JP4464671B2 - Quantum state generation device, quantum teleportation device, and control NOT operation device - Google Patents

Description

  The present invention relates to a quantum state generation device that generates a quantum state, a quantum teleportation device that performs quantum teleportation, and a control NOT operation device that performs a control NOT operation. The present invention relates to a teleportation device and a control NOT arithmetic device.

In recent years, it has been theoretically proposed that new information processing that has not been possible before can be performed by using quantum mechanics for information processing (quantum information processing). The basic unit of this quantum information processing is a qubit, and the basic operation is a unitary transformation for one qubit and a control NOT operation (C-NOT). Here, the control NOT operation is a 2-input 2-output operation. When the control bit is | 0>, the target bit is left as it is. When the control bit is | 1>, the target bit is | 0>. → | 1>, | 1> → | 0> and the NOT calculation. The control bit is output in the same state as the input. And it is known that arbitrary calculation is possible by combining these.
However, it is very difficult to actually realize this basic operation C-NOT directly in a physical system.
On the other hand, Gottesman, Chuang (see, for example, Non-Patent Document 1) indirectly performs a control NOT operation (C-NOT), which is a basic operation of quantum computation, in two stages of quantum state generation and quantum teleportation. Shown that it is possible to do. Hereinafter, this is called a GC system.

FIG. 12 is a diagram showing a C-NOT quantum circuit according to the GC method.
As shown in FIG. 12, this quantum circuit includes a quantum state generation unit 610 that generates a quantum state, bell measurement units 621 and 622 that perform bell measurement, and unitary conversion units 631 to 633 and 641 to 643 that perform unitary conversion. ing. In this figure, the alternate long and short dash line indicates a channel for classical information, B indicates bell measurement, and X and Z indicate unitary transformations of σ _x and σ _z , respectively. Further, | ψ> and | φ> indicate one qubit states respectively corresponding to the target bit and the control bit, and | χ> is a four qubit state | χ> = of the resource generated by the quantum state generation unit 610 (1/2) [(| 0> ₁ | 0> ₂ + | 1> ₁ | 1> ₂ ) | 0> ₃ | 0> ₄ + (| 0> ₁ | 1> ₂ + | 1> ₁ | 0 > ₂ ) | 1> ₃ | 1> ₄ ]. Here, the subscripts 1, 2, 3, and 4 represent the first, second, fourth, and third qubits from the top of | χ> in FIG.

Of the four qubit states | χ>, the first and fourth (FIG. 12) two qubit states from the top are input to the bell measurement units 621 and 622, respectively, which are separately input to the bell measurement units 621 and 622. Bell measurement is performed together with each input 1-qubit state | ψ>, | φ>. The classical information of the measurement result in the bell measurement unit 621 is sent to the unitary conversion units 632, 633, and 643, and the classical information of the measurement result in the bell measurement unit 622 is sent to the unitary conversion units 631, 641, and 642.
On the other hand, the second and third (FIG. 12) two qubit states from the top among the four qubit states | χ> generated by the quantum state generation unit 610 are unitary conversion units 631 to 633 and unitary conversion unit 641, respectively. The unitary conversion units 631 to 633 and the unitary conversion units 641 to 643 are unitary according to the observation results sent from the bell measurement units 621 and 622, respectively, for the input two qubit states. Convert and output. This output 2-qubit state corresponds to the control NOT operation result.

At present, it is considered to use light as one method for realizing quantum information processing, and several methods for performing quantum computation using an optical element are also known for the above-described GC method. For example, the Koashi et al. Method (for example, see Non-Patent Document 2), the Knill et al. Method (for example, Non-Patent Document 3), and the Yoran, Reznik method (for example, Non-Patent Document 4). It hits. The Yoran and Reznik system proposes to use deterministic quantum teleportation proposed by Popescu (see, for example, Non-Patent Document 5). The implementation experiment of this deterministic quantum teleportation is performed by Boschi et al. (For example, see Non-Patent Document 6).
D. Gottesman and IL Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations.Nature, Vol. 402, pp. 390-393, Nov 1999 M. Koashi, T. Yamamoto, and N. Imoto.Probabilistic manipulation of entangled photons.Phys. Rev. A, Vol. 63, p. 030301, 2001. E. Knill, R. Laflamme, and GJ Milburn.A scheme for efficient quantum computation with linear optics.Nature, Vol. 409, pp. 46-52, Jan 2001. N. Yoran and B. Reznik. Deterministic linear optics quantum computation with single photon qubits.Phys. Rev. Lett., Vol. 91, p.037903, 2003. S. Popescu. An optical method for teleportation.quant-ph / 9501020, 1995. D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu. Experimental realization of teleporting an unknown pure quantum state via dual classical and einstein-podolsky-rosen channels. 80, p.1121, 1998.

However, in the past, it has been difficult at the current technical level to realize the GC system as a practically mountable one.
That is, conventionally, a specific method for actually generating the 4-qubit state | χ> used for this GC quantum computation has not been known.
The above-mentioned Koashi et al. Method requires generation of one photon pair and two single photons. Conventionally, when photons are actually generated, “when one photon pair and two single photons are generated”. And “when two photon pairs are generated” and “when four single photons are generated” cannot be distinguished. Furthermore, this method requires 6 photons, but it is quite difficult to handle 6 photons with the current technology.
Furthermore, the Knill et al. Method required a detector capable of distinguishing the number of photons. This is a difficult technique at present.

Also, definitive teleportation proposed by Popescu was experimented by Boschi et al., But a more efficient method is conceivable.
Furthermore, Yoran and Reznik proposed the theory of the GC method, but did not propose a specific implementation method.
The present invention has been made in view of these points, and an object of the present invention is to provide a quantum state generation device that realizes the GC method within the current technical scope.
Another object of the present invention is to provide a quantum teleportation device that efficiently implements the GC scheme within the current technical scope.
Furthermore, the other object of this invention is to provide the control NOT arithmetic unit which implement | achieves GC system within the present technical range.

  In order to solve the above-described problem, in the first aspect of the present invention, a photon emitting section that emits the first to fourth photons, a position where the second photon and the third photon enter, and the second photon The first polarization direction wave function and the third photon second polarization direction wave function are guided to the first path, the second photon second polarization direction wave function and the third photon. A first polarization beam splitter for guiding the first polarization direction wave function to the second path, and a second photon wave function guided from the first polarization beam splitter to the first path, and a third A first polarization rotation element that rotates the polarization direction of the wave function of the incident photon, a wave function of the photon emitted from the first polarization rotation element, and 4 is provided at the position where the photon is incident, and is emitted from the first polarization rotation element. The wave function in the first polarization direction and the wave function in the second polarization direction of the fourth photon are guided to the third path, and the wave in the second polarization direction of the photon emitted from the first polarization rotation element. A second polarization beam splitter that guides the function and the wave function of the first photon in the first polarization direction to the fourth path, the position where the first photon is incident, and the wave function of the incident photon The second polarization rotation element that rotates the polarization direction and the first polarization beam splitter are provided at positions where the wave function of the photon guided to the second path is incident, and the polarization direction of the wave function of the incident photon is changed. There is provided a quantum state generation device having a third polarization rotation element to be rotated.

Here, the wave function of the emitted light of the second polarization rotating element, the wave function of the emitted light of the third polarization rotating element, the wave function of the photon guided to the third path in the second polarizing beam splitter, and By performing post-selection of the wave function of the photon guided to the fourth path in the second polarization beam splitter, it is possible to actually generate the 4-qubit state | χ> used for the GC quantum calculation.
Also, by determining whether or not this post-selection is successful, whether one photon pair and two single photons are generated, two photon pairs are generated, It is possible to distinguish whether four have occurred. Thereby, it can be determined whether or not the generated four-qubit state | χ> is correct.

