Quantum gate device, quantum computing system, and manufacturing method

Abstract

To reduce errors of a measurement type quantum calculation method using a three-dimensional cluster state.SOLUTION: A quantum gate device comprises: a first polarization beam splitter; a first resonator provided on the side of receiving first polarized light output from the first polarization beam splitter; a first mirror provided on the side of receiving second polarized light output from the first polarization beam splitter; a second polarization beam splitter; a second resonator provided on the side of receiving first polarized light output from the second polarization beam splitter; and a second mirror provided on the side of receiving second polarized light output from the second polarization beam splitter. In the quantum gate device in which the first polarization beam splitter and the second polarization beam splitter are connected, the reflectance of the first mirror and the reflectance of the second mirror, and the position of the first mirror and the position of the second mirror are set so as to reduce errors in measurement type quantum calculation using a three-dimensional cluster state.SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The present invention relates to a quantum gate device based on cavity QED. [Background technology]

[0002] In recent years, research has been actively conducted into new information processing techniques using quantum mechanics, which promises ultrafast calculations that exceed the limits of current computers. One of the most pressing issues in the realization of quantum information processing is the implementation of quantum gates that utilize the interactions between quantum bits.

[0003] To address this issue, cavity quantum electrodynamics (QED), which allows light and atoms trapped in a cavity to interact electromagnetically at the single-photon level, has attracted attention as a method for deterministically manipulating the interaction between optical bits and atomic bits.

[0004] Non-Patent Document 1 discloses a controlled Z gate between an optical bit and an atomic bit, which utilizes the interaction between the optical bit and the atomic bit. Non-Patent Document 2 discloses a controlled Z gate between two atomic bits mediated by photons, which is realized by executing this controlled Z gate twice. In addition, Non-Patent Document 4 envisions the construction of an error-tolerant quantum computing method called a concatenated code (see Non-Patent Document 3) using controlled Z gates between the above-mentioned atomic bits, and discloses the design of a resonator QED system that minimizes the computational errors. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] L.-M. Duan and J. Kimble, "Scalable photonic quantum computation through cavity-assisted interactions", Phys. Rev. Lett. 92, 127902 (2004). [Non-Patent Document 2] L.-M. Duan, B. Wang, and HJ Kimble, "Robust quantum gates on neutral atoms with cavity-assisted photon scattering", Phys. Rev. A 72, 032333 (2005). [Non-Patent Document 3] Hayato Goto and Kouichi Ichimura, "Fault-tolerant quantum computation with probabilistic two-qubit gates", Phys. Rev. A 80, 040303(R) (2009). [Non-Patent Document 4] Hayato Goto and Kouichi Ichimura, "Condition for fault-tolerant quantum computation with a cavity-QED scheme", Phys. Rev. A 82, 032311 (2010). [Non-Patent Document 5] K. Fujii and Y. Tokunaga, "Fault-tolerant topological one-way quantum computation with probabilistic two-qubit gates" Phys. Rev. Lett. 105, 250503 (2010). Summary of the Invention [Problem to be solved by the invention]

[0006] In recent years, it has been pointed out that a measurement-based quantum computing method that uses a three-dimensional cluster state of quantum bits (see Non-Patent Document 5) may be compatible with quantum computing that uses light and atoms in terms of implementation. However, the design of an optimal resonator system for a measurement-based quantum computing method that uses a three-dimensional cluster state has not been clarified.

[0007] The present invention has been made in consideration of the above-mentioned points, and has an object to provide a quantum gate device for reducing errors in a measurement-type quantum computing method that utilizes a three-dimensional cluster state. [Means for solving the problem]

[0008] According to the disclosed technology, a first polarizing beam splitter, a first resonator provided on a side receiving the first polarized light output from the first polarizing beam splitter; a first mirror provided on a side receiving the second polarized light output from the first polarizing beam splitter; A second polarizing beam splitter; and a second resonator provided on a side receiving the first polarized light output from the second polarizing beam splitter; a second mirror provided on a side receiving the second polarized light output from the second polarizing beam splitter; The first polarizing beam splitter and the second polarizing beam splitter are connected to each other using a waveguide, a reflectance of the first mirror is determined so that a photon loss in the first resonator is equal to a photon loss in the first mirror; The reflectance of the second mirror is determined so that the photon loss in the second resonator is equal to the photon loss in the second mirror. A quantum gate device is provided. Effect of the Invention

