Information processing device, control device, information processing method, and program

Abstract

When performing a solution search using a k-parametric oscillator, if candidate solutions have been obtained, these obtained candidate solutions should be incorporated into the solution search. [Solution] The information processing device comprises a quantum computing circuit and a control means, the quantum computing circuit comprises a qubit element using a parametric oscillator having Kerr nonlinearity, and the control means initializes the quantum state of the qubit element to show one of the two values ​​of the qubit using a coherent drive signal, and then controls the quantum computing circuit to increase the detuning of the qubit element.

Description

[Technical Field]

[0001] The present invention relates to an information processing device, a control device, an information processing method, and a program. [Background technology]

[0002] Quantum annealing is sometimes performed using a parametric oscillator. For example, Patent Document 1 describes setting the initial state of a parametric oscillator to a vacuum state and gradually increasing the pump amplitude of the parametric amplification from zero. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2017-073106 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] When using a k-parametric oscillator to search for solutions to combinatorial optimization problems, if candidate solutions are available, it is expected that incorporating these candidate solutions into the solution search will make it easier to obtain the desired solution, depending on the candidate solutions.

[0005] One example of the purpose of this disclosure is to provide an information processing device, a control device, an information processing method, and a program that can solve the above-mentioned problems. [Means for solving the problem]

[0006] According to a first aspect of the present disclosure, the information processing device comprises a quantum computing circuit and a control means, the quantum computing circuit comprises a qubit element using a parametric oscillator having Kerr nonlinearity, and the control means initializes the quantum state of the qubit element to show one of the two values ​​of the qubit using a coherent drive signal, and then controls the quantum computing circuit to increase the detuning of the qubit element.

[0007] According to a second aspect of the present disclosure, the control device includes a control means for controlling a quantum computing circuit that comprises a qubit element using a parametric oscillator having Kerr nonlinearity, after initializing the quantum state of the qubit element to show one of the two values ​​of the qubit using a coherent drive signal, and then increasing the detuning of the qubit element.

[0008] According to a third aspect of this disclosure, the information processing method includes a computer controlling a quantum computing circuit comprising a qubit element having a Kerr nonlinearity, initializing the quantum state of the qubit element to show one of the two values ​​of the qubit using a coherent drive signal, and then controlling the quantum computing circuit to increase the detuning of the qubit element.

[0009] According to a fourth aspect of this disclosure, the program is a program that causes a computer that controls a quantum computing circuit equipped with a qubit element having Kerr nonlinearity to initialize the quantum state of the qubit element using a coherent drive signal to show one of the two values ​​of the qubit, and then control the quantum computing circuit to increase the detuning of the qubit element. [Effects of the Invention]

[0010] According to this disclosure, when performing a solution search using a k-parametric oscillator, if candidate solutions have been obtained, these candidate solutions can be reflected in the solution search. [Brief explanation of the drawing]

