JP4552577B2 - Quantum state restoration device - Google Patents

Description

  The present invention relates to a quantum state restoration device that performs restoration processing for returning broken quantum information to an original state when the quantum information is broken by processing such as quantum computation or quantum communication in quantum information processing.

  For example, classical information processing (referred to as conventional information processing in order to distinguish it from quantum information processing) is realized by a backup in which information is redundantly copied and stored. There are many cases. For example, (2m, m) encoding in which a code word is assigned to m-bit information (Equation 1) as shown in (Equation 2).

  If this can be done for the quantum information, the quantum information ρ is encoded by a tensor product of ρ as shown in (Equation 3).

  However, when quantum information is represented by a quantum state of superposition characteristic in quantum information processing, it is proved by the quantum non-replicatable theorem that such copying is impossible (for example, non-replication theorem) (See Patent Document 1, Chapter 2.4). Therefore, backup by simple encoding as in (Equation 3) is impossible. Therefore, quantum error correction specific to the quantum state is required for error correction of quantum information (see, for example, Chapter 13 of Non-Patent Document 1 and Non-Patent Document 2).

  Here, the quantum error correction method will be briefly described with reference to FIG.

  In FIG. 2, 201 is an entanglement generation unit that generates entanglement with an input quantum state | Ψ> and an auxiliary quantum state | Φ> representing information to be processed, and 202 is generated by the entanglement generation unit 201. Information processing quantum memory storing the entanglement state | Ψ ′>, and 203 is a quantum information processing unit that performs quantum information processing on the quantum state | Ψ ′> stored in the information processing quantum memory 202 204 is a quantum error correction unit that restores the quantum state stored in the information processing quantum memory 202 when an error occurs due to an external fluctuation during the processing of the quantum information processing unit 203. .

  The operation of the conventional quantum restoration device configured as described above will be described below.

  First, information is expressed by the input quantum state. As a representation of quantum information, qubits represented by two orthogonal states | 0> and | 1> of a quantum two-level system are typical. For example, quantum bits can be expressed by photon polarization, nuclear spin of ions doped in a semiconductor, electrons in quantum dots, and the like.

  The entanglement generation unit 201 generates entanglement between the input quantum state | ψ> and the auxiliary quantum state | Φ>. For example, when the control NOT of | Ψ> and | Φ> is taken, the output | Ψ ′> is in an entanglement state. For example, when realizing a qubit with nuclear spins of ions, a voltage is applied to the J-Gate provided between adjacent ions by using the interaction between the local spins of adjacent ion spins as a medium. By controlling the spread of localized electrons, it is possible to realize a control NOT operation of rotating the other nuclear spin only when one nuclear spin is upward. Alternatively, when the qubit is realized by the polarization of photons, it can be realized by an optical element such as a beam splitter.

  What entanglement is to be generated needs to be determined by the quantum error correction unit 204 so that an error of the qubit can be corrected. Usually, as shown in Non-Patent Document 1, an appropriate control NOT is often applied between the input quantum state | ψ> and the auxiliary quantum state | Φ>.

  The entanglement state quantum state | Ψ '> generated by the entanglement generation unit 201 is stored in the information processing quantum memory 202.

  The quantum information processing unit 203 performs processing on the quantum state stored in the information processing quantum memory 202. For example, various operations for quantum computation have been developed (for example, see Non-Patent Document 2). There are various physical operations, such as irradiating lasers to ions holding a quantum state from the outside, changing the magnetic field by NMR to molecules in the liquid, and passing the photons through a circuit combining optical elements ( For example, refer nonpatent literature 3).

  When an error occurs in the qubit during the processing of the quantum information processing unit 203, the quantum error correction unit 204 performs error correction processing of the qubit as described in Non-Patent Document 1 and performs information processing quantum. The quantum state stored in the memory 202 is restored.

  Further, an error correction method for efficiently correcting an error of a qubit at a specific position has been proposed (see, for example, Non-Patent Document 4 and Non-Patent Document 5).

