, 1002, and 1003 respectively emitted from the EPR state generators 212a to 212c are in the GHZ state (for example, , “Z.-H. Wei, Y.-J. Han, CH Oh, and L.-M. Duan,“ Improving noise threshold for optical quantum computing with the EPR photon source, ”Physical Review A 81, 060301 (R (See (2010).) Etc.) In addition, as described above, it is in a cluster state. The three photons generated as described above or the three photons subjected to the unitary conversion operation for each photon are set as the second photon set. Others are the same as the first embodiment.

[Modifications, etc.]
The present invention is not limited to the embodiment described above. For example, in the first embodiment, when | V> is observed in the X measurement (step S105), a unitary transformation for each photon is performed on the photon set after the measurement to generate a second photon set ( Step S106). However, the second photon set may be generated only when | H> is observed in the X measurement. Thereby, generation | occurrence | production of the loss at the time of producing | generating a 2nd photon set can be suppressed. Further, when the same process is executed a plurality of times, a plurality of processing units having the same configuration may execute the processes, or one processing unit may execute the same process a plurality of times. In addition, the above-described functions may be obtained without using a quantum memory.
The various processes described above are not only executed in time series according to the description, but may also be executed in parallel or individually as required by the processing capacity of the apparatus that executes the processes. Needless to say, other modifications are possible without departing from the spirit of the present invention.

  Further, the control processing content of the quantum state generation method described above is described by a program. For example, when a photon is used for a qubit, this program is used to cause a computer to control the characteristics of each optical element necessary for quantum processing (for example, the mirror angle and the phase shifter control voltage). When a nuclear spin is used for a qubit, it means a program for causing a computer to control the frequency and time of an electromagnetic wave applied to the nuclear spin. By executing this program on a computer, the above control processing contents are realized on the computer.

  The program describing the contents of the control processing can be recorded on a computer-readable recording medium. The computer-readable recording medium may be any medium such as a magnetic recording device, an optical disk, a magneto-optical recording medium, or a semiconductor memory. Specifically, for example, the magnetic recording device may be a hard disk device or a flexible Discs, magnetic tapes, etc. as optical disks, DVD (Digital Versatile Disc), DVD-RAM (Random Access Memory), CD-ROM (Compact Disc Read Only Memory), CD-R (Recordable) / RW (ReWritable), etc. As the magneto-optical recording medium, MO (Magneto-Optical disc) or the like can be used, and as the semiconductor memory, EEP-ROM (Electronically Erasable and Programmable-Read Only Memory) or the like can be used.

  The program is distributed by selling, transferring, or lending a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of the server computer and transferring the program from the server computer to another computer via a network.

  A computer that executes such a program first stores, for example, a program recorded on a portable recording medium or a program transferred from a server computer in its own storage device. When executing the process, the computer reads a program stored in its own recording medium and executes a process according to the read program. As another execution form of the program, the computer may directly read the program from a portable recording medium and execute processing according to the program, and the program is transferred from the server computer to the computer. Each time, the processing according to the received program may be executed sequentially. Also, the program is not transferred from the server computer to the computer, and the above-described processing is executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by the execution instruction and result acquisition. It is good. Note that the program in this embodiment includes information that is used for processing by an electronic computer and that conforms to the program (data that is not a direct command to the computer but has a property that defines the processing of the computer).

  1, 2 Quantum state generator

Claims (11)