[0009] According to the disclosed technique, it is possible to realize a quantum gate device for reducing errors in a measurement-type quantum computing method that utilizes a three-dimensional cluster state. [Brief description of the drawings]

[0010] [Figure 1] 1 is a diagram illustrating an example of a configuration of a quantum computing system according to an embodiment of the present invention. [Diagram 2] 1 is a diagram illustrating a configuration example of a quantum gate device according to an embodiment of the present invention. [Diagram 3]FIG. 2 is a diagram for explaining the state of atoms in a resonator. [Figure 4] 4A and 4B are diagrams for explaining the position and reflectance of a mirror. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Hereinafter, an embodiment of the present invention (the present embodiment) will be described with reference to the drawings. The embodiment described below is merely an example, and the embodiment to which the present invention is applied is not limited to the following embodiment.

[0012] (Outline of the embodiment) The measurement-based quantum computing method using three-dimensional cluster states disclosed in Non-Patent Document 5 is more resistant to errors due to photon loss than the concatenated code method in Non-Patent Document 4, but is vulnerable to computational errors other than photon loss.

[0013] In this embodiment, focusing on this characteristic, a quantum gate device using two resonators based on the design of an optical system that suppresses errors other than photon loss at the expense of sacrificing the survival probability of photons will be described. Specifically, the quantum gate device intentionally reduces the reflectance of the mirrors around the resonators required to construct a controlled Z gate, thereby suppressing errors other than photon loss. In addition, the mirror positions are also optimized at the same time in order to further reduce calculation errors other than photon loss.

[0014] (Example of overall system configuration) 1 shows an example of the configuration of a quantum computing system 300 according to this embodiment. The "quantum computing system" may also be called a "quantum computer."

[0015] 1, a quantum computing system 300 includes a control device 100 and a quantum processor 200. The control device 100 performs quantum computing by transmitting control signals and the like to the quantum processor 200 and acquiring calculation results (measurement results) from the quantum processor 200. The control device 100 can be realized by, for example, a classical computer.

[0016] The quantum processor 200 in this embodiment forms a three-dimensional cluster state having a large number of atomic bits (which may be called atomic quantum bits) as vertices. The three-dimensional cluster state is created by placing atomic bits in a certain state at each vertex of a three-dimensional graph consisting of edges and vertices, and if two vertices are connected by an edge, applying a controlled Z gate to the two vertices. The controlled Z gate may be called a controlled phase gate.

[0017] The control device 100 performs measurement on each atomic bit in the above-mentioned three-dimensional cluster state, thereby performing measurement-based quantum computation.

[0018] In this embodiment, the quantum processor 200 is provided with a plurality (a large number) of quantum gate devices, which will be described later. One quantum gate device has two atomic bits corresponding to two vertices connected by an edge, and has a function of applying a controlled Z gate between these two atomic bits.

[0019] (Example of quantum gate device configuration) An example of the configuration of a quantum gate device is shown in Fig. 2. The configuration of this quantum gate device itself is an existing technology disclosed in Non-Patent Document 2.

[0020] As shown in FIG. 2, the quantum gate device of this embodiment includes resonators 10 and 20, polarizing beam splitters 33, 37, and 40, mirror A 34, mirror B 38, optical circulators 32 and 36, half-wave plates 31, 35, and 39, and photon detectors 41 and 42, and these elements are connected using a waveguide (e.g., an optical fiber) as shown.

[0021] A resonator is a device that confines light (electromagnetic field) in a narrow space using low-loss optical media such as mirrors. When light is confined in a resonator the size of the wavelength, the wavelength becomes discrete from a continuous mode, and one of these modes can be made to interact with an atom. The quantum mechanics of such a system is called resonator quantum electrodynamics (resonator QED).

[0022] Resonators 10 and 20 have the same structure, with two highly reflective mirrors facing each other. A single atom is trapped inside each resonator as an atomic bit. As shown in Figure 2, atomic bit 1 is inside resonator 10, and atomic bit 2 is inside resonator 20.

[0023] Of the mirrors 11 and 12 that compose the resonator 10, the mirror 12 has a slight transparency, so that photons can be incident on the resonator 10 via the mirror 12 and reflected (output) from the resonator 10. The same applies to the resonator 20.

[0024] The polarizing beam splitters 33, 37, and 40 split the photon pulse input from the input port into two orthogonal polarization states, H polarization and V polarization, and output the split light. As shown in Fig. 2, a mirror A34 is provided on the output side of the V polarization of the polarizing beam splitter 33, and a resonator 10 is provided on the output side of the H polarization of the polarizing beam splitter 33. The same applies to the resonator 20.