On the other hand, as a method of reducing errors in quantum states, quantum state destruction that reduces the occurrence of errors by preventing quantum states from being destroyed due to external fluctuations without using quantum error correction processing. There is a prevention process. As an example of such a process, the quantum state of the qubit is dissipated by intermittently irradiating a light pulse to a qubit in which quantum information is stored and repeatedly inducing a physical phenomenon equivalent to the optical echo phenomenon. There are things that prevent destruction of the quantum state by returning to the quantum state before the occurrence (see, for example, Patent Document 1).
Hosoya Ikuo, “Basics of Quantum Computers” Science, December 25, 1999, Chapter 13 Quantum Error Correction, p. 20-22, p. 100-p. 112 M.M. A. Nielsen, I.M. L. Chuang, “Quantum Computation and Quantum Information”, Cambridge University Press, 2000 Shigeki Takeuchi, “Experiment in Quantum Computation”, Mathematical Science “Quantum Information Science and its Development”, Science, p. 57-p. 63, April 2003 H. Shiraki, S .; Usami, T .; S. Usuda, and I.I. Takami, “Quantum error correcting code for specific position errors and its applications”, ERATO Conference on Quantum Information Science 2003 (EQIS3) 111-112, September 2003 Takamine Tanaka, Hiroyuki Shiraki, Shogo Usami, Satoshi Usuda “Study of Correction Method for Specific Position Quantum Error Correction Code”, 26th Symposium on Information Theory and Its Applications, vol. 2, pp. 659-662 (2003.12) Japanese Patent Laid-Open No. 11-213652

  However, in the quantum state restoration device based on the quantum error correction as described above, the quantum error correction unit 204 is designed on the assumption that an error may occur equally in all qubits including the auxiliary quantum state. As a result, there is a problem that as a whole, only a small number of errors in qubits can be handled. Quantum error correction was originally created for the purpose of algorithmic correction of minority qubit errors caused by external fluctuations, and it is difficult to deal with many qubit errors caused by quantum information processing. is there. For example, as described in D.C. P. Divincenzo and Shor's 5 qubit quantum error correction codes cannot recover errors of 2 qubits or more.

  In addition, the method of reducing the quantum state error itself by the quantum state destruction prevention process aims to keep the stored quantum state for the stored quantum state. There is a problem that coexistence with quantum information processing that artificially changes the quantum state is difficult. In addition, since the quantum state destruction prevention process is always performed, the collision of access to the quantum state with the quantum information processing is also a problem.

  The present invention has been made to solve the above problems, and an object of the present invention is to perform quantum information processing that can cope with many errors of qubits caused by quantum information processing and frequently changes the quantum state. It is another object of the present invention to provide a quantum state restoration device that can also be used.

  In order to solve the above-described conventional problems, a quantum state restoration device according to the present invention includes a quantum coding unit that performs quantum coding on an input quantum state, and a part of a quantum bit of the quantum state that has been quantum coded. The state of the information processing quantum memory unit, the storage quantum memory unit for storing the rest of the quantum-coded quantum state qubits so as to prevent the destruction of the quantum state, and the state of the information processing quantum memory unit In the case of destruction, a quantum restoration unit that restores the quantum state from the destroyed qubit and the qubit stored in the storage quantum memory unit is provided.

  As described above, the present invention performs quantum reconstruction from a broken qubit and an unbroken qubit in a storage quantum memory even when there are many errors in the information quantum memory caused by errors in the quantum information processing unit. By doing so, it becomes possible to correctly restore the original quantum state.

  Embodiments of the present invention will be described below with reference to the drawings.

(Embodiment 1)
FIG. 1 shows a quantum state restoration device according to a first embodiment of the present invention. In FIG. 1, reference numeral 101 denotes a quantum encoding unit that performs quantum encoding from an input quantum state | ψ> to generate an encoded quantum state | ψ _c >, and 102 denotes a quantum generated by the quantum encoding unit 101. An information processing quantum memory for storing a part of the state qubits, 103 is a storage quantum memory for storing the remaining qubits of the quantum state generated by the quantum encoding unit 101, Reference numeral 104 denotes a quantum information processing unit that performs quantum information processing on the qubits stored in the information processing quantum memory. Reference numeral 105 denotes a quantum state destruction that prevents destruction of the quantum states stored in the storage quantum memory 103. 106 is a prevention processing unit, and when a quantum bit in the information processing quantum memory 102 is broken and becomes an errored quantum bit, the quantum bit stored in the storage quantum memory 103 is also A quantum restorer for restoring the _Ψ> | Ψ _'c> Karamoto input quantum state of | Umate, the quantum state with errors.

  The operation will be described below. First, the quantum coding unit 101 performs quantum coding so that the error correction in the quantum restoration unit 106 functions well. For example, based on the (3m, m) specific position quantum error correction code and the (2m + 1, m) specific position quantum error correction code proposed in Non-Patent Document 2, the input quantum state | Ψ> is encoded. The entanglement generation may be performed using the auxiliary quantum state | Φ> for.