β ₀₁ , β ₀₂ , β ₀₃ , β ₀₄ represent complex numbers, | η ₁ >, | η ₂ >, | η ₃ >, | η ₄ > each represent an arbitrary quantum state, | Φ ₁ >, When | Φ ₂ >, | Φ ₃ >, and | Φ ₄ > each represent a quantum state of one qubit, | H> and | V> each represent a quantum state of a calculation basis. (Β ₀₁ | η ₁ > | Φ ₁ > + β ₀₂ | η ₂ > | Φ ₂ >) | H> (β ₀₃ | Φ ₃ > | η ₃ > + β ₀₄ | Φ ₄ > | η ₄ >) + ( β ₀₁ | η ₁ > | Φ ₁ > −β ₀₂ | η ₂ > | Φ ₂ >) | V> (β ₀₃ | Φ ₃ > | η ₃ > −β ₀₄ | Φ ₄ > | η ₄ >) X measurement is performed on one qubit in a superposed state of quantum states | H> and | V> included in a first qubit set including three or more qubits in the entanglement state. , The X measured one qubit is converted into the first qubit set. A second qubit set which is a complementary set removed from the first qubit is generated, and the specific quanta included in the second qubit set in the adjacent entanglement state with the one qubit measured in X When the bit quantum state is overlapped with | Φ ₁ > | Φ ₃ > and | Φ ₂ > | Φ ₄ >, and the quantum states of the second qubit set are represented by β ₁₃ and β ₂₄ as complex numbers Measuring step in which β ₁₃ | η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + β ₂₄ | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ >
Quantum state | Φ ₅ > and quantum state in the case where α ₅ and α ₆ represent complex numbers and | η ₅₁ >, | η ₅₂ >, | η ₆₁ >, | η ₆₂ > each represent an arbitrary quantum state Quantum state α ₅ | η ₅₁ > | Φ ₅ > | of the third qubit set composed of three or more qubits in the entanglement state including one qubit superposed with | Φ ₆ > η ₅₂ > + α ₆ | η ₆₁ > | Φ ₆ > | η ₆₂ > or α ₅ | Φ ₅ > | η ₅₂ > + α ₆ | Φ ₆ > | η ₆₂ > and the quantum state β of the second qubit set ₁₃ | η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + β ₂₄ | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ > and <Φ _i | When Φ _j > ≠ 0, when i ≠ j, <Φ _i | Φ _j > = 0, and when γ ₁ and γ ₂ represent complex numbers, γ ₁ <Φ ₃ | <Φ ₅ | + γ ₂ <Φ ₄ | <Φ ₆ | in performs quantization operation represented, quantum state | [Phi _3> And a quantum state | Φ ₄ > and a complementary set obtained by removing one qubit from the second qubit set, and a quantum state | Φ ₅ > and a quantum state | Φ ₆ > A fourth qubit set that is the union of a complementary set obtained by removing one qubit that was in the combined state from the third qubit set is generated, and the quantum state of the fourth qubit set is expressed as α _7. , α ₈ represents a complex number, and α ₇ | η ₇₁ > | Φ ₁ > | in the case where | η ₇₁ >, | η ₇₂ >, | η ₈₁ >, | η ₈₂ > each represents an arbitrary quantum state. a coupling step of η ₇₂ > + α ₈ | η ₈₁ > | Φ ₂ > | η ₈₂ >;
A quantum state generation method comprising: The quantum state generation method according to claim 1,
The measuring step includes
As a result of X measurement of one qubit in which the quantum states | H> and | V> are overlapped, the measurement base | H> or | V> is obtained when the measurement result is obtained. A quantum state generation method, which is a step of generating a two-qubit set. The quantum state generation method according to claim 1 or 2,
The measuring step includes
The result obtained by X-measuring one qubit in which the quantum states | H> and | V> are superposed is the calculation basis | V>, and the X-measured one The quantum state of the complementary set obtained by removing the qubit from the first qubit set is β ₁₄ | η ₁ > | Φ ₁ > | Φ ₄ > | η ₄ > + β ₂₃ | η ₂ > | Φ ₂ > | Φ ₃ > When | η ₃ > contracts, a quantum operation for each qubit represented by unitary transformation is performed, and the quantum state of the second qubit set is changed to β ₁₃ | η ₁ > | Φ ₁ > | Φ ₃ > | A quantum state generation method including a unitary transformation step of η ₃ > + β ₂₄ | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ >. The quantum state generation method according to claim 1 or 2,
The measuring step includes
Only when the result obtained by X measurement of one qubit in which the quantum states | H> and | V> are overlapped is the calculation basis | H>, the second quantum A quantum state generation method, which is a step of generating a bit set. The quantum state generation method according to any one of claims 1 to 4,
Even if X measurement is performed on one qubit in which the quantum states | H> and | V> are superposed in the measurement step, the measurement result of the calculation basis | H> or | V> cannot be obtained. In such a case, at least one qubit in the superposition state of the quantum states | Φ ₃ > and | Φ ₄ > among the qubits included in the first qubit set is defined as a base | Φ ₃ >, | A set of qubits measured with Φ ₄ > and thereby a quantum state contracted to | η ₃ > or | η ₄ >, or a set of qubits whose child states contracted to | η ₃ > or | η ₄ > A first reuse step in which a set of qubits obtained by performing a quantum operation for each qubit represented by unitary transformation is set as the new first qubit set or the third qubit set A quantum state generation method further comprising: The quantum state generation method according to any one of claims 1 to 5,