  In order to solve the above-described problem, in the second aspect of the present invention, the first photon is incident on the photon emitting section that emits the first and second photons in an entangled state that the polarization directions are the same. A first polarization direction wave function of the first photon is guided to the first path, and a second polarization direction wave function of the first photon is guided to the second path. 1 polarization beam splitter and the first polarization beam splitter are provided at positions where the wave function of the first photon guided to the second path is incident, and the polarization direction of the wave function of the first photon is rotated. The first polarization rotating element that emits to the second path and the wave function of the first photon guided to the first path in the first polarization beam splitter are converted into an input 1-qubit state. To the first path and the second from the first polarization rotation element. A first polarization phase control element that converts the wave function of the first photon emitted to the path into a 1-qubit state and emits it to the second path, and a second path from the first polarization phase control element The second polarization rotation element that rotates the polarization direction of the wave function of the first photon emitted to the second path and emits the second path to the second path, and the first polarization phase control element that emits the first polarization to the first path. The wave function of the first photon and the wave function of the first photon emitted from the second polarization rotation element to the second path are provided at a position where the wave function of the first photon is incident. And a beam splitter for separating the first photon and a wave function of the first photon guided to the third path in the beam splitter, and a first polarization of the first photon. A wave function of direction to the fifth path and the second polarization of the first photon A second polarization beam splitter that guides a directional wave function to the sixth path, and a second polarization beam splitter provided at a position where the wave function of the first photon guided to the fifth path in the second polarization beam splitter can be detected. 1 detector, a second detector provided at a position where the wave function of the first photon guided to the sixth path in the second polarizing beam splitter can be detected, and a fourth path in the beam splitter. The wave function of the first photon thus guided is provided at the incident position, the wave function of the first polarization direction of the first photon is guided to the seventh path, and the second polarization of the first photon is A third polarization beam splitter that guides the directional wave function to the eighth path, and a third polarization beam splitter provided at a position where the wave function of the first photon guided to the seventh path in the third polarization beam splitter can be detected. 3 detectors and a third bias In the optical beam splitter, a fourth detector provided at a position where the wave function of the first photon guided to the eighth path can be detected, and detection in the first to fourth detectors for the second photon A quantum teleportation device having a second polarization phase control element that performs unitary conversion according to the result is provided.

Here, in the present invention, only the path of the first photon is separated in the first polarization beam splitter, and the path of the second photon is not separated. On the other hand, in the apparatus experimented by Boschi et al., Two photon paths are separated into two paths. Therefore, the quantum teleportation device of the present invention has fewer paths and better circuit efficiency than the device of Boschi et al.
Furthermore, in order to solve the above problems, in the third aspect of the present invention, a control NOT arithmetic unit is configured using two quantum teleportation apparatuses of the second aspect of the present invention.

This makes it possible to actually implement the GC method. Further, in the present invention, since it is not necessary to distinguish the number of photons, it can be sufficiently realized even at the current technical level.
The control NOT arithmetic device of the present invention preferably has the quantum state generation device of the first present invention. As a result, it is possible to actually generate the 4-qubit state | χ> that is a resource for this quantum calculation.

As described above, the quantum state generation apparatus of the present invention can actually generate the four qubit states | χ> used for the quantum calculation, and whether or not the generated four qubit states | χ> are correct. Can be judged.
Further, in the quantum teleportation device of the present invention, a highly efficient circuit is configured with few paths.
Furthermore, the control NOT arithmetic unit according to the present invention can be realized as a GC system that can be actually implemented at the current technical level.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
In this embodiment, a control NOT gate (C-NOT), which is a basic operation of quantum computation, is mounted using optics. That is, in this embodiment, a quantum calculation method (GC method) divided into a quantum state generation unit and a quantum teleportation unit by Gottesman and Chuang is specifically implemented by an optical element.
In the following description, photon polarizations | H> and | V> (horizontal polarization and vertical polarization) are used as calculation bases | 0> and | 1>. Here, the horizontal direction corresponds to the “first polarization direction”, and the vertical direction corresponds to the “second polarization direction”.

[Quantum state generator (corresponding to claims 1 to 4)]
First, a quantum state generation device (quantum state generation unit) in this embodiment will be described.
FIG. 1 is a block diagram illustrating the configuration of a quantum state generation device 1 according to this embodiment.
<Configuration>
First, the configuration of the quantum state generation device 1 will be described.
As illustrated in FIG. 1, the quantum state generation device 1 includes a photon emitting unit 11 to 13, a polarizing beam splitter 21 and 22 (corresponding to “first and second polarizing beam splitters”), and wave plates 31 to 34 ( The detectors 41 to 44 (corresponding to “first to fourth detectors”) and the controller 50 are included.

<Photon emission part>
FIG. 2 is a block diagram illustrating the configuration of the photon emission unit 11 in this embodiment.
In this example, the photon emission unit 11 has a parametric down conversion (PDC) (for example, “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.” “PG Kwiat, E. Waks, AG White, I. Appelbaum, and PH Eberhard,“ Ultrabright source of polarization-entangled photons, Phys. Rev. A, 60: R773-R776, 1999. etc.) and two photons 61 and 62 ("first" in an entanglement state) in which the polarization directions are the same. , Second photon ”).
As illustrated in FIG. 2, the photon emission unit 11 of this example includes a laser emission unit 11a, a nonlinear crystal 11b, and an absorption unit 11c.

Here, the laser emitting unit 11a is a laser device that emits the pump light 81, and is, for example, an argon ion laser device that emits an argon ion laser (0.351 μm single frequency CW laser) or the like. The nonlinear crystal 11b is, for example, KDP, ADP, RDA, CDA, LiNbO ₃ , LiIO ₃ , Ba ₂ NaNb ₅ O ₁₅ , Ag ₃ AsS ₃ , AgGaS ₂ , KTP, BBO, LBO, etc., and the absorption part 11c. For example, the pump light 81 that absorbs the frequency well and does not easily scatter the light having the frequency used as the single photon 61 is used.
The pump light 81 emitted from the laser emitting unit 11a enters the nonlinear crystal 11b, and is converted into two photons different from the frequency of the incident light in the nonlinear crystal 11b with a probability inherent to the crystal. . This process is called a parametric fluorescence process, and the two photons are called parametric fluorescence. One parametric fluorescence is emitted as photons 61, and the other parametric fluorescence is emitted as photons 62.

As described above, the photons 61 and 62 emitted in this way are in an intertwined state in which the polarization directions are the same, and the quantum state is
(1 / √2) (| HH> + | VV>) (1)
It has become. Here, “H” and “V” on the left side of | HH> and | VV> in this expression correspond to the polarization direction of the photon 61, and “H” and “V” on the right side are the polarization direction of the photon 62. Corresponding to Further, | HH> + | VV> indicates that the quantum state of | HH> and the quantum state of | VV> are superposed. Further, the pump light 81 that has not been split in the nonlinear crystal 11b is absorbed by the absorber 11c.
FIG. 3 is a block diagram illustrating the configuration of the photon emission unit 12 in this embodiment.
The photon emitting unit 12 of this example emits a single photon 63 (corresponding to “third photon”) using parametric down conversion.

As illustrated in FIG. 2, the photon emission unit 12 of this example includes a laser emission unit 12a, a nonlinear crystal 12b, an absorption unit 12c, and a detection unit 12d. Here, the laser emission part 12a, the nonlinear crystal 12b, and the absorption part 12c are configured in the same manner as the laser emission part 11a, the nonlinear crystal 11b, and the absorption part 11c, for example. The detection unit 12d is a detector that can be used in a photon counting region such as a photomultiplier tube, a streak camera, a photodiode, or an avalanche photodiode.
The pump light 82 emitted from the laser emitting unit 12a is incident on the nonlinear crystal 12b and is converted into two parametric fluorescence therein. One parametric fluorescence is emitted as a photon 63, and the other parametric fluorescence is measured as a reference photon 82a in the detection unit 12d. In addition, by setting it as the structure which measures the reference photon 82a by the detection part 11d in this way, it can know when the single photon 63 was inject | emitted. Further, the pump light 82 that has not been split in the nonlinear crystal 12b is absorbed by the absorber 12c.
Here, the quantum state of the photon 63 emitted as described above is
(1 / √2) (| H> + | V>) (2)
It has become.

Note that the photon emission unit 13 has a quantum state of (1 / √2) (| H> + | V>) (3), for example, by the same configuration as the photon emission unit 12.
Single photons 64 (corresponding to “fourth photons”).
Moreover, it is good also as a structure which comprises the photon emission parts 12 and 13 integrally, and radiate | emits the single photon 63 and 64 from this integral photon emission part. For example, the configuration shown in FIG. 2 may be configured to emit single photons 63 and 64. FIG. 4 is a block diagram illustrating the configuration of the photon emission unit 92 configured in this way.

As shown in FIG. 4, the photon emission unit 92 includes a laser emission unit 12a, a nonlinear crystal 12b, a mirror 92c, and detection units 12d and 12e.
Pump light 82 emitted from the laser emitting portion 12a is incident on the nonlinear crystal 13b. The pump light 82 is separated into two parametric fluorescences in the nonlinear crystal 12b. One parametric fluorescence is emitted as a single photon 63, and the other parametric fluorescence is incident on the detection unit 12d as a reference photon 82a. . The pump light 82 that has not been split in the nonlinear crystal 12b is reflected by the mirror 92c and is incident on the nonlinear crystal 12b again. The reflected light 82b is separated into two parametric fluorescences in the nonlinear crystal 12b. One parametric fluorescence is emitted as a single photon 64, and the other parametric fluorescence is incident on the detection unit 12e as a reference photon 82c. .
Further, the photon emitting units 11, 12, and 13 may be configured integrally, and a pair of photons 61 and 62 and a single photon 63 and 64 that are intertwined from the integrated photon emitting unit may be emitted. .

