Error correction device, error correction method, and program

Abstract

To easily achieve quantum error correction in a squeezed cat code.SOLUTION: An error correction device according to an aspect of the present disclosure achieves quantum error correction using a squeezed cat code, and the error correction device has a control unit that, by using a quantum processor having mounted thereon a quantum circuit including a quantum gate for achieving a dissipation operator built from a stabilizer operator in a momentum direction in a squeezed cat state in the squeezed cat code, causes the quantum circuit to repeatedly execute quantum information processing on a quantum state represented by error correction code quantum bits and auxiliary quantum bits, to correct a quantum error in the error correction code quantum bits.SELECTED DRAWING: Figure 6

Description

[Technical Field]

[0001] The present disclosure relates to an error correction device, an error correction method, and a program. [Background technology]

[0002] A type of code used in the field of quantum information processing is known as a code called a Squeezed Cat Code (Non-Patent Document 1). The Squeezed Cat Code is known to be robust against photon loss. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Schlegel, David S., Fabrizio Minganti, and Vincenzo Savona. "Quantum error correction using squeezed Schrodinger cat states." Physical Review A 106.2 (2022): 022431. Summary of the Invention [Problem to be solved by the invention]

[0004] However, the only quantum error correction methods available for the squeezed-cat code require very strong nonlinearity and complex interactions with the auxiliary quantum system, and there has been no quantum error correction method that can be implemented with simple operations.

[0005] The present disclosure has been made in consideration of the above points, and aims to easily realize quantum error correction in compressed-CAT codes. [Means for solving the problem]

[0006] An error correction device according to one aspect of the present disclosure is an error correction device that realizes quantum error correction using a squeezed-cat code, and has a control unit that corrects quantum errors in the error correcting code quantum bits by repeatedly performing quantum information processing using a quantum processor that implements a quantum circuit including a quantum gate that realizes a dissipation operator constructed from a stabilizer operator in the momentum direction of the squeezed-cat state in the squeezed-cat code, on a quantum state represented by the error correcting code quantum bits and auxiliary quantum bits. [Effects of the Invention]

[0007] Quantum error correction in squeezed-CAT codes can be easily realized. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 10 is a diagram showing an example of the position and momentum of a GKP code and a squeezed-cat code in a phase plane display. [Figure 2] FIG. 1 is a diagram illustrating an example of a quantum circuit that realizes error correction using the Sharpen-Trim method. [Figure 3] FIG. 1 is a diagram illustrating an example of the configuration of a quantum computing device according to an embodiment of the present invention. [Figure 4] FIG. 2 is a diagram illustrating an example of a hardware configuration of a control device according to the present embodiment. [Figure 5] FIG. 2 is a diagram illustrating an example of a functional configuration of a control device according to the present embodiment. [Figure 6] 10 is a flowchart illustrating an error correction process according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0009] An embodiment of the present invention will be described in detail below with reference to the drawings. In the following embodiment, we propose a method for easily realizing quantum error correction in squeezed-Cat codes by applying the dissipation-based quantum error correction method proposed in GKP (Gottesman-Kitaev-Preskill) codes (Reference 1). More specifically, since GKP codes have imperfect translational symmetry with respect to both the position axis and the momentum axis on the phase plane, dissipation-based quantum error correction is performed by utilizing these translational symmetries. In contrast, since squeezed-Cat codes have translational symmetry only with respect to one axis (hereinafter referred to as the momentum axis) on the phase plane, the following embodiment proposes a method for performing dissipation-based quantum error correction only in the momentum direction. For simplicity, quantum error correction will also be referred to simply as "error correction" below.

[0010] Here, dissipation-based quantum error correction can be achieved by a simple operation of controlling the error-correcting code qubit in the quantum register from the auxiliary qubit and initializing the auxiliary qubit. Therefore, according to the proposed method, error correction in the squeezed-CAT code can be easily achieved with a simple operation.

[0011] <Advantages of applying dissipation-based error correction to compressed-CAT codes> As shown in Figure 1, the GKP code has imperfect translational symmetry with respect to both the position axis and the momentum axis on the phase plane. On the other hand, the squeezed-Cat code has imperfect translational symmetry only with respect to the momentum axis on the phase plane. Therefore, the squeezed-Cat code only requires dissipation-based error correction in the momentum direction. As a result, the depth of the error correction gate is shallower, which has the advantage of increasing tolerance to errors that occur in the ancillary qubits. The left and right figures in Figure 1 are plots of the quantum states of the GKP code and the squeezed-Cat code, respectively, on the phase plane. The horizontal axis represents the position axis, and the vertical axis represents the momentum axis. The Wigner function was used for the plots.