The connecting step includes
A polarization beam splitter including first and second incident portions and first and second emission portions, first and second polarization rotation elements that emit light by changing the polarization direction of the incident qubit by 45 °, and the polarization direction is the first A first and a second polarizing plate that pass a qubit that is a polarization direction, and that block a qubit that is a second polarization direction whose polarization direction is orthogonal to the first polarization direction, and a first and a second detector, The first emitting part emits the qubit in the first polarization direction incident on the first incident part and the qubit in the second polarization direction incident on the second incident part, and the second emitting part A qubit in the second polarization direction incident on the first incident portion and a qubit in the first polarization direction incident on the second incident portion are emitted from the first emission portion to the first polarization rotation element. The emitted qubit enters and the second polarization rotation The quantum bit emitted from the second emission part is incident on the child, the quantum bit emitted from the first polarization rotating element is incident on the first polarizing plate, and the second polarizing plate is incident on the second polarizing plate. A qubit emitted from the polarization rotation element enters, a qubit transmitted through the first polarizing plate enters the first detector, and a qubit transmitted through the second polarizing plate enters the second detector. The first incident portion of the integrated gate portion configured to be incident is superposed with the quantum state | Φ ₃ > and the quantum state | Φ ₄ > included in the two specific qubits. One qubit is made incident, and the second incident part is made to be a superposed state of quantum state | Φ ₅ > and quantum state | Φ ₆ > included in the third qubit set. Of qubits, and both the first and second detectors The second and second detectors are determined to have detected qubits, and the second qubit set is excluded from the qubits incident on the first incident portion. The sum of the set and the complementary set excluding the qubit incident on the second incident part from the third qubit set when it is determined that both of the first and second detectors detect the qubit. Making a set the fourth qubit set;
The qubit is a photon, the quantum state is a polarization direction of the photon, the quantum state | H> is the first polarization direction, and the quantum state | V> is the second polarization direction; Each of Φ ₁ >, | Φ ₃ >, | Φ ₅ > is the first polarization direction, and each of | Φ ₂ >, | Φ ₄ >, | Φ ₆ > is the second polarization direction. State generation method. The quantum state generation method according to claim 6,
When it is determined that any of the first and second detectors does not detect a qubit, the first adjacent quantum that is a qubit in an adjacent entanglement state with the qubit incident on the first incident unit. A second adjacent qubit that is a qubit in an adjacent entanglement state with the bit is Z-measured, and a third adjacent quanta that is a qubit in an adjacent entanglement state with the qubit incident on the second incident unit A fourth adjacent qubit, which is a qubit that is in an adjacent entanglement state with the bit, is Z-measured, and the qubit incident on the first incident unit, the first adjacent qubit, and the second adjacent qubit are A subset of the first complementary set excluded from the second qubit set, a qubit incident on the second incident portion, the third adjacent qubit, and the fourth adjacent Quantities obtained by performing a quantum operation for each qubit represented by unitary transformation on a subset of the second complementary set obtained by removing child bits from the third qubit set, and a subset of the first complementary set At least a part of a set of bits and a set of qubits obtained by performing a quantum operation for each qubit represented by unitary transformation on a subset of the second complementary set is used as a new first quantum The quantum state generation method further comprising a second reuse step that is a bit set or a new third quantum bit set. The quantum state generation method according to any one of claims 1 to 7,
By measuring any specific qubit included in the fifth qubit set including a plurality of entangled qubits, a sixth quanta obtained by removing the specific qubit from the fifth qubit set A removal step for generating a bit set,