FIG. 5 is a block diagram illustrating the configuration of the photon emission section 93 configured in this way.
The difference between the configuration of FIG. 5 and the configuration of FIG. 4 is that the detectors 12d and 12e are not provided, and the phase plates 93a and 93b and the wave plates 93c and 93d are provided. In this configuration, the pump light 82 emitted from the laser emitting portion 12a and incident on the nonlinear crystal 11b is separated into two parametric fluorescence in the nonlinear crystal 12b, and one parametric fluorescence is emitted as a photon 61, and the other parametric fluorescence. The fluorescence is emitted as photons 62. Here, the photons 61 and 62 are in an entangled state. The reflected light 82b reflected by the mirror 92c is separated into two parametric fluorescence in the nonlinear crystal 12b. One parametric fluorescence is emitted as a photon 63, and the other parametric fluorescence is emitted as a photon 64. When this configuration is adopted, means for removing the entangled state of the photons 63 and 64 emitted from the nonlinear crystal 12b (the state in which the quantum states of the photons 63 and 64 are represented by tensor products of the respective quantum states). Must be provided. In this example, the phase plates 93a and 93b are used to pass only the | HH> of the superposition of (| HH> + | VV>), the polarization is rotated by the wave plates 93c and 93d, and a single photon (1 / √2) The entanglement state of the photons 63 and 64 is removed by means for generating (| H> + | V>). This success probability is ½. Further, for example, a means for providing another different nonlinear crystal 94b that generates single photons 63 and 64, such as the photon emitting section 94 of FIG. 6, may be used.

<Polarized beam splitter>
The polarization beam splitters 21 and 22 transmit the photon straight when the polarization direction of the incident photon is 0 ° (H: horizontal polarization), and the polarization direction of the photon is 90 ° (V: vertical polarization). In this case, the optical element reflects the photon at 90 °.
<Wave plate>
The wave plates 31 to 33 are, for example, quarter wave plates that rotate the polarization direction of the wave function of incident photons by 45 °. Instead of the wave plate, an electro-optic effect modulator (for example, a Faraday rotator, a modulator using the electro-optic effect of a crystal such as LiNbO ₃ ), an acoustic element, or a liquid crystal element may be used.

<Detector>
The detection units 41 to 44 are detectors that can be used in a photon counting region such as a photomultiplier tube, a streak camera, a photodiode, or an avalanche photodiode, and supply the detection result to the control unit 50. In addition, when using this quantum state production | generation apparatus 1 as a quantum state production | generation part of the above-mentioned GC system, this detection parts 41-44 are the detection part which detects the bell measurement result in a quantum teleportation part, and finally a calculation result This corresponds to a detection unit that observes and detects.
<Control unit>
The control unit 50 is configured using, for example, a known CPU (Central processing Unit) or the like, and uses the detection results supplied from the detection units 41 to 44 to determine whether the post-selection has succeeded, that is, the quantum state correctly. It is determined whether or not is generated.

<Arrangement>
As illustrated in FIG. 1, the polarizing beam splitter 21 of this example is located at a position where the photon 62 emitted from the photon emitting unit 11 to the path h and the photon 63 emitted from the photon emitting unit 12 to the path e are incident. A wave function of the horizontally polarized light of the incident photon 62 and a wave function of the vertically polarized light of the photon 63 are guided to a path j (corresponding to the “first path”), and the wave function of the vertically polarized light of the photon 62 and the photon 63 are guided. Are arranged so as to guide a wave function of the horizontally polarized light to a path k (corresponding to a “second path”).
The wave plate 31 is provided at a position where the wave function of the photon 62 guided from the polarization beam splitter 21 to the path j and the wave function of the photon 63 are incident, so that the wave function of the emitted light is emitted to the path j ′. Placed in.

The polarization beam splitter 22 is provided at a position where the wave function of photons emitted from the wave plate 31 to the path j ′ and the photons 64 emitted from the photon emission unit 13 to the path f are incident and emitted from the wave plate 31. The wave function of the horizontally polarized light of the photon and the wave function of the vertically polarized light of the photon 64 are guided to the path n (corresponding to the “third path”), and the wave function of the vertically polarized light of the photon emitted from the wave plate 31 and The wave function of the horizontally polarized light of the photon 64 is arranged to guide the path m (corresponding to the “fourth path”).
The wave plate 32 is provided at a position where the photon 61 emitted from the photon emission unit 11 to the path g is incident, and is disposed so as to emit the wave function of the emitted light to the path g ′. The wave plate 33 is provided at a position where the photon guided to the path k in the polarization beam splitter 21 is incident, and is disposed so as to emit the wave function of the emitted light to the path k ′.

Further, the detector 41 is provided at a position where the wave function of the photon 61 emitted from the wave plate 32 to the path g ′ can be detected. Further, the detector 42 is at a position where the wave function of the photon emitted from the wave plate 33 to the path k ′ can be detected (position where the wave function of the photon guided to the path k in the polarization beam splitter 21 can be detected). Provided. The detection unit 43 is provided at a position where the wave function of the photon guided to the path n in the polarization beam splitter 22 can be detected, and the detection unit 44 is the wave function of the photon guided to the path m in the polarization beam splitter 22. Is provided at a position where it can be detected.
In FIG. 1, the optical elements are arranged linearly. However, when the optical elements are connected by an optical fiber or the like, the optical elements do not need to be arranged linearly. Moreover, the control part 50 is electrically connected with each detection part 41-44 (not shown), and becomes a structure into which the detection signal output from each detection part 41-44 is input.

<Operation>
Next, the operation of the quantum state generation device 1 in this embodiment will be described.
The quantum state of the resource in the GC scheme for performing C-NOT is
| Χ> = (1/2) [(| H> | H> + | V> | V>) | H> | H> + (| H> | V> + | V> | H>) | V> | V>] (4)
It is. The quantum state generation device 1 generates this quantum state from the emitted four photons 61 to 64. Hereinafter, this generation method will be described.
First, the photon emitting unit 11 emits photons 61 and 62 whose quantum states are represented by the above-described equation (1) to the paths g and h, respectively. 2) Single photons 63 and 64 represented by (3) are emitted to paths e and f, respectively.

The photons 62 and 63 are incident on the polarization beam splitter 21. Thereby, the horizontally polarized wave function of the photon 62 is emitted to the path j, the vertically polarized wave function is emitted to the path k, the horizontally polarized wave function of the photon 63 is emitted to the path k, and the vertically polarized wave function is output. Is emitted to the path j. At this time, the quantum states of the photons 61 to 63 are
(1/2) (| HHH> + | VVV> + | HHV> + | VVH>) (5)
It becomes.
Here, “H” or “V” at the left end of | HHH> or the like indicates a quantum state corresponding to the photon 61, and “H” or “V” in the middle indicates a quantum state corresponding to the photon 62, “H” and “V” on the right end indicate a quantum state corresponding to the photon 63. Further, | HHH> indicates that the wave function of the photons 61 to 63 is horizontally polarized light, and in the polarization beam splitter 21, the wave function of the photon 62 is transmitted through the path j, and the wave function of the photon 63 is transmitted through the path k. It shows the state. Similarly, in | VVV>, the wave function of the photons 61 to 63 is vertical polarization, and in the polarization beam splitter 21, the wave function of the photon 62 reflects to the path k, and the wave function of the photon 63 reflects to the path j. It shows the state. Also, | HHV> indicates that the wave function of the photons 61 and 62 is horizontally polarized light, the wave function of the photon 63 is vertically polarized light, and the wave function of the photon 62 is transmitted to the path j in the polarization beam splitter 21, and the photon 63 shows a state in which 63 wave functions are reflected to the path j. In addition, | VVH> indicates that the wave function of the photons 61 and 62 is vertically polarized light, the wave function of the photon 63 is horizontally polarized light, and the wave function of the photon 62 is reflected to the path k in the polarization beam splitter 21. A state where 63 wave functions are transmitted through the path k is shown. The quantum states of the photons 61 to 63 here are in a superposed state.

From this superposed state, if the state in which the wave functions of the photons 61 to 63 are emitted one by one in the three paths g, k, j is selected and left,
(1/2) (| HHH> + | VVV>) (6)
It becomes the quantum state. This is because when the photons are detected in all the detection units 41 to 44 later (when post-selection is successful), the quantum state represented by the above equation (5) contracts to the quantum state represented by the equation (6). This is true. That is, selecting and leaving the state in which the wave functions of the photons 61 to 63 are emitted one by one in the three paths g, k, and j means that only the quantum state when the post-selection is succeeded later is the correct state. It is to use as.