[0012] In addition, the GKP code has a drawback that there is a reading error because the logical 0 state and the logical 1 state are orthogonal only in the limit of infinite squeezing degree, and the logical 0 state and the logical 1 state cannot always be distinguished at a finite squeezing degree. On the other hand, the squeezed cat code has an advantage that the reading error can be suppressed low because the logical 0 state and the logical 1 state are orthogonal.

[0013] <Dissipation-based error correction method for GKP code> Hereinafter, as a preparation for explaining the proposed method, the outline of the dissipation-based error correction method for the GKP code, which is a conventional technique, will be described. For the details of the dissipation-based error correction method for the GKP code, for example, refer to Reference 1 etc.

[0014] For complex numbers ξ, z and annihilation operator a, displacement operator D(ξ) and squeezing operator S(z) are defined as follows, respectively.

[0015]

Equation

[0016] An ideal GKP code has complete translational symmetry, and its stabilizer operator can be written as S X = D(α), S Z = D(β). Here, α and β are generally complex numbers, and αβ * - α * β = 4iπ is satisfied. Hereinafter, α is assumed to be a real number and β is assumed to be a pure imaginary number.

[0017] An ideal GKP code state with infinite squeezing degree and infinite translational symmetry is expressed as follows for z → ∞.

[0018]

Equation

[0019] However, since it is impossible to realize a quantum state with infinite compression, a quantum state in which an operator called an envelope operator acts on the ideal quantum state is often used as a model of the quantum state for the code. Specifically, the envelope operator is as follows:

[0020]

number

[0021] In this case, the ideal GKP code state |gkp μ 〉(μ=0,1), the following quantum state obtained by applying the envelope operator shown in the above equation 3 is often used as a model of the quantum state for the code.

[0022]

number

[0023] Under the envelope operator shown in Equation 3, the stabilizer operator S X and S Z are changed as follows:

[0024]

number

[0025]

number

[0026]

number

[0027] Hereinafter, in the text of this specification, a bar "-" or a hat "^" placed above a symbol will be written immediately before the symbol. For example, in the text of this specification, the stabilizer operators shown in the above formula 6 will be written as " - S X,Δ " and " - S Z,Δ Similarly, for example, in the text of this specification, the position operator and momentum operator shown in Equation 7 above will be written as "^x" and "^p", respectively.

[0028] The stabilizer operator shown in Equation 6 above - S X,Δ and - S Z,Δ By constructing operators called dissipative operators from the above, it is possible to realize dissipative error correction from the dissipative operators to the GKP code space. Note that a dissipative operator is an operator that dissipates and descends a quantum state into the code space.

[0029] Below, stabilizer operators - S Z,Δ Let us consider the case where dissipative error correction is realized by constructing a dissipative operator from |gkp0〉 and |gkp1〉. The linear sum of |gkp0〉 and |gkp1〉 (where the sum of the squares of the norms of the coefficients is 1) is expressed as the GKP code state |ψ GKP 〉. In this case, the stabilizer operator - S Z,Δ Due to the nature of - S Z,Δ |ψ GKP 〉=|ψ GKP 〉. Therefore, the stabilizer operator - S Z,ΔWe can construct the following dissipative operator from

[0030]

number

[0031] The dissipation operator d shown in Eq. Δ,β' Since an environment is required to realize dissipation by Δ,β' For example, when the Sharpen-Trim method is used as the gate decomposition method, the dissipation operator d Δ,β' It can be decomposed into the following gate sequence, which performs dissipation using: Gate decomposition is a method of decomposing a quantum operation into a combination of basic quantum gates (gate sequences).