[0011] [Figure 1] This figure shows an example of the configuration of an information processing device according to at least one embodiment. [Figure 2] This figure shows an example of the time evolution of the values ​​of each parameter in a first control method according to at least one embodiment. [Figure 3] This figure shows a first example of the initial state of the qubit element 110 in a first control method according to at least one embodiment. [Figure 4] This figure shows a second example of the initial state of the qubit element 110 in a first control method according to at least one embodiment. [Figure 5] This figure shows an example of the expected value of the position operator of the quantum state of the first qubit element in Case 1 of the first control method according to at least one embodiment. [Figure 6] This figure shows an example of the expectation value of the position operator of the quantum state of the second qubit element in Case 1 of the first control method according to at least one embodiment. [Figure 7] This figure shows an example of the dispersion of the position operator of the quantum state of the first qubit element in Case 1, using a first control method according to at least one embodiment. [Figure 8] This figure shows an example of the dispersion of the position operator of the quantum state of the second qubit element in Case 1 of the first control method according to at least one embodiment. [Figure 9] This figure shows an example of the expectation value of the position operator of the quantum state of the first qubit element in Case 2 of the first control method according to at least one embodiment. [Figure 10] This figure shows an example of the expectation value of the position operator of the quantum state of the second qubit element in Case 2 of the first control method according to at least one embodiment. [Figure 11] This figure shows an example of the dispersion of the position operator of the quantum state of the first qubit element in Case 2 of the first control method according to at least one embodiment. [Figure 12] This figure shows an example of the dispersion of the position operator of the quantum state of the second qubit element in Case 2 of the first control method according to at least one embodiment. [Figure 13] This figure shows an example of the expected value of the position operator of the quantum state of the first qubit element in Case 3, using a first control method according to at least one embodiment. [Figure 14] This figure shows an example of the expectation value of the position operator of the quantum state of the second qubit element in Case 3, using the first control method according to at least one embodiment. [Figure 15] This figure shows an example of the dispersion of the position operator of the quantum state of the first qubit element in Case 3, using a first control method according to at least one embodiment. [Figure 16] This figure shows an example of the dispersion of the position operator of the quantum state of the second qubit element in Case 3, using a first control method according to at least one embodiment. [Figure 17] This figure shows an example of the expected value of the position operator of the quantum state of the first qubit element in Case 4 of the first control method according to at least one embodiment. [Figure 18] This figure shows an example of the expectation value of the position operator of the quantum state of the second qubit element in Case 4 of the first control method according to at least one embodiment. [Figure 19] This figure shows an example of the dispersion of the position operator of the quantum state of the first qubit element in Case 4 of the first control method according to at least one embodiment. [Figure 20] This figure shows an example of the dispersion of the position operator of the quantum state of the second qubit element in Case 4 of the first control method according to at least one embodiment. [Figure 21] This figure shows an example of the time evolution of the values ​​of each parameter in a second control method according to at least one embodiment. [Figure 22] This figure shows a first example of the initial state of a qubit element in a second control method according to at least one embodiment. [Figure 23] This figure shows a second example of the initial state of a qubit element in a second control method according to at least one embodiment. [Figure 24] This figure shows an example of the expectation value of the position operator of the quantum state of the first qubit element in Case 1, using a second control method according to at least one embodiment. [Figure 25] This figure shows an example of the expectation value of the position operator of the quantum state of the second qubit element in Case 1, using a second control method according to at least one embodiment. [Figure 26] This figure shows an example of the dispersion of the position operator of the quantum state of the first qubit element in Case 1, using a second control method according to at least one embodiment. [Figure 27] This figure shows an example of the dispersion of the position operator of the quantum state of the second qubit element in Case 1, using a second control method according to at least one embodiment. [Figure 28] This figure shows an example of the expectation value of the position operator of the quantum state of the first qubit element in Case 2 of the second control method according to at least one embodiment. [Figure 29] This figure shows an example of the expectation value of the position operator of the quantum state of the second qubit element in Case 2 of the second control method according to at least one embodiment. [Figure 30] This figure shows an example of the dispersion of the position operator of the quantum state of the first qubit element in Case 2 of the second control method according to at least one embodiment. [Figure 31] This figure shows an example of the dispersion of the position operator of the quantum state of the second qubit element in Case 2 of the second control method according to at least one embodiment. [Figure 32] This figure shows an example of the expectation value of the position operator of the quantum state of the first qubit element in Case 3, using a second control method according to at least one embodiment. [Figure 33]This figure shows an example of the expectation value of the position operator of the quantum state of the second qubit element in Case 3, using a second control method according to at least one embodiment. [Figure 34] This figure shows an example of the dispersion of the position operator of the quantum state of the first qubit element in Case 3, using a second control method according to at least one embodiment. [Figure 35] This figure shows an example of the dispersion of the position operator of the quantum state of the second qubit element in Case 3, using a second control method according to at least one embodiment. [Figure 36] This figure shows an example of the expectation value of the position operator of the quantum state of the first qubit element in Case 4, using a second control method according to at least one embodiment. [Figure 37] This figure shows an example of the expectation value of the position operator of the quantum state of the second qubit element in Case 4, using a second control method according to at least one embodiment. [Figure 38] This figure shows an example of the dispersion of the position operator of the quantum state of the first qubit element in Case 4, using a second control method according to at least one embodiment. [Figure 39] This figure shows an example of the dispersion of the position operator of the quantum state of the second qubit element in Case 4, using a second control method according to at least one embodiment. [Figure 40] This figure shows a first example of the procedure for processing performed by an information processing device 1 according to at least one embodiment. [Figure 41] This figure shows a second example of the processing procedure performed by the information processing device 1 according to at least one embodiment. [Figure 42] This figure shows an example of the configuration of an information processing device according to at least one embodiment. [Figure 43] This figure shows an example of the configuration of a control device according to at least one embodiment. [Figure 44] This figure shows an example of a processing procedure in an information processing method according to at least one embodiment. [Figure 45]This figure shows an example of a computer configuration according to at least one embodiment. [Modes for carrying out the invention]

[0012] The embodiments will be described below with reference to the drawings. In the following, the dagger symbol will be referred to as: + It is sometimes represented with a superscript +.

[0013] <First Embodiment> Figure 1 shows an example of the configuration of an information processing device according to at least one embodiment. In the configuration shown in Figure 1, the information processing device 1 comprises a quantum computing circuit 100, a control unit 200, and an observation unit 300. The quantum computing circuit 100 comprises a qubit element 110 and a coupler 120.