Next, the wave function of the photon 61 emitted to the path g is incident on the wave plate 32, where the polarization direction is rotated by 45 ° and then emitted to the path g ′. The wave function of the photons emitted to the path k is incident on the wave plate 33, where the polarization direction is rotated by 45 ° and then emitted to the path k ′. Further, the wave function of the photons emitted to the path j is incident on the wave plate 31, where the polarization direction is rotated by 45 ° and then emitted to the path j ′. Here, the conversion performed by the wave plates 31 to 33 is
| H> → (1 / √2) (| H> − | V>)
| V> → (1 / √2) (| H> + | V>)
It becomes.
Therefore, the quantum states (6) of the photons 61 to 63 that have traveled one by one in the paths g, k, and j are caused by these wave plates 31 to 33, respectively.
(1/2) (| HHH> + | VVV>)
→ (1 / 2√2) (| HHH> + | VVH> + | HVV> + | VHV>) (7)
Is converted.

Further, the wave function of the photons emitted from the wave plate 31 to the path j ′ and the photons 64 emitted from the photon emission section 64 to the path f are incident on the polarization beam splitter 22. Accordingly, the wave function of the horizontally polarized light of the photon emitted from the wave plate 31 to the path j ′ is emitted to the path n, the wave function of the vertically polarized light is emitted to the path m, and the wave function of the horizontally polarized light of the photon 64 is the path. The wave function of vertically polarized light is emitted to the path n. At this time, among the quantum states of the photons 61 to 64 that are superposed, the wave functions of the photons 61 to 63 are emitted one by one in the four paths g ′, k ′, m, and n. If you leave it selected,
(1/4) [(| H> | H> + | V> | V>) | H> | H> + (| H> | V> + | V> | H>) | V> | V>] … (8)
It becomes. Here, selecting and leaving the state where the wave functions of the photons 61 to 64 are emitted one by one in the four paths g ′, k ′, m and n means that when the following post-selection is successful, Only the quantum state is used as the correct state.

Then, the detection units 41 to 44 each receive the incidence of a photon, and send information to the control unit 50 as to whether or not a photon has entered each. The control unit 50 determines whether or not the post selection is successful based on the sent information. That is, the control unit 50 determines that the post-selection is successful when the photons are detected in all the detection units 41 to 44. Here, when the post-selection is successful, the quantum state of the wave function of the photons 61 to 64 that has traveled along the paths g ′, k ′, m, n before the detection is performed is set as the quantum state of the target resource. If the post-selection is not successful, the quantum state is discarded. The success probability of post-selection is obtained as the sum of the squares of the coefficients in equation (8) and is 1/4.
Then, by normalizing the equation (8), the quantum state | χ> of the target resource represented by the above equation (4) is obtained.

The post-selection is successful when one photon pair is emitted from the photon emission unit 11 and one single photon is emitted from the photon emission units 12 and 13 one by one. Therefore, the probability that “one photon pair and two single photons are generated”, the probability that “two photon pairs are generated at the same time”, and the probability that “four single photons are generated” are generated from the photon emission units 11 to 13. Even in the same case, by judging whether or not this post-selection is successful, only the state where “one photon pair and two single photons are generated” necessary for generating the target quantum state | χ> is obtained. You can choose. That is, the control unit 50 determines that the quantum state has been correctly generated when photons are detected in all the detection units 41 to 44.
When this quantum state generation device 1 is used as a GC quantum state generation unit, these photons are detected and post-selection is performed during the quantum teleportation process described later.

[Quantum teleportation device (corresponding to claims 5 and 6)]
Next, the quantum teleportation device (quantum teleportation unit) in this embodiment will be described.
FIG. 7 is a block diagram illustrating the configuration of the quantum teleportation apparatus 100 in this embodiment.
<Configuration>
First, the configuration of the quantum teleportation device 100 will be described.
As illustrated in FIG. 7, the quantum teleportation apparatus 100 includes a bell measuring unit 101, a photon emitting unit 102, a polarizing beam splitter 111 (corresponding to a “first polarizing beam splitter”), a mirror 121, and a wave plate 131 (“ Equivalent to "first polarization rotation element"), polarization phase control element 140 (corresponding to "first polarization phase control element"), control unit 170, polarization phase control elements 181, 182 ("second polarization phase control element") ”). The bell measuring unit 101 includes a wave plate 132 (corresponding to a “second polarization rotation element”), mirrors 122 to 125, a beam splitter 150, and polarization beam splitters 112 and 113 (“second and third polarization beam splitters”). And detectors 161 to 164 (corresponding to “first to fourth detectors”).

<Photon emission part>
For example, the photon emitting unit 102 is configured in the same manner as the photon emitting unit 11 described above, and includes photons 103 and 104 (corresponding to “first and second photons”) in an entangled state that the polarization directions are the same. Exit.
<Polarized beam splitter>
The polarization beam splitters 111 to 113 are configured, for example, in the same manner as the polarization beam splitters 21 and 22 described above. When the wave function of the incident photon is horizontal polarization, the polarization beam splitter 111 to 113 transmits the photon straight and is vertical polarization. The photon is reflected at 90 °.

<Wave plate>
The wave plates 131 and 132 are, for example, half-wave plates that rotate the polarization direction of the wave function of incident photons by 90 °. Further, instead of the wave plate, an electro-optic effect modulator, an acoustic element, or a liquid crystal element may be used.
<Polarization phase control element>
The polarization phase control elements 140, 181, and 182 are configured using, for example, an electro-optic effect modulator that can control the polarization angle and phase of the passing light by a control voltage, a (1/2, 1/4) wavelength plate, and the like. The In addition, an acoustic element or a liquid crystal element can be used.

で示されるユニタリ変換を施す。 Note that the polarization phase control element 181 responds to an instruction from the control unit 170 with respect to the quantum state of the incident photon.

The unitary transformation indicated by

で示されるユニタリ変換を施す。
＜検出部・制御部＞
検出部１６１〜１６４は、例えば、前述の検出部４１〜４４と同様に構成され、制御部１７０は、例えば、前述の制御部５０と同様に構成される。 Further, the polarization phase control element 182 responds to an instruction from the control unit 170 with respect to the quantum state of the incident photon.

The unitary transformation indicated by
<Detection unit / control unit>
For example, the detection units 161 to 164 are configured in the same manner as the detection units 41 to 44 described above, and the control unit 170 is configured in the same manner as the control unit 50 described above, for example.

<Arrangement>
As illustrated in FIG. 7, the polarization beam splitter 111 is provided at a position where the photon 103 emitted from the photon emitting unit 102 is incident, and the horizontal polarization wave function of the photon 103 (“wave function of the first polarization direction”). ”) To the path a1 (corresponding to“ first path ”), and the vertical polarization wave function of the photon 103 (corresponding to“ second wave direction wave function ”) is converted to the path b1 (“ second path ”). (Corresponding to “route”).
The mirror 121 is provided at a position where the wave function of the photon 103 guided to the path b 1 in the polarization beam splitter 111 is incident, and is disposed so as to reflect the wave function of the photon 103 at 90 °.

The wave plate 131 is provided at a position where the wave function of the photon 103 guided by the polarization beam splitter 111 and reflected by the mirror 121 is incident, and rotates the polarization direction of the wave function of the photon 103 to rotate the path b 2 (“ It corresponds to the “second path”).
The polarization phase control element 140 includes a wave function of the photon 103 guided to the path a1 in the polarization beam splitter 111 and a wave function of the photon 103 guided to the paths b1 and b2 in the polarization beam splitter 111, the mirror 121, and the wave plate 131. Is provided at a position where the light enters. In addition, the polarization phase control element 140 converts the wave function of the photon 103 guided to the path a1 into an input 1-qubit state (α | H> + β | V>), thereby converting the path a2 (“first path”). ), And the wave function of the photon 103 emitted from the wave plate 131 to the path b3 is converted into this one qubit state (α | H> + β | V>) to convert the path b3 (“second” (Corresponding to “the path of”).

The wave plate 132 is provided at a position where the wave function of the photon 103 emitted from the polarization phase control element 140 to the path b3 (corresponding to the “second path”) is incident, and rotates the polarization direction to rotate the path b4 ( (Corresponding to “second path”).
The mirror 122 is provided at a position where the wave function of the photon 103 emitted from the wave plate 132 to the path b4 enters, and the wave function of the emitted photon 103 is reflected to the beam splitter 150 by reflecting the wave function. It arrange | positions so that it may inject.
The mirror 124 is provided at a position where the wave function of the photon 103 emitted from the polarization phase control element 140 to the path a2 is incident, and reflects the wave function to thereby convert the wave function of the emitted photon 103 into a beam splitter. 150 so as to be incident on 150.