[0032]

number

[0033] The quantum gate (unitary operation) U shown in the above equation (9) ST (i) and U ST (ii) By using this, the quantum state of the error-correcting code qubit can be dissipated in the momentum direction of the GKP code space. Specifically, after preparing an ancillary qubit in the |0〉 state, we can dissipate the quantum state represented by the tensor product of the error-correcting code qubit and the ancillary qubit by using U ST (i) The operation of initializing an ancillary qubit after performing a gate operation by U ST(ii) By repeating the gate operation by and the operation of initializing the ancillary qubit, the quantum state of the error-correcting code qubit can be dissipated in the momentum direction of the GKP code space. - S X,Δ Similarly, we construct a dissipation operator for , and by decomposing the gates and performing gate operations so that dissipation using the dissipation operator can be performed, we can dissipate the quantum state of the error-correcting code qubit in the position direction of the GKP code space. This realizes dissipation-based error correction in the GKP code.

[0034] The quantum gate U ST (i) and U ST (ii) The error correction using can be implemented, for example, by the quantum circuit shown in Figure 2. The upper diagram of Figure 2 shows the quantum gate U ST (i) The figure below shows the quantum gate U ST (ii) Here, in Figure 2, l=(β' / 2)coshΔ 2 , ε=(β' / 2)sinhΔ 2 Also, R π / 2 represents a π / 2 rotation around the z-axis of the ancillary qubit system, and the black circle represents a control operation that means performing a gate operation when the quantum state of the ancillary qubit is |1〉. Furthermore, |+〉 represents the quantum state obtained by the Hadamard transform of the ancillary qubit in the |0〉 state, and Reset represents the initialization of the ancillary qubit. In this way, the quantum circuit shown in Figure 2 is implemented with simple operations: a control operation from the ancillary qubit to the error-correcting code qubit of the quantum register, and initialization of the ancillary qubit.

[0035] In addition to the Sharpen-Trim method, other gate decomposition methods exist, such as the Big-Small-Big method and the Small-Big-Small method. Even when gate decomposition is performed using these methods, it is known that the quantum circuit can be implemented with a simple operation of controlling the error-correcting code qubit of the quantum register from the ancillary qubit and initializing the ancillary qubit (Reference 1).

[0036] <Proposed method> In the proposed method, we apply the dissipation-based error correction method for GKP codes to one axis (momentum axis) of the squeezed-Cat code. Unless otherwise stated, the definition of each symbol is assumed to be the same as that of the dissipation-based error correction method for GKP codes.

[0037] The squeezed cat state is expressed as a superposition of two squeezed coherent states |ξ,z〉 = D(ξ)S(z)|0〉 and |-ξ,z〉, where ξ,z are real numbers. That is, the logic 0 and logic 1 states of the squeezed cat state are expressed as follows, respectively.

[0038]

number

[0039]

number

[0040] The infinitely compressed cat code has the following stabilizer operator as a momentum direction stabilizer (Reference 2):

[0041]

number

[0042]

number

[0043]

number

[0044]

number

[0045] Furthermore, the quantum gate U ST (i) and U ST (ii) Similar to the dissipation-based error correction method for GKP codes, error correction using the error correction code qubit can be realized with a quantum circuit implemented by simple operations of control operations from the auxiliary qubit to the error-correcting code qubit in the quantum register and initialization of the auxiliary qubit.

[0046] In addition to the Sharpen-Trim method, other gate decomposition methods include the Big-small-Big method, the small-Big-small method, etc., which can be used to calculate the dissipation operator d Δ,ξ Even in this case, the quantum circuit can be implemented by a simple operation of controlling the error-correcting code qubit in the quantum register from the ancillary qubit and initializing the ancillary qubit (Reference 1).

[0047] In this way, the proposed method can realize dissipation-based error correction in squeezed-CAT codes, and the error correction can be achieved using a quantum circuit implemented with simple operations: control operations from the auxiliary qubit to the error-correcting code qubit in the quantum register and initialization of the auxiliary qubit. Therefore, the proposed method makes it easy to realize quantum error correction in squeezed-CAT codes.

[0048] The quantum computing device 10 that realizes quantum error correction using the proposed method will be described below.

[0049] <Configuration example of quantum computing device 10> An example of the configuration of the quantum computing device 10 according to this embodiment will be described with reference to Fig. 3. Fig. 3 is a diagram showing an example of the configuration of the quantum computing device 10 according to this embodiment.

[0050] As shown in FIG. 3, the quantum computing device 10 according to this embodiment includes a control device 100 and a quantum processor 200.

[0051] The control device 100 transmits a control signal to the quantum processor 200 and obtains a calculation result from the quantum processor 200. This allows quantum calculation including quantum error correction to be performed. The control device 100 is realized by, for example, a classical computer or the like.