When the input quantum state | Ψ> is composed of m qubits, it can be expressed as (Equation 4). In this case, in the (3m, m) specific position quantum error correction code, the input quantum state | Ψ> in (Expression 4) is converted into the quantum state | Ψ as expressed in (Expression 5) by 3m quantum bit encoding. Quantize to _c >.

Here, | S _j > is an orthogonal state represented by (Expression 6), and j and k each represent an m-digit binary number expression. Further, W _H (j · k) is a Hamming weight, and represents a value obtained by calculating the Hamming weight after performing AND for each bit with respect to the m-digit binary representation of j and k.

  In this (3m, m) specific position quantum error correction code, 3 m qubits are required to represent the input quantum state | Ψ> of m qubits.

Among the encoded quantum states | Ψ _c >, 1 to m qubits are stored in the information processing quantum memory 102, and the remaining m + 1 to 3 m qubits are stored in the storage quantum memory 103.

As a more efficient encoding, there is a (2m + 1, m) specific position quantum error correction code. In this case, the input quantum state | ψ> of m qubits of (Equation 4) is quantum-encoded by 2m + 1 qubit coding into the quantum state | ψ _c > encoded as shown in (Equation 7). Here, | S _j > is an orthogonal state represented by (Expression 8), and j represents an m-digit binary number expression.

  In this (2m + 1, m) specific position quantum error correction code, 2m + 1 qubits are required to represent the input quantum state | Ψ> of m qubits.

In this case, 1 to m qubits of the encoded quantum state | Ψ _c > are stored in the information processing quantum memory 102, and the remaining m + 1 to 2m + 1 qubits are stored in the storage quantum memory 103.

  The quantum information processing unit 104 performs processing on the quantum state stored in the information processing quantum memory 102. Examples of the processing here include processing of a quantum computer described in Non-Patent Document 3 and the like, reading and writing of quantum states, and communication of quantum states.

  The quantum state destruction prevention processing unit 105 performs processing so that the qubits stored in the storage quantum memory 103 are destroyed due to external oscillation and no error occurs. As an example of such a process, there is a quantum state destruction prevention process using an optical echo phenomenon by an optical pulse disclosed in Patent Document 1.

  In the quantum restoration unit 106, when an error occurs due to the qubit of the information processing quantum memory 102 being broken by the processing of the quantum information processing unit 104, the broken qubit is stored in the storage quantum memory 103. Quantum restoration processing is performed using both qubits to restore the input quantum state | Ψ>.

The restoration of the quantum state is performed on the quantum state | Ψ ′ _c > stored separately in the information processing quantum memory 102 and the storage quantum memory 103. Of these quantum states, an error has occurred only in the qubits stored in the information processing quantum memory 102. If it is known that an error has occurred at such a specific position, it is described in Non-Patent Document 2, which has a higher capability than normal quantum error correction in the case where it is not known where the error occurs. Such specific position quantum error correction can be used. An example of this specific position quantum error correction processing is shown below.

  First, consider a decoding method in the case of (3m, m) encoding as shown in (Equation 5). The Stabilizer S of this code has 3m−m = 2m elements and can be expressed as (Equation 9).

Here, the element g _{k of} Stabilizer S is given by (Equation 10).

  In such a case, the following decoding method can be considered.

(1) i = 1, 2,. . . , M, if the measurement result of g _i is −1, the phase of the i-th qubit is inverted.

(2) i = 1, 2,. . . , M, if the measurement result of g _{m + i} is −1, the i-th qubit is bit-inverted.

  Furthermore, an efficient decoding method as described below, in which decoding is performed using only some qubits, can be considered.

(1) An observable represented by Z _{m + 1 to} Z _2m (corresponding to a spin in the Z-axis direction in a spin system) is measured.

(2) i = 1, 2,. . . , M, if the measurement result of the observable Z _{m + i} is −1, the phase of the 2m + i qubit is inverted.

  (3) The 2m + 1 to 3m qubits are equal to the input quantum state | Ψ>.

  Next, a decoding method when (2m + 1, m) encoding is performed as shown in (Expression 7) will be described. Stabilizer S of this encoding has (2m + 1) −m = m + 1 elements and can be expressed as (Equation 11).

Here, the element g _{k of} Stabilizer S is given by (Equation 12).