The beam splitter 150 receives the wave function of the photon 103 emitted from the polarization phase control element 140 in the path a2 and reflected by the mirror 124, and the wave function of the photon 103 emitted from the wavelength plate 132 to the path b4 and reflected by the mirror 122. The wave function of the incident photon 103 is provided at an incident position and is arranged so as to be separated into a path a′1 (corresponding to “third path”) and a path b′1 (corresponding to “fourth path”). Is done.
The mirror 125 is provided at a position where the wave function of the photon 103 emitted from the beam splitter 150 to the path a ′ 1 is incident, and reflects this wave function to the path a ′ 2 (corresponding to the “third path”). Are arranged as follows. The mirror 123 is provided at a position where the wave function of the lecturer 161 emitted from the beam splitter 150 to the path b′1 is incident, and this wave function is set to the path b′2 (corresponding to the “fourth path”). It arrange | positions so that it may reflect.

The polarization beam splitter 113 is provided at a position where the wave function of the photon 103 guided by the beam splitter 150 to the path a′1 and reflected by the mirror 125 to the path a′2 is incident. The wave function is arranged to guide the path a′3 (corresponding to “fifth path”), and the wave function of the vertically polarized light of the photon 103 is guided to the path a′4 (corresponding to “sixth path”). The
The polarization beam splitter 112 is provided at a position where the wave function of the photon 103 guided by the beam splitter 150 to the path b′1 and reflected by the mirror 123 is incident, and the horizontal polarization wave function of the incident photon 103 is obtained. It is arranged so as to guide the path b′3 (corresponding to “seventh path”) and guide the wave function of the vertically polarized light of the photon 103 to the path b′4 (corresponding to “eighth path”).

The detection unit 161 (corresponding to the “first detection unit”) is provided at a position where the wave function of the photon 103 guided to the path a′3 in the polarization beam splitter 113 can be detected, and the detection unit 162 (“first detection unit”). 2 ”is provided at a position where the wave function of the photon 103 guided to the path a′4 in the polarization beam splitter 113 can be detected.
Furthermore, the detection unit 163 (corresponding to a “third detection unit”) is provided at a position where the wave function of the photon 103 guided to the path b′3 in the polarization beam splitter 112 can be detected. 4 ”is provided at a position where the wave function of the photon 103 guided to the path b′4 in the polarization beam splitter 112 can be detected.

The polarization phase control element 181 is provided at a position where the photon 104 emitted from the photon emission unit 102 enters, and the polarization phase control element 182 receives the wave function of the photon 104 emitted from the polarization phase control element 181. Provided in position.
Further, the control unit 170 is communicably connected to the bell measurement unit 101 through a classical communication path, and is configured to be able to acquire detection results of the detection units 161 to 164. Further, the control unit 170 is communicably connected to the polarization phase control elements 181 and 182 through the classical communication path, and can provide the polarization phase control elements 181 and 182 with classical information indicating unitary conversion according to the detection result. It is like that.

<Operation>
Next, the operation of the quantum teleportation apparatus 100 in this embodiment will be described.
First, as described above, the photons 103 and 104 in an entangled state are emitted from the photon emission unit 102. Here, the quantum states of these photons 103 and 104 are
(1 / √2) (| HH> + | VV>) (11)
It has become. The photon 103 emitted in this manner enters the polarization beam splitter 111, and the photon 104 enters the polarization phase control element 181.
The wave function of the photon 103 incident on the polarization beam splitter 111 is transmitted or reflected by the polarization beam splitter 111 according to the polarization direction (horizontal polarization | H>, vertical polarization | V>). As a result, the wave function of the photon 103 is superposed with the one that travels along the path a1 with the horizontal polarization | H> and the one that travels along the path b1 with the vertical polarization | V>.

The wave function of the vertical polarization | V> of the photon 103 that has traveled along the path b 1 is reflected by the mirror 121 and then enters the wave plate 131. The wave plate 131 rotates the polarization direction of the wave function of the incident vertical polarized light | V> by 90 °, converts the polarized light into horizontal polarized light | H>, and then outputs it to the path b2. Thus, the quantum state of the wave function of the photon 104 emitted from the photon emitting unit 102, the wave function of the photon 103 in the path a1, and the wave function of the photon 103 in the path b2 is the photon in the photon emitting unit 102. The entanglement between the polarization of the photon 103 and the polarization of the photon 104 at the time of emission of 103 and 104 is changed to the entanglement of the path of the photon 103 and the polarization of the photon 104. This quantum state is expressed by an equation:
(1 / √2) (| a> ₁ | H> ₂ + | b> ₁ | V> ₂ ) | H> ₁ (12)
It becomes. Here, | a> indicates a quantum state of a photon existing in any of paths a1 to a2 and a′1 to a′4, and | b> indicates a path b1 to b4 and b′1 to b′4. Shows the quantum state of a photon present in any of the above. | H> indicates the quantum state of a horizontally polarized photon, and | V> indicates the quantum state of a vertically polarized photon. Further, the subscript “1” indicates the quantum state of the photon 103, and “2” indicates the quantum state of the photon 104. As shown in this equation (12), in this state, the polarization of the wave function of the photon 103 is free with respect to the polarization of the wave function of the photon 104. That is, the polarization direction of the wave function of the photon 103 can be taken with respect to the predetermined polarization direction of the wave function of the photon 104.

The wave function of the photon 103 traveling along the path a1 and the wave function of the photon 103 traveling along the path b2 are incident on the polarization phase control element 140. Here, the polarization phase control element 140 is controlled to convert the quantum state of the wave function of the incident photon 103 into one quantum state (α | H> + β | V>) corresponding to the input information to be teleported. ing. Then, the polarization phase control element 140 performs this conversion (input) on the incident photon 103 to generate the following quantum state.
(1 / √2) (| a> ₁ | H> ₂ + | b> ₁ | V> ₂ ) (α | H> + β | V>) ₁
…(13)
If we rewrite equation (13) here,
= (1 / 2√2) (| a> | H> + | b> | V>) ₁ (α | H> + β | V>) ₂
…(14)
+ (1 / 2√2) (| a> | H> − | b> | V>) ₁ (α | H> −β | V>) ₂
… (15)
+ (1 / 2√2) (| a> | V> + | b> | H>) ₁ (β | H> + α | V>) ₂
… (16)
+ (1 / 2√2) (| a> | V> − | b> | H>) ₁ (β | H> −α | V>) ₂
… (17)
It becomes. This indicates that this quantum state is in a superposition state of the quantum states of Expressions (14) to (17).

As described above, the wave function of the photon 103 converted by the polarization phase control element 140 is incident on the bell measurement unit 101, where the four orthogonal bases | e ±> = (1 / √2) (| a> | H> ± | b> | V>) ₁
| F ±> = (1 / √2) (| a> | V> ± | b> | H>) ₁
Is used (bell measurement). Hereinafter, the contents of the bell measurement will be described.
The wave function of the photon 103 of the horizontally polarized light | H> that travels along the path b 2 and is emitted from the polarization phase control element 140 to the path b 3 is incident on the wave plate 132. The wave plate 132 rotates the polarization direction of the wave function of the incident photon 103 by 90 ° to obtain the vertically polarized light | V>, and then emits it to the path b4 (corresponding to the “second path”). The wave function of the photon 103 emitted to the path b4 is reflected by the mirror 122 and then enters the beam splitter 150. At the same time, the wave function of the photon 103 of the vertically polarized light | V> that travels along the path a 1 and is emitted from the polarization phase control element 140 to the path a 2 is reflected by the mirror 124 and enters the beam splitter 150.

Here, when only the wave function (| e +>) corresponding to the above equation (14) among the wave functions of the photon 103 incident on the beam splitter 150 is seen, the beam splitter 150 emits this wave function to the path a′1. Will do. This wave function is further reflected by the mirror 125, is then output to the path a ′ 2, and enters the polarization beam splitter 113. Since this wave function is horizontal polarization | H> (the wave function of the photon 103 traveling in the path b4 is converted into horizontal polarization | H> in the wave plate 132), the wave function is transmitted through the polarization beam splitter 113, and It is detected by the detector 161. Similarly, among the wave functions of the photons 103 incident on the beam splitter 150, those corresponding to the above equation (15) (| e->) are detected by the detection unit 163 and correspond to the above equation (16). A thing (| f +>) is detected by the detection unit 164, and a thing (| f->) corresponding to the above-described equation (17) is detected by the detection unit 162. That means
When it is detected by the detection unit 161, | e +> is detected,
When detected by the detection unit 162, | f-> is detected,
When detected by the detection unit 163, | e-> is detected,
When detected by the detection unit 164, it can be seen that | f +> has been detected.

Then, when the wave function of the photon 103 is observed by any of the detection units 161 to 164, the quantum state of the equation (13) is expressed by the equation (14) corresponding to the detection units 161 to 164 where it is observed. It will shrink | contract to the quantum state of-Formula (17). That means
When detected by the detector 161, the quantum state of the formula (14) contracts,
When detected by the detection unit 162, the quantum state of Expression (17) contracts,
When detected by the detection unit 163, the quantum state of Expression (15) contracts,
When it is detected by the detection unit 164, it contracts to the quantum state of Expression (16).
That is, this contraction also contracts the quantum state of the photon 104 in an entangled state with the photon 103.