[0052] The quantum processor 200 configures a quantum two-level system called a qubit (physical qubit), and by executing a quantum circuit in response to a control signal from the control device 100, it realizes quantum information processing using physical operations such as initialization, gate operation (unitary operation), measurement, etc., for the physical qubit. There are no particular limitations on the quantum system for realizing the qubit, and any quantum system may be used. For example, quantum systems realized by superconducting circuits, ion traps, photons, quantum dots, etc. may be used.

[0053] In addition, the quantum computing device 10 according to this embodiment may be called, for example, a "quantum error correction device" or simply an "error correction device," since the control device 100 controls the quantum processor 200 to realize quantum error correction using the above-mentioned proposed method.

[0054] <Example of hardware configuration of control device 100> An example of the hardware configuration of the control device 100 according to this embodiment will be described with reference to Fig. 4. Fig. 4 is a diagram showing an example of the hardware configuration of the control device 100 according to this embodiment.

[0055] 4, the control device 100 according to this embodiment includes an input device 101, a display device 102, an external I / F 103, a communication I / F 104, a RAM (Random Access Memory) 105, a ROM (Read Only Memory) 106, an auxiliary storage device 107, and a processor 108. Each of these pieces of hardware is connected to each other via a bus 109 so as to be able to communicate with each other.

[0056] The input device 101 is, for example, a keyboard, a mouse, a touch panel, a physical button, etc. The display device 102 is, for example, a display, a display panel, etc. Note that the control device 100 does not necessarily have to have at least one of the input device 101 and the display device 102, for example.

[0057] The external I / F 103 is an interface with an external device such as a recording medium 103a. Examples of the recording medium 103a include a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), and a USB (Universal Serial Bus) memory card.

[0058] The communication I / F 104 is an interface for transmitting and receiving various signals to and from the quantum processor 200. The RAM 105 is a volatile semiconductor memory (storage device) that temporarily stores programs and data. The ROM 106 is a non-volatile semiconductor memory (storage device) that can store programs and data even when the power is turned off. The auxiliary storage device 107 is a non-volatile storage device (storage device) such as an HDD (Hard Disk Drive), SSD (Solid State Drive), or flash memory. The processor 108 is an arithmetic device such as a CPU (Central Processing Unit).

[0059] 4 is an example, and the hardware configuration of the control device 100 is not limited to this. For example, the control device 100 may have multiple auxiliary storage devices 107 or multiple processors 108, may not have some of the hardware shown in the figure, or may have various hardware other than the hardware shown in the figure.

[0060] <Example of functional configuration of control device 100> An example of the functional configuration of the control device 100 according to this embodiment will be described with reference to Fig. 5. Fig. 5 is a diagram showing an example of the functional configuration of the control device 100 according to this embodiment.

[0061] 5, the control device 100 according to this embodiment includes an initialization unit 110 and a gate operation unit 120. These units are realized, for example, by processing in which one or more programs installed in the control device 100 are executed by a processor 108 or the like.

[0062] The initialization unit 110 initializes the auxiliary quantum bits by controlling the quantum processor 200. The gate operation unit 120 controls the quantum processor 200 to perform various gate operations (unitary operations) on the quantum state represented by the tensor product of the error-correcting code quantum bit and the auxiliary quantum bit.

[0063] <Error correction processing> As an example, the dissipation operator d Δ,ξ The quantum gate U shown in Equation 15 can be implemented using ST (i) and U ST (ii) The error correction process when gate decomposition is performed will be described with reference to Fig. 6. Fig. 6 is a flowchart showing the error correction process in one embodiment.

[0064] The initialization unit 110 prepares an auxiliary quantum bit in the |0> state by controlling the quantum processor 200 (step S101). Hereinafter, the quantum state represented by the tensor product of the error-correcting code quantum bit and the auxiliary quantum bit will be referred to as |φ>.

[0065] The following steps S102 to S105 are repeatedly executed an appropriate number of times (for example, a number of times preset by the user, etc.).

[0066] The gate operation unit 120 controls the quantum processor 200 to generate U ST (i) A gate operation (unitary operation) is performed (step S102).

[0067] Initialization unit 110 initializes the ancillary quantum bits by controlling quantum processor 200 (step S103).