[0025] Each half-wave plate provided in the optical path performs a Hadamard transformation on the polarization state of the photon pulse.

[0026] (Example of quantum gate device operation) A photon pulse passes through the half-wave plate 31 and reaches the polarizing beam splitter 33. If the polarization state of the photon pulse is H-polarized, the photon pulse enters the resonator 10 from the polarizing beam splitter 33, is reflected (output) from the resonator 10, and travels toward the resonator 20. The state of the photon pulse reflected from the resonator 10 differs depending on the state of the atomic bit 1 in the resonator 10.

[0027] When the polarization state of the photon pulse input to the polarizing beam splitter 33 is V-polarized, the photon pulse is reflected by the polarizing beam splitter 33 and travels toward mirror A34, is reflected by mirror A34, reaches the polarizing beam splitter 33, is reflected by the polarizing beam splitter 33, and travels toward the resonator 20.

[0028] In the same manner, the photon pulse passes through the half-wave plate 35 and reaches the polarizing beam splitter 37. If the polarization state of the photon pulse is H-polarized, the photon pulse enters the resonator 20, is reflected (output) from the resonator 20, and travels toward the polarizing beam splitter 40. The state of the photon pulse reflected from the resonator 20 differs depending on the state of the atomic bit 2 in the resonator 20.

[0029] When the polarization state of the photon pulse input to the polarizing beam splitter 37 is V-polarized, the photon pulse is reflected by the polarizing beam splitter 37 and travels toward mirror B38, is reflected by mirror B38, reaches the polarizing beam splitter 37, is reflected by the polarizing beam splitter 37, and travels toward the polarizing beam splitter 40.

[0030] As described above, photon pulses are successively incident on the resonators 10 and 20, causing interaction between the atoms and the photons in each resonator.

[0031] 3 is a diagram for explaining the state of the atomic bit 1 in the resonator 10. The state of the atomic bit 2 in the resonator 20 is similar. As shown in FIG. 3, the atom used as the atomic bit is a three-level system, and |0> a and |1〉 a The level of |1〉 is used as the second level of the quantum bit. a -|e〉 a An atom that resonates with the incident photon only between levels is used.

[0032] For photons, the two orthogonal polarization states of H-polarization and V-polarization mentioned above are respectively represented as |0〉 p and |1〉 p Used as.

[0033] The states of photons and atoms in each resonator will be described below. The following explanation applies to both resonator 10 and resonator 20.

[0034] The initial states of the photon bit (which may be called a photon quantum bit) entering the resonator and the atomic bit (which may be called an atomic quantum bit) inside the resonator are |ψ〉 p =p0|0〉 p +p1|1〉 p , |ψ〉 a =a0|0〉 a +a1|1〉 a If, due to the selective interactions described above, the final state of the whole including the photon and the atom is |ψ〉=p0a0|0〉 p |0〉 a +p0a1|0〉 p |1〉 a +p1a0|1〉 p |0〉 a -p1a1|1〉 p |1〉 a The sign is reversed only when both the photon and atom are |1〉. Note that the subscript p represents the photon, and the subscript a represents the atom.

[0035] In the quantum gate device shown in Figure 2, if this operation is performed twice in succession between one photon and two atoms, and finally the state of atomic bit 1 is appropriately manipulated by a laser depending on the result of the detection of the photon, both atomic bit 1 and atomic bit 2 will be in the |1〉 state. a It is possible to realize a controlled Z-gate that reverses sign only when in the

[0036] (About the optical system that suppresses errors) The above operation of the controlled Z-gate is the ideal case where there are no errors. However, in reality, there are errors due to imperfections in the resonator system. The main errors are of the following three types: (i) Photon loss; (ii) The state of the photon and the atom is |0〉 p |0〉 a , |0〉 p |1〉 a , |1〉 p |0〉 a , |1〉 p |1〉 a Errors due to the different probability of losing a photon depending on which of the following: (iii) Errors arising from the difference in the speed at which the photon is reflected from the resonator depending on the four states of the photon and the atom.

[0037] As mentioned above, the measurement-based quantum computation using the three-dimensional cluster state is highly resistant to the photon loss (i), but is vulnerable to the errors (ii) and (iii). In this embodiment, to address this issue, we set the reflectance R of the external mirrors A and B that minimizes the error (ii) and the mirror position Δx that minimizes the error (iii). mir The reflectance R and the position Δx of mirror A and mirror B are calculated using the following formula. mir However, depending on the difference in parameters between the resonators 10 and 20, the calculated reflectance R and position Δx mir Mirror A and Mirror B may each be called an "external mirror."