The bell measurement unit 101 sends the classical information of the measurement result (which detection unit 161 to 164 has detected the photon) to the control unit 170. The control unit 170 sends classical information indicating the unitary conversion method to the polarization phase control elements 181 and 182 in order to perform unitary conversion on the photon 104 according to the detection result. The polarization phase control elements 181 and 182 convert the unitary transformations I, σ _x , σ _z , and σ _z σ _x according to the measurement results | e +>, | e−>, | f +>, | f−> into the photons 104. The photon 105 indicating the quantum state (α | H> + β | V>) indicating the input information input by the polarization phase control element 140 is generated and emitted. Here, I represents a basic matrix, and σ _x and σ _z are unitary transformations represented by equations (9) and (10).
As described above, in this quantum teleportation apparatus 100, only the path of the photon 103 is separated in the polarization beam splitter 111, and the path of the photon 104 is not separated. This is because Boschi et al., Which separates the path of two photons into two paths, has fewer paths than the experimental device, and circuit efficiency is good.

[Control NOT operation device (corresponding to claims 7 and 8)]
Next, a control NOT operation device that performs control NOT operation (C-NOT) by the GS method by combining the above-described quantum state generation device and quantum teleportation device will be described. In addition, below, description is abbreviate | omitted about the matter which is common in description of the quantum state production | generation apparatus and quantum teleportation apparatus mentioned above. In the drawings used below, the same reference numerals as those in the above-described drawings are assigned to the same configurations as those described above.

<Configuration>
FIG. 8 is a diagram illustrating the overall configuration of the control NOT arithmetic device 200 in the present embodiment.
First, the overall configuration of the control NOT arithmetic unit 200 will be described using this figure.
As illustrated in FIG. 8, the control NOT operation device 200 includes a quantum state generation device 300 and quantum teleportation devices 400 and 500. The quantum teleportation apparatus 400 includes a bell measurement unit 101 and polarization phase control elements 181, 182, and 481, and the quantum teleportation apparatus 500 includes a bell measurement unit 501 and polarization phase control elements 581 to 583.

FIG. 9 is a diagram illustrating a configuration of the quantum state generation device 300 in the present embodiment.
The configuration of the quantum state generation device 300 is substantially the same as that of the quantum state generation device 1 (see FIG. 1) described above, except that the detection units 41 to 44 and the control unit 50 included in the quantum state generation device 1 are not included. Is different.
Here, the polarization beam splitters 21 and 22 correspond to “seventh and eighth polarization beam splitters”, the wave plates 31 to 33 correspond to “fifth to seventh polarization rotation elements”, and photons 271 to 274 correspond to “first to fourth photons”, and photons 61 to 64 correspond to “fifth to eighth photons”. Here, the route j corresponds to the “17th route”, the route k corresponds to the “18th route”, the route n corresponds to the “19th route”, and the route m corresponds to the “20th route”. Corresponding to “path of”.

FIG. 10 is a diagram illustrating a configuration of the quantum teleportation apparatus 400 in this embodiment.
The configuration of the quantum teleportation device 400 is substantially the same as that of the quantum teleportation device 100 (see FIG. 7) described above (including the correspondence with claim 7), and the quantum state generation device 300 is used as the photon emitting unit 102. The only difference is that a polarization phase control element 481 (corresponding to a “second polarization phase control element”) is added. The polarization phase control element 481 is configured in the same manner as the polarization phase control element 181 and performs unitary transformation represented by the above-described equation (9) on the quantum state of the incident photon. The polarization phase control element 481 is provided at a position where the photon 272 is incident, and is arranged so that the emitted photon is incident on the polarization phase control element 181.

FIG. 11 is a diagram illustrating a configuration of the quantum teleportation apparatus 500 in the present embodiment.
The configuration of the quantum teleportation apparatus 500 is substantially the same as that of the quantum teleportation apparatus 100 (see FIG. 7) described above, and polarization phase control elements 581 to 583 are provided instead of the polarization phase control elements 181 and 182. Only the point is different. Here, the polarization phase control element 581 is configured in the same manner as the polarization phase control element 181, and performs unitary transformation represented by the above-described equation (9) on the quantum state of the incident photon. The polarization phase control elements 582 and 583 are configured in the same manner as the polarization phase control element 182, and perform unitary transformation represented by the above-described equation (10) on the quantum state of the incident photon. The polarization phase control element 581 is provided at a position where the photon 274 is incident, the polarization phase control element 582 is provided at a position where the photon 274 emitted from the polarization phase control element 581 is incident, and the polarization phase control element 583 is The photon 274 emitted from the polarization phase control element 582 is provided at a position where it enters. In addition, the polarization phase control element 481 and the polarization phase control element 581, the polarization phase control element 182 and the polarization phase control element 583 are respectively connected by a classical communication path, and are configured to simultaneously perform the same unitary conversion.

  Here, the bell measuring unit 501 corresponds to the bell measuring unit 101, the wave plate 532 (corresponding to the “fourth polarization rotation element”) is the wave plate 132, the mirrors 522 to 525 are the mirrors 122 to 125, the beam splitter. 550 (corresponding to “second beam splitter”) corresponds to beam splitter 150 (corresponding to “first beam splitter”), and polarizing beam splitters 512 and 513 (corresponding to “fifth and sixth polarizing beam splitters”) Corresponds to the polarization beam splitters 112 and 113, and the detectors 561 to 564 (corresponding to “fifth to eighth detectors”) correspond to the detectors 161 to 164, respectively.

The polarization beam splitter 511 (corresponding to “third polarization beam splitter”) is the polarization beam splitter 111, the mirror 521 is mirror 121, and the wave plate 531 (corresponding to “third polarization rotation element”) is the wave plate. 131, the polarization phase control element 540 (corresponding to the “third polarization phase control element”) is the polarization phase control element 140, the control unit 570 is the control unit 170, the polarization phase control elements 581 and 582 (“the fourth phase control element”). Corresponds to the polarization phase control elements 181 and 182 (see FIG. 7).
Further, here, the routes c1 and c2 correspond to the “ninth route”, the routes c′1 and c′2 correspond to the “11th route”, and the route c′3 corresponds to the “13th route”. The route c′4 corresponds to the “fourteenth route”. The routes d1 to d4 correspond to the “tenth route”, the routes d′ 1 and d′ 2 correspond to the “twelfth route”, and the route d′ 3 corresponds to the “fifteenth route”. The route d′ 4 corresponds to the “sixteenth route” (see FIG. 11).

<Operation>
Next, the operation of the control NOT arithmetic unit 200 in this embodiment will be described.
First, in the quantum state generation device 300, | χ> = (1/4) [(| H of the quantum state that is in the entanglement state by polarization according to the procedure described in the section of [Quantum state generation device]. _{> 5 | H> 6 + |} V> 5 | V> 6) | H> 7 | H> 8 + (| H> 5 | V> 6 + | V> 5 | H> 6) | V> 7 | V > ₈ ]… (18)
Photons 271 to 274 are generated and emitted as resources. Here, as shown in FIG. 9, the wave function of the photon 271 is a wave function of the photon emitted from the wave plate 32, and the wave function of the photon 272 is the wave function of the photon emitted from the polarization rotation element 33. The wave function of the photon 273 is the wave function of the photon guided to the path n in the polarizing beam splitter 22, and the wave function of the photon 274 is the photon of the photon guided to the path m in the polarizing beam splitter 22. It is a wave function. In addition, the subscript “5” in the equation (18) indicates the quantum state of the photon 271, “6” indicates the quantum state of the photon 272, and “7” indicates the quantum state of the photon 273. “8” indicates that the photon 274 is in a quantum state.

Note that this state generation is probabilistic, and when one photon is finally detected at each of the two bell measurement units 101 and 501 and the two output ports (emission sides of the polarization phase control elements 182 and 583). Only if this state generation is successful.
The photons 271 and 273 emitted as described above are incident on the polarization beam splitters 111 and 511, respectively, and are in a superposed state of different paths as described above. Then, the wave function of one path is passed through the wave plates 131 and 531 to rotate the polarized light by 90 °. Thereby, the quantum states of photons 271 to 274 are
_{(1/2) [(| a>} 5 | H> 6 + | b> 5 | V> 6) | H> 7 | c> 8 + (| a> 5 | V> 6 + | b> 5 | H > ₆ ) | V> ₇ | d> ₈ ] | H> ₅ | H> ₈
It becomes the superposition state by the path | route represented by these, and polarization | polarized-light. Here, | a> indicates a quantum state of a photon existing in any of paths a1 to a2 and a′1 to a′4, and | b> indicates a path b1 to b4 and b′1 to b′4. Shows the quantum state of a photon present in any of the above. Further, | c> indicates a quantum state of a photon existing in any one of the paths c1 to c2 and c′1 to c′4, and | d> indicates a path d1 to d4 and d′ 1 to d′ 4. Indicates the quantum state of a photon present anywhere.