[0068] The gate operation unit 120 controls the quantum processor 200 to generate U ST (ii) Then, a gate operation (unitary operation) is performed (step S104).

[0069] Initialization unit 110 controls quantum processor 200 to initialize the ancillary quantum bits (step S105).

[0070] This achieves dissipation-based error correction in squeezed-CAT codes, removing quantum errors from error-correcting code qubits.

[0071] <Summary> As described above, the quantum computing device 10 according to this embodiment can realize dissipation-based error correction in the compressed-Cat code by applying a technique similar to the dissipation-based error correction method for the GKP code to the compressed-Cat code. Moreover, since the dissipation-based error correction in the compressed-Cat code can be realized by a quantum circuit implemented with simple operations (control operations and initialization of ancillary qubits), the quantum computing device 10 according to this embodiment can realize error correction in the compressed-Cat code with simple operations. In addition, the compressed-Cat code has the advantage of being able to reduce the gate depth compared to the GKP code and the advantage of being able to suppress read errors to a low level. Therefore, the quantum computing device 10 according to this embodiment can realize error correction with these advantages.

[0072] In the above embodiment, the dissipation operator d Δ,ξ However, for example, the Big-small-Big method or the small-Big-small method can be used to perform the dissipation operator d Δ,ξ In the Big-small-Big method and the small-Big-small method, the dissipative error correction corresponding to the dissipative operator d Δ,ξ Since one gate sequence can be obtained from the above, it is sufficient to repeat the gate operation using the quantum gate representing this gate sequence and the initialization of the ancillary quantum bit.

[0073] The present invention is not limited to the above-described specifically disclosed embodiments, and various modifications, changes, and combinations with known technologies are possible without departing from the scope of the claims.

[0074] [References] Reference 1: Royer, B., Singh, S., and Girvin, SM (2020). Stabilization of finite-energy Gottesman-Kitaev-Preskill states. Physical Review Letters, 125(26), 260509. Reference 2: Endo, S., Anai, K., Matsuzaki, Y., Tokunaga, Y., & Suzuki, Y. (2024). Projective squeezing for translation symmetric bosonic codes. arXiv preprint arXiv:2403.14218. [Explanation of symbols]

[0075] 10 Quantum computing device 100 control device 101 Input Device 102 Display device 103 External I / F 103a Recording media 104 Communication I / F 105 RAM 106 ROM 107 Auxiliary storage 108 processors 109 Bus 200 quantum processors 110 Initialization section 120 Gate operation unit

Claims

1. An error correction device that realizes quantum error correction using a compressed cat code, a control unit that corrects quantum errors in the error-correcting code quantum bits by repeatedly executing quantum information processing by the quantum circuit on quantum states represented by error-correcting code quantum bits and auxiliary quantum bits, using a quantum processor that implements a quantum circuit including a quantum gate that realizes a dissipation operator constructed from a stabilizer operator in the momentum direction of the squeezed-cat state in the squeezed-cat code; An error correction device having:

2. The quantum circuit comprises:

2. The error correction device according to claim 1, further comprising a gate sequence obtained by decomposing the dissipative operator into gates using a predetermined gate decomposition technique.

3. The gate decomposition technique includes:

3. The error correction device according to claim 2, wherein the error correction method is one of the Sharpen-Trim method, the Big-Small-Big method, and the Small-Big-Small method.

4. The quantum circuit comprises: The error correction device according to claim 2 or 3, further comprising the gate sequence and the initialization of the ancillary quantum bit.

5. An error correction method for realizing quantum error correction using a compressed cat code, a control procedure for correcting quantum errors in the error-correcting code qubits by repeatedly executing quantum information processing by a quantum processor that implements a quantum circuit including a quantum gate that realizes a dissipation operator constructed from a stabilizer operator in the momentum direction of the squeezed-cat state in the squeezed-cat code, on a quantum state represented by an error-correcting code qubit and an ancillary qubit; A method by which a computer performs error correction.

6. A program for realizing quantum error correction using a compressed cat code, a control procedure for correcting quantum errors in the error-correcting code qubits by repeatedly executing quantum information processing by a quantum processor that implements a quantum circuit including a quantum gate that realizes a dissipation operator constructed from a stabilizer operator in the momentum direction of the squeezed-cat state in the squeezed-cat code, on a quantum state represented by an error-correcting code qubit and an ancillary qubit; A program that causes a computer to execute the following.

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