[0038]

number

[0039]

number

[0040]

number

[0041] Reflectance R and position Δx mir In the above formula for calculating int is the loss rate of photons due to absorption and scattering in the mirrors that compose the resonator, and κ extis the coupling rate between the resonator and the external waveguide, and C int ≡g2 / 2γκ int It is.

[0042] The reflectivity R is determined by the state |0〉 a and |1〉 a κ such that the photon loss in the cavity is the same in both states. ext First, we determine the reflectivity R so that the photon loss in the resonator is equal to the photon loss in the external mirror. This minimizes the error (ii).

[0043] On the other hand, the position of the exterior mirror Δx mir means that the atom in the cavity is in state |0〉 a The distance τ0 corresponds to the delay of the photon pulse reflected from the resonator when the atom in the resonator is in state |1〉 a The delay of the photon pulse reflected from the resonator when the photon pulse is incident on the resonator is the average of the delay and the distance τ1, which corresponds to the delay of the photon pulse reflected from the resonator when the photon pulse is incident on the resonator. The above "delay of the photon pulse reflected from the resonator" refers to the time from when the photon pulse is incident on the resonator to when the photon pulse is output from the resonator.

[0044] The above position Δx mir By placing the exterior mirrors at the

[0045] In other words, by setting the optical system as described above, errors (ii) and (iii), which are errors that should be particularly suppressed in measurement-based quantum computing using three-dimensional cluster states, are both minimized. Note that in this specification, "minimization" may be replaced with "suppression" or "reduction."

[0046] In a quantum gate device having such an optical system, mirrors A and B, each having a reflectance R calculated by the above formula, are rotated at a position Δx mir The elements shown in FIG. 2 can be connected by waveguides so as to be arranged as shown in FIG.

[0047] (Effects of the embodiment) As described above, the quantum gate device in this embodiment makes it possible to minimize the types of errors that are difficult to occur in measurement-type quantum computing that uses three-dimensional cluster states based on resonator QED.

[0048] (Additional Note) This specification discloses at least the following quantum gate device, quantum computing system, and manufacturing method. (Section 1) A first polarizing beam splitter; a first resonator provided on a side receiving the first polarized light output from the first polarizing beam splitter; a first mirror provided on a side receiving the second polarized light output from the first polarizing beam splitter; A second polarizing beam splitter; and a second resonator provided on a side receiving the first polarized light output from the second polarizing beam splitter; a second mirror provided on a side receiving the second polarized light output from the second polarizing beam splitter; The first polarizing beam splitter and the second polarizing beam splitter are connected to each other using a waveguide, The reflectance of the first mirror, the reflectance of the second mirror, and the positions of the first mirror and the second mirror are set to reduce errors in measurement-type quantum computing using a three-dimensional cluster state. Quantum gate device. (Section 2) a reflectance of the first mirror is determined so that a photon loss in the first resonator is equal to a photon loss in the first mirror; The reflectance of the second mirror is determined so that the photon loss in the second resonator is equal to the photon loss in the second mirror. 2. A quantum gate device as described in claim 1. (Section 3) the position of the first mirror is a position determined based on an average of a distance corresponding to a delay from when a photon incident on the first resonator is incident to when it is reflected when the atoms in the first resonator are in a first state, and a distance corresponding to a delay from when a photon incident on the first resonator is incident to when it is reflected when the atoms in the first resonator are in a second state; The position of the second mirror is a position determined based on the average of a distance corresponding to the delay from when a photon incident on the second resonator is incident to when it is reflected when the atoms in the second resonator are in a first state, and a distance corresponding to the delay from when a photon incident on the second resonator is incident to when it is reflected when the atoms in the second resonator are in a second state. 3. A quantum gate device according to claim 1 or 2. (Section 4) A quantum processor including a plurality of quantum gate devices according to any one of claims 1 to 3, and a control device for performing measurements on each atom constituting a three-dimensional cluster state in the quantum processor. A quantum computing system comprising: (Section 5) A first polarizing beam splitter; a first resonator provided on a side receiving the first polarized light output from the first polarizing beam splitter; a first mirror provided on a side receiving the second polarized light output from the first polarizing beam splitter; A second polarizing beam splitter; and a second resonator provided on a side receiving the first polarized light output from the second polarizing beam splitter; a second mirror provided on a side receiving the second polarized light output from the second polarizing beam splitter; A method for manufacturing a quantum gate device, comprising: determining a reflectance of the first mirror such that a photon loss in the first resonator is equal to a photon loss at the first mirror; determining a reflectance of the second mirror such that a photon loss in the second resonator is equal to a photon loss at the second mirror; the first mirror is disposed at a position determined based on an average of a distance corresponding to a delay between when a photon incident on the first resonator is incident and when it is reflected when the atoms in the first resonator are in a first state and a distance corresponding to a delay between when a photon incident on the first resonator is incident and when it is reflected when the atoms in the first resonator are in a second state; The second mirror is disposed at a position determined based on an average of a distance corresponding to a delay between when a photon incident on the second resonator is incident and when it is reflected when the atoms in the second resonator are in a first state and a distance corresponding to a delay between when a photon incident on the second resonator is incident and when it is reflected when the atoms in the second resonator are in a second state. Manufacturing method.