Next, the wave functions of the photons 271 and 273 are incident on the polarization phase control elements 140 and 540, respectively, where the wave function of the photon 271 is converted into the quantum state | ψ> = α | H> + β | V of the input target bit. >, The wave function of the photon 273 is represented by the quantum state of the input control bit | φ> = γ | H> + δ | V>
Convert to
Thereby, the quantum states of photons 271 to 274 are
_{(1/2) [(| a>} 5 | H> 6 + | b> 5 | V> 6) | H> 7 | c> 8 + (| a> 5 | V> 6 + | b> 5 | H > ₆ ) | V> ₇ | d> ₈ ] (α | H> + β | V>) ₅ (γ | H> + δ | V>) ₈
It becomes.

Next, the quantum state of the photon 271 is changed into four orthogonal bases | e ±> ₅ = (1 / √ by the bell measurement unit 101 by the same procedure as described in the column of [Quantum state generator]. 2) (| a> | H> ± | b> | V>) ₅
| F ±> ₅ = (1 / √2) (| a> | V> ± | b> | H>) ₅
Observe using. Here, detection of photons by the detectors 161, 162, 163, and 164 means that in the bell measurement, | e +> ₅ , | f-> ₅ , | e-> ₅ , and | f +> ₅ were measured. Corresponding to

In the bell measurement unit 501, the quantum state of the photon 273 is changed to four orthogonal bases | e ±> ₅ = (1 / √2) (| c> | H> ± | d> | V> by the same procedure. ₈
| F ±> ₅ = (1 / √2) (| c> | V> ± | d> | H>) ₈
Observe using. Here, detection of photons by the detection units 561, 562, 563, 564 means that | e +> ₈ , | f-> ₈ , | e-> ₈ , | f +> ₈ were measured in the bell measurement, respectively. Corresponding to
These detection results are sent from the bell measurement units 101 and 501 to the control units 170 and 570, respectively. Each of the control units 170 and 570 sends classical information indicating unitary transformation determined based on the received observation results to the polarization phase control elements 181, 182, 583 and 581 582, 481. The polarization phase control elements 481, 181 and 182 perform predetermined unitary conversion on the photon 272 based on the polarization phase control elements 481, 181 and 182, and the polarization phase control elements 581 and 582 and 583 perform predetermined unitary conversion on the photon 274 based on the unit.

Here, the unitary conversion performed on the photons 272 and 274 is as follows.
Photon detection by the detector 161: I (x) I
Photon detection by the detector 162: σ _z σ _x (×) σ _z
Photon detection by the detection unit 163: σ _x (×) I
Photon detection by the detection unit 164: σ _z (×) σ _z
Photon detection by the detection unit 561: I (x) I
Photon detection by the detection unit 562: σ _x (×) σ _x σ _z
Photon detection by the detection unit 563: σ _x (×) σ _x
Photon detection by the detection unit 564: I (x) σ _z
Here, p (x) q represents a tensor product of p and q. In addition, I represents a basic matrix, and σ _x and σ _z are unitary transformations represented by equations (9) and (10).
As a result, the two quantum states of the photons 275 and 276 emitted from the polarization phase control elements 182 and 583 are
αγ | HH> + αδ | VV> + βγ | VH> + βδ | HV> (19)
It becomes.

Here, the quantum state | φ> = α | H> + β | V> of the input control bits converted by the polarization phase control elements 140 and 540, respectively, and the quantum state | ψ> = γ | H> + of the input target bits The tensor product with δ | V> is
(Α | H> + β | V>) (×) (γ | H> + δ | V>)
= Αγ | HH> + αδ | HV> + βγ | VH> + βδ | VV> (20)
It becomes.
Here, in Expression (19) and Expression (20), the right side in | **> indicates a control bit, and the left side indicates a target bit. As can be seen from these, the quantum state represented by the equation (19) is a state in which the control NOT gate acts on the input quantum state represented by the equation (20).
With the above configuration, the GC method can be actually implemented. In this configuration, it is not necessary to distinguish the number of photons, and only four photons have to be generated. Therefore, it can be sufficiently realized even at the current technical level.

The present invention is not limited to the embodiment described above. For example, quantum non-demolition measurement may be used for post-selection (for example, “P. Kok, H. Lee, and JP Dowling, Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements, Physical Review A 66, 063814 (2002) ").
In this quantum nondestructive measurement, the existence of a photon can be detected while maintaining the information such as polarization without annihilating the existence of the photon. Post-selection can be performed by placing these at the emission positions of the wave plates 32 and 33 and the polarization beam splitter 22 and confirming the existence of photons. When the post-selection in a state where the photon is not annihilated is successful, the quantum state is correctly generated and the quantum state is maintained.
Needless to say, other modifications are possible without departing from the spirit of the present invention.

  According to the present invention, a control NOT operation, which is a basic operation of a quantum computer, can be implemented practically.

The block diagram which illustrated the composition of the quantum state generating device. The block diagram which illustrated the composition of the photon emission part. The block diagram which illustrated the composition of the photon emission part. The block diagram which illustrated the composition of the photon emission part constituted integrally. The block diagram which illustrated the composition of the photon emission part constituted integrally. The block diagram which illustrated the composition of the photon emission part constituted integrally. 1 is a block diagram illustrating a configuration of a quantum teleportation device 100. FIG. The figure which illustrated the whole control NOT arithmetic unit composition. The figure which illustrated the composition of the quantum state generating device. The figure which illustrated the composition of the quantum teleportation device. The figure which illustrated the composition of the quantum teleportation device. The figure which showed the quantum circuit of C-NOT by GC system.

Explanation of symbols

1,300 Quantum state generation device 100,400,500 Quantum teleportation device 200 Control NOT operation device

Claims (8)