  This code is characterized in that the state does not change even if a phase inversion error occurs in any even number of qubits of the 1 to m qubits. In such a case, the following decoding method can be considered.

(1) If the measurement result of g ₀ is −1, the phase of any of the 1st to m-th qubits is inverted.

(2) i = 1, 2,. . . , M, if the measurement result of g _i is −1, the i-th qubit is bit-inverted.

  Furthermore, if an error does not occur in all qubits of a codeword but an error occurs in 1 to m qubits, but no error occurs in other bits, an efficient decoding method as described below can be used. Conceivable.

(1) The observable Z _{m + 1} is measured.

(2) If the measurement result of Z _{m + 1} is 1, the phase of the m + 2 qubit is inverted.

  (3) The (m + 2 to 2m + 1) th qubit is equal to the input quantum state | Ψ>.

  Thus, the quantum restoration unit 106 can restore the original input quantum state | ψ> from the broken qubit of the information processing quantum memory 102 and the qubit of the storage quantum memory 103. Therefore, using the original input quantum state | Ψ>, the processing of the quantum information processing unit 104 can be performed again from the beginning.

  Note that the quantum information processing unit 104 does not process all the steps at once, but at the stage where a certain number of steps are completed, the quantum state of the result is quantum encoded again by the quantum encoding unit 101, It is also possible to perform the process automatically. In this case, even when the quantum state is broken by the quantum information processing, it is possible to resume from an intermediate stage instead of returning to the beginning.

  As processing in the quantum information processing unit 104, in addition to quantum computation in the quantum computer, as quantum memory, processing for simply reading and writing qubits stored in the information processing quantum memory 102, and storage in the information processing quantum memory 102 There are processes such as quantum communication that transmits the transmitted qubits over a communication path. In a quantum memory, for example, a case where a quantum bit is broken due to unauthorized access or a case where a quantum bit is broken due to a transmission error or wiretapping in quantum communication can be considered. Even in such a case, high-capacity quantum restoration is possible by using together the qubits that prevent the storage quantum memory 103 from being destroyed.

  The quantum restoration device of the present invention can restore the quantum state even when an error occurs in a large number of qubits due to quantum information processing, quantum information transmission, and the like. This is useful as a backup for quantum communication.

  Further, the present invention can be applied to a quantum memory, a quantum credit card, etc. when storing quantum information.

The figure which shows the structure of the quantum decompression | restoration apparatus by the 1st Embodiment of this invention The figure which shows the structure of the conventional quantum restoration device

Explanation of symbols

DESCRIPTION OF SYMBOLS 101 Quantum encoding part 102 Information processing quantum memory 103 Storage quantum memory 104 Quantum information processing part 105 Quantum state destruction prevention processing part 106 Quantum reconstruction part 201 Entanglement generation part 202 Information processing quantum memory 203 Quantum information processing part 204 Quantum Error correction section

Claims (8)

A quantum coding unit that performs quantum coding on the input quantum state;
An information processing quantum memory unit for storing a part of the quantum-encoded quantum state;
A storage quantum memory for storing the rest of the quantum-encoded quantum state to prevent destruction of the quantum state;
A quantum state restoration device comprising a quantum restoration unit that restores a quantum state from the destroyed quantum state and the quantum state stored in the storage quantum memory unit when the state of the information processing quantum memory unit is destroyed. The quantum state restoration device according to claim 1, wherein the quantum encoding unit generates entanglement of quantum states. The quantum restoration unit restores the quantum state by performing at least one of phase inversion and bit inversion , which are unitary transformations, on the destroyed quantum state and the quantum state stored in the storage quantum memory unit, respectively. The quantum state restoration device according to claim 1. The quantum state restoration apparatus according to claim 1, wherein the quantum state of the information processing quantum memory unit is transmitted. The quantum state restoration device according to claim 4, wherein the quantum state of the information processing quantum memory unit is transmitted, and the quantum restoration unit performs quantum restoration when a transmission error occurs. The quantum state restoration device according to claim 1, wherein the quantum state of the information processing quantum memory unit is read and written as a quantum memory. 7. The quantum state restoration device according to claim 6, wherein the quantum state of the information processing quantum memory unit is read and written as a quantum memory, and the quantum restoration unit performs quantum restoration when there is an unauthorized access. The quantum state restoration device according to claim 1, wherein a result of information processing on the quantum state of the information processing memory unit is quantum-encoded by the quantum encoding unit.

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