[0049] Although the present embodiment has been described above, the present invention is not limited to such a specific embodiment, and various modifications and variations are possible within the scope of the gist of the present invention described in the claims. [Explanation of symbols]

[0050] 100 Control device 200 Quantum Processors 300 Quantum Computing System 10, 20 resonators 33, 37, 40 Polarizing beam splitter 34 Mirror A 38 Mirror B 32, 36 Optical circulator 31, 35, 39 half wave plate 41, 42 Photon detector

Claims

1. A first polarizing beam splitter; a first resonator provided on a side receiving the first polarized light output from the first polarizing beam splitter; a first mirror provided on a side receiving the second polarized light output from the first polarizing beam splitter; A second polarizing beam splitter; and a second resonator provided on a side receiving the first polarized light output from the second polarizing beam splitter; a second mirror provided on a side receiving the second polarized light output from the second polarizing beam splitter; The first polarizing beam splitter and the second polarizing beam splitter are connected to each other using a waveguide, a reflectance of the first mirror is determined so that a photon loss in the first resonator is equal to a photon loss in the first mirror; The reflectance of the second mirror is determined so that the photon loss in the second resonator is equal to the photon loss in the second mirror. Quantum gate device.

2. the position of the first mirror corresponds to an average of a distance corresponding to a delay between when a photon incident on the first resonator is incident and when it is reflected when the atoms in the first resonator are in a first state and a distance corresponding to a delay between when a photon incident on the first resonator is incident and when it is reflected when the atoms in the first resonator are in a second state; The position of the second mirror is a position corresponding to the average of a distance corresponding to a delay from when a photon incident on the second resonator is incident to when it is reflected when the atoms in the second resonator are in a first state, and a distance corresponding to a delay from when a photon incident on the second resonator is incident to when it is reflected when the atoms in the second resonator are in a second state. The quantum gate device according to claim 1 .

3. A quantum processor comprising a plurality of quantum gate devices according to claim 1 or 2; and a control device for performing measurements on each atom constituting a three-dimensional cluster state in the quantum processor. A quantum computing system comprising:

4. A first polarizing beam splitter; a first resonator provided on a side receiving the first polarized light output from the first polarizing beam splitter; a first mirror provided on a side receiving the second polarized light output from the first polarizing beam splitter; A second polarizing beam splitter; and a second resonator provided on a side receiving the first polarized light output from the second polarizing beam splitter; a second mirror provided on a side receiving the second polarized light output from the second polarizing beam splitter; A method for manufacturing a quantum gate device, comprising: determining a reflectance of the first mirror such that a photon loss in the first resonator is equal to a photon loss at the first mirror; determining a reflectance of the second mirror such that a photon loss in the second resonator is equal to a photon loss at the second mirror; the first mirror is disposed at a position corresponding to an average of a distance corresponding to a delay between when a photon incident on the first resonator is incident and when it is reflected when the atoms in the first resonator are in a first state and a distance corresponding to a delay between when a photon incident on the first resonator is incident and when it is reflected when the atoms in the first resonator are in a second state; The second mirror is disposed at a position corresponding to the average of a distance corresponding to a delay between when a photon incident on the second resonator is incident and when it is reflected when the atoms in the second resonator are in a first state and a distance corresponding to a delay between when a photon incident on the second resonator is incident and when it is reflected when the atoms in the second resonator are in a second state. Manufacturing method.

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