The superposition state of | η ₁ > and | η ₂ > is an entanglement state, the superposition state of | η ₃ > and | η ₄ > is an entanglement state, and | η ₅₁ > and | η ₆₁ > The superposition state is an entanglement state, the superposition state of | η ₅₂ > and | η ₆₂ > is an entanglement state, the superposition state of | η ₇₂ > and | η ₈₂ > is an entanglement state,
Until the fourth qubit set or the sixth qubit set becomes a desired qubit set, the fourth qubit set or the sixth qubit set, or the fourth qubit set or the sixth qubit set. A set of qubits obtained by performing a quantum operation for each qubit represented by unitary transformation on the bit set is defined as the new first qubit set or the new third qubit set, and the measurement step and A process in which the connecting step is executed again, a process in which the fourth qubit set obtained in any of the connecting steps is set as the fifth qubit set, and the removing step is executed, and the sixth quantum At least a part of the process in which the bit set is set as the new fifth qubit set and the removal step is executed again is repeatedly executed. Child state generation method. The quantum state generation method according to any one of claims 1 to 8,
The first qubit set is in a cluster state, the quantum state of the fourth qubit set is in a cluster state,
Each of the plurality of qubits included in the set of qubits in the cluster state is in an adjacent cluster state with any other qubit included in the plurality of qubits included in the set of qubits in the cluster state. ,
The adjacent cluster state is
A control Pauli Z operation for a quantum state obtained by performing a control Pauli Z operation on a quantum state | +> | +> of a pair of qubits and a quantum state of a pair of qubits in the adjacent cluster state And a quantum state obtained by further subjecting each quantum bit to a quantum operation represented by unitary transformation on the quantum state of a pair of qubits in the adjacent cluster state. , | +> = (| H> + | V>) (1 / √2). β ₀₁ , β ₀₂ , β ₀₃ , β ₀₄ represent complex numbers, | η ₁ >, | η ₂ >, | η ₃ >, | η ₄ > each represent an arbitrary quantum state, | Φ ₁ >, When each of | Φ ₂ >, | Φ ₃ >, | Φ ₄ > represents a quantum state of one qubit, and | H>, | V> represents a quantum state of a calculation basis, _{01 | η 1> | Φ 1} > + β 02 | η 2> | Φ 2>) | H> (β 03 | Φ 3> | η 3> + β 04 | Φ 4> | η 4>) + (β 01 | Η ₁ > | Φ ₁ > −β ₀₂ | η ₂ > | Φ ₂ >) | V> (β ₀₃ | Φ ₃ > | η ₃ > −β ₀₄ | Φ ₄ > | η ₄ >) X measurement is performed on one qubit that is included in a first qubit set including three or more qubits in a certain entanglement state and is in a superposition state of quantum states | H> and | V>. X is a complement obtained by removing one measured qubit from the first qubit set. A second qubit set that is a set, and the quantum states of two specific qubits included in the second qubit set that are in an adjacent entanglement state with the one qubit measured in X the | Φ _1> | Φ _3> and | [Phi _2> | when the overlapping state of the [Phi _4>, the quantum state of the second qubit set, the beta _13, beta ₂₄ represents a complex number, beta ₁₃ | Η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + β ₂₄ | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ >
Quantum state | Φ ₅ > and quantum state in the case where α ₅ and α ₆ represent complex numbers and | η ₅₁ >, | η ₅₂ >, | η ₆₁ >, | η ₆₂ > each represent an arbitrary quantum state Quantum state α ₅ | η ₅₁ > | Φ ₅ > | of the third qubit set composed of three or more qubits in the entanglement state including one qubit superposed with | Φ ₆ > η ₅₂ > + α ₆ | η ₆₁ > | Φ ₆ > | η ₆₂ > or α ₅ | Φ ₅ > | η ₅₂ > + α ₆ | Φ ₆ > | η ₆₂ > and the quantum state β of the second qubit set ₁₃ | η ₁ > | Φ ₁ > | Φ ₃ > | η ₃ > + β ₂₄ | η ₂ > | Φ ₂ > | Φ ₄ > | η ₄ > and <Φ _i | When Φ _j > ≠ 0, when i ≠ j, <Φ _i | Φ _j > = 0, and when γ ₁ and γ ₂ represent complex numbers, γ ₁ <Φ ₃ | <Φ ₅ | + γ ₂ <Φ ₄ | <Φ ₆ | in performs quantization operation represented, quantum state | [Phi _3> And a quantum state | Φ ₄ > and a complementary set obtained by removing one qubit from the second qubit set, and a quantum state | Φ ₅ > and a quantum state | Φ ₆ > A fourth qubit set that is the union of a complementary set obtained by removing one qubit that was in the combined state from the third qubit set is generated, and the quantum state of the fourth qubit set is expressed as α _7. , α ₈ represents a complex number, and α ₇ | η ₇₁ > | Φ ₁ > | in the case where | η ₇₁ >, | η ₇₂ >, | η ₈₁ >, | η ₈₂ > each represents an arbitrary quantum state. η ₇₂ > + α ₈ | η ₈₁ > | Φ ₂ > | η ₈₂ >
A quantum state generation device having:   The program for making a computer perform control processing of the quantum state production | generation method in any one of Claim 1 to 9.

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