A photon emitter for emitting first to fourth photons;
A wave function of the second photon in the first polarization direction and a wave function of the third photon in the second polarization direction are provided at positions where the second photon and the third photon are incident. A first polarization leading to a second path, a wave function of the second photon in the second polarization direction and a wave function of the third photon in the first polarization direction to the second path; A beam splitter,
Polarization of the wave function of the incident photon provided at a position where the wave function of the second photon and the wave function of the third photon guided to the first path from the first polarization beam splitter are incident. A first polarization rotation element that rotates the direction;
A wave function of a photon emitted from the first polarization rotation element and a position of the photon emitted from the first polarization rotation element are provided at a position where the fourth photon is incident, and the first polarization direction of the photon emitted from the first polarization rotation element is A wave function and a wave function of the fourth photon in the second polarization direction are guided to a third path, and the wave function of the second polarization direction of the photon emitted from the first polarization rotation element, and A second polarizing beam splitter that guides a wave function of the first polarization direction of the fourth photon to a fourth path;
A second polarization rotation element provided at a position where the first photon is incident, and rotating a polarization direction of a wave function of the incident photon;
A third polarization rotation element that is provided at a position where a wave function of a photon guided to the second path is incident in the first polarization beam splitter, and rotates a polarization direction of the wave function of the incident photon;
Having
A quantum state generator characterized by the above. The quantum state generation device according to claim 1,
The first and second photons emitted from the photon emission unit are:
In an entangled state that the polarization direction is the same,
A quantum state generator characterized by the above. The quantum state generating device according to claim 1 or 2,
The first polarization direction is:
Horizontal,
The second polarization direction is:
Vertical direction,
The polarizing beam splitter is
When the wave function of the incident photon is horizontal polarization, the photon is transmitted, and when the wave function is vertical polarization, the photon is reflected.
The polarization rotation element is
Rotate the polarization direction of the wave function of the incident photon by 45 °,
A quantum state generator characterized by the above. The quantum state generation device according to any one of claims 1 to 3,
A first detector provided at a position where the wave function of the emitted light of the second polarization rotation element can be detected;
A second detector provided at a position where the wave function of the emitted light of the third polarization rotation element can be detected;
A third detector provided at a position where the wave function of a photon guided to the third path in the second polarization beam splitter can be detected;
A fourth detector provided at a position where the wave function of a photon guided to the fourth path in the second polarization beam splitter can be detected;
A control unit that determines that a quantum state has been correctly generated when a photon is detected in all of the first to fourth detection units;
Having
A quantum state generator characterized by the above. A photon emitter that emits the first and second photons in an entangled state that the polarization directions are the same;
The first photon is provided at a position where the first photon is incident, the wave function of the first photon in the first polarization direction is guided to the first path, and the wave function of the first photon in the second polarization direction is A first polarizing beam splitter leading to a second path;
The first polarization beam splitter is provided at a position where the wave function of the first photon guided to the second path is incident, and the polarization direction of the wave function of the first photon is rotated to change the first photon wave function. A first polarization rotator that exits the two paths;
The wave function of the first photon guided to the first path in the first polarization beam splitter is converted into a 1-qubit state of input information and emitted to the first path. The first polarization phase control element that converts the wave function of the first photon emitted from the polarization rotation element to the second path into the one-qubit state of the input and emits it to the second path When,
A second polarization rotation element that rotates the polarization direction of the wave function of the first photon emitted from the first polarization phase control element to the second path and emits the second path to the second path;
The wave function of the first photon emitted from the first polarization phase control element to the first path, and the first photon emitted from the second polarization rotation element to the second path. A beam splitter for separating the wave function of the incident first photon into a third path and a fourth path.
The beam splitter is provided at a position where the wave function of the first photon guided to the third path is incident, and the wave function of the first photon in the first polarization direction is set to the fifth path. A second polarizing beam splitter for guiding and guiding a wave function of the second polarization direction of the first photon to a sixth path;
A first detector provided at a position where the wave function of the first photon guided to the fifth path in the second polarization beam splitter can be detected;
A second detector provided at a position where the wave function of the first photon guided to the sixth path in the second polarization beam splitter can be detected;
The beam splitter is provided at a position where the wave function of the first photon guided to the fourth path is incident, and the wave function of the first polarization direction of the first photon is set to the seventh path. A third polarizing beam splitter for guiding and guiding a wave function of the second polarization direction of the first photon to an eighth path;
A third detector provided at a position where the wave function of the first photon guided to the seventh path in the third polarization beam splitter can be detected;
A fourth detector provided at a position where the wave function of the first photon guided to the eighth path in the third polarization beam splitter can be detected;
A second polarization phase control element that performs unitary conversion on the second photon according to the detection results of the first to fourth detectors;
Having
Quantum teleportation device characterized by that. The quantum teleportation device according to claim 5,
The first polarization direction is:
Horizontal,
The second polarization direction is:
Vertical direction,
The polarizing beam splitter is
When the wave function of the incident first photon is horizontal polarization, the photon is transmitted; when the wave function is vertical polarization, the photon is reflected;
The polarization rotation element is
Rotating the polarization direction of the wave function of the incident first photon by 90 °;
Quantum teleportation device characterized by that. A quantum state generator that emits first to fourth photons in an entangled state;
The first photon is provided at a position where the first photon is incident, the wave function of the first photon in the first polarization direction is guided to the first path, and the wave function of the first photon in the second polarization direction is A first polarizing beam splitter leading to a second path;
The first polarization beam splitter is provided at a position where the wave function of the first photon guided to the second path is incident, and the polarization direction of the wave function of the first photon is rotated to change the first photon wave function. A first polarization rotator that exits the two paths;
The wave function of the first photon guided to the first path in the first polarization beam splitter is converted into a 1-qubit state that is a target bit, and is emitted to the first path, The first polarized light that is converted from the wave function of the first photon emitted from the one polarization rotation element to the second path into the one qubit state that becomes the target bit and is emitted to the second path. A phase control element;
A second polarization rotation element that rotates the polarization direction of the wave function of the first photon emitted from the first polarization phase control element to the second path and emits the second path to the second path;
The wave function of the first photon emitted from the first polarization phase control element to the first path, and the first photon emitted from the second polarization rotation element to the second path. A first beam splitter which is provided at a position where the wave function of the first photon is incident and which separates the wave function of the incident first photon into a third path and a fourth path;
The first beam splitter is provided at a position where the wave function of the first photon guided to the third path is incident, and the wave function of the first photon in the first polarization direction is changed to a fifth wave function. A second polarization beam splitter that guides the wave function of the first photon in the second polarization direction to the sixth path;
A first detector provided at a position where the wave function of the first photon guided to the fifth path in the second polarization beam splitter can be detected;
A second detector provided at a position where the wave function of the first photon guided to the sixth path in the second polarization beam splitter can be detected;
The first beam splitter is provided at a position where the wave function of the first photon guided to the fourth path is incident, and the wave function of the first polarization direction of the first photon is changed to a seventh wave function. A third polarizing beam splitter that guides the wave function of the first photon in the second polarization direction to the eighth path,
A third detector provided at a position where the wave function of the first photon guided to the seventh path in the third polarization beam splitter can be detected;
A fourth detector provided at a position where the wave function of the first photon guided to the eighth path in the third polarization beam splitter can be detected;
A second polarization phase control element that performs unitary conversion on the second and fourth photons according to the detection results of the first to fourth detectors;
Comprising
A first quantum teleportation device;
The third photon is provided at a position where the third photon is incident, and a wave function of the first photon in the first polarization direction is guided to a ninth path, and the wave of the first photon in the second polarization direction is guided. A fourth polarizing beam splitter leading the function to the tenth path;
The fourth polarization beam splitter is provided at a position where the wave function of the third photon guided to the tenth path is incident, and the polarization direction of the wave function of the third photon is rotated to change the first photon wave function. A third polarization rotation element that emits to 10 paths;
The wave function of the third photon guided to the ninth path in the fourth polarization beam splitter is converted into a 1-qubit state serving as a control bit and emitted to the ninth path, A third polarization that is output from the third polarization rotation element to the tenth path, converted into a 1-qubit state that serves as the control bit, and output to the tenth path. A phase control element;
A fourth polarization rotation element that rotates the polarization direction of the wave function of the third photon emitted from the third polarization phase control element to the tenth path and emits it to the tenth path;
The wave function of the third photon emitted from the third polarization phase control element to the ninth path, and the third photon emitted from the fourth polarization rotation element to the tenth path. A second beam splitter that separates the wave function of the incident third photon into an eleventh path and a twelfth path.
The second beam splitter is provided at a position where the wave function of the third photon guided to the eleventh path is incident, and the wave function of the third photon in the first polarization direction is changed to the thirteenth. A fifth polarization beam splitter for guiding the wave function of the third photon in the second polarization direction to the fourteenth path;
A fifth detector provided at a position where the wave function of the third photon guided to the thirteenth path in the fifth polarization beam splitter can be detected;
A sixth detector provided at a position where the wave function of the third photon guided to the fourteenth path in the fifth polarization beam splitter can be detected;
The second beam splitter is provided at a position where the wave function of the third photon guided to the twelfth path is incident, and the wave function of the third photon in the first polarization direction is changed to the fifteenth wave function. A sixth polarization beam splitter that guides the wave function of the third photon in the second polarization direction to the sixteenth path;
A seventh detector provided at a position where the wave function of the third photon guided to the fifteenth path in the sixth polarizing beam splitter can be detected;
An eighth detector provided at a position where the wave function of the third photon guided to the sixteenth path in the sixth polarization beam splitter can be detected;
A fourth polarization phase control element that performs unitary conversion on the second and fourth photons according to the detection results of the fifth to eighth detectors;
Comprising
A second quantum teleportation device;
Having
The control NOT arithmetic unit characterized by the above-mentioned. The control NOT arithmetic device according to claim 7,
The quantum state generator is
A photon emitting section for emitting the fifth to eighth photons;
A wave function of the sixth photon in the first polarization direction, and a wave function of the seventh photon in the second polarization direction, provided at a position where the sixth photon and the seventh photon are incident. A function to a seventeenth path, and a wave function of the sixth photon in the second polarization direction and a wave function of the seventh photon in the first polarization direction to the eighteenth path, A polarizing beam splitter,
Polarization of the wave function of the incident photon provided at a position where the wave function of the sixth photon and the wave function of the seventh photon guided to the seventeenth path from the seventh polarization beam splitter are incident. A fifth polarization rotation element for rotating the direction;
A wave function of a photon emitted from the fifth polarization rotation element and a position where the eighth photon is incident are provided in the first polarization direction of the photon emitted from the fifth polarization rotation element. A wave function and a wave function of the eighth photon in the second polarization direction are guided to a nineteenth path, and the wave function of the second polarization direction of the photon emitted from the fifth polarization rotation element; An eighth polarizing beam splitter for guiding a wave function of the first polarization direction of the eighth photon to a twentieth path;
A sixth polarization rotation element that is provided at a position where the fifth photon is incident and that emits by rotating the polarization direction of the wave function of the incident photon;
A seventh polarization rotation element provided at a position where the wave function of the photon guided to the eighteenth path is incident in the seventh polarization beam splitter, and emitting by rotating the polarization direction of the wave function of the incident photon; When,
Have
The wave function of the first photon is
A wave function of photons emitted from the sixth polarization rotation element,
The wave function of the second photon is
A wave function of photons emitted from the seventh polarization rotation element,
The wave function of the third photon is
A wave function of photons guided to the nineteenth path in the eighth polarization beam splitter,
The wave function of the fourth photon is
It is a wave function of photons guided to the twentieth path in the eighth polarization beam splitter.
The control NOT arithmetic unit characterized by the above-mentioned.

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