[0014] The qubit element 110 is constructed using a Kerr nonlinear parametric oscillator. A Kerr nonlinear parametric oscillator is a parametric oscillator that possesses Kerr nonlinearity. The coupler 120 interacts with multiple qubit elements 110 according to the control of the control unit 200.

[0015] The information processing device 1 performs quantum annealing. Quantum annealing, in this context, is the process of searching for an estimated solution to an optimization problem by utilizing the quantum mechanical properties of qubit elements. In this context, an estimated solution is the value of the objective variable (the variable being sought) in an optimization problem, or the qubit value representing the objective variable in an optimization problem. The term "estimated" in "estimated solution" means that it is not necessarily the optimal solution. An estimated solution is also referred to as a candidate solution, or simply a solution.

[0016] One method for performing quantum annealing using a Kerr nonlinear parametric oscillator as a qubit element is to perform quantum annealing with the initial state of the qubit element (initial state of the quantum state) set to a vacuum state. In response, the information processing device 1 performs quantum annealing by setting the initial state of the qubit element 110 to a state that represents some estimated solution. According to the information processing device 1, the estimated solution can be reflected in the solution search by quantum annealing. For example, if the estimated solution set as the initial state of the qubit element 110 is relatively close to the optimal solution, it is expected that the information processing device 1 can obtain the optimal solution in a shorter time than when quantum annealing is performed with the initial state of the qubit element in a vacuum state. In this context, setting the estimated solution as the initial state of the qubit element 110 means setting the initial state of the qubit element 110 to a state that represents the estimated solution.

[0017] The estimated solution that the information processing device 1 sets as the initial state of the qubit element 110 is not limited to a specific one. For example, the information processing device 1 may set the estimated solution obtained by quantum annealing as the initial state of the qubit element 110. Alternatively, the information processing device 1 may set the estimated solution that is relatively close to the optimal solution, such as an estimated solution obtained manually, as the initial state of the qubit element 110. Alternatively, the information processing device 1 may randomly determine the value of the qubit to be set as the initial state of each qubit element 110 to one of the two values ​​of the qubit. If the desired solution, such as the optimal solution, cannot be obtained, the information processing device 1 may change the estimated solution set as the initial state of the qubit element 110 to another estimated solution and perform quantum annealing again.

[0018] In the case of an information processing device (quantum annealing machine) that uses a transverse magnetic field to create a quantum superposition state of a qubit element, it is conceivable to set an optimal solution as the initial state of the qubit element, and then use the transverse magnetic field to bring the state of the qubit element closer to a quantum superposition state before performing quantum annealing.

[0019] On the other hand, in an information processing device that uses a Kerr nonlinear parametric oscillator as a qubit element, a pump signal and a coherent drive signal are input to the qubit element, and the quantum state of the qubit element is controlled using the pump strength (amplitude of the pump signal) and detuning (detuning of the Kerr nonlinear parametric oscillator) as control parameters to perform quantum annealing.

[0020] In this case, an information processing device using a Kerr nonlinear parametric oscillator as a qubit element does not use a transverse magnetic field, nor does it perform any operation to bring the state of the qubit element closer to a quantum superposition state. In this regard, it was unclear whether it was possible to perform quantum annealing by setting an estimated solution as the initial state of a qubit element in an information processing device that uses a Kerr nonlinear parametric oscillator as a qubit element, and if so, how to perform quantum annealing. In response to this, the inventors of the present invention have found that in an information processing device using a Kerr nonlinear parametric oscillator as a qubit element, it is possible to perform quantum annealing by setting an estimated solution as the initial state of the qubit element, and have also found a method for performing this.

[0021] The control unit 200 controls the quantum computing circuit 100 to perform quantum annealing. In particular, the control unit 200 controls the state of the qubit element 110 by inputting a pump signal and a coherent drive signal to the qubit element 110. At the start of quantum annealing (the start of a single solution search by quantum annealing), the control unit 200 uses the coherent drive signal to set the estimated solution as the initial state of the qubit element 110. Furthermore, the control unit 200 controls the coupling strength of the qubit elements 110 by the coupler 120 (the strength of the interaction of the qubit elements 110).

[0022] The control unit 200 is an example of a control means. The control unit 200 may be configured using a von Neumann type computer. The information processing device 1 is an example of a control device in that it includes a control unit 200. Alternatively, a control device may be provided separately from the quantum computing circuit 611, and this control device may include the control unit 200.

[0023] The control unit 200 controls the quantum computing circuit 100 to perform quantum annealing, for example, based on the Hamiltonian H shown in equation (1).

[0024]

number

[0025] N is an integer such that N≧1, representing the number of qubit elements 110. In equation (1), i and j are both identification numbers that identify the N qubit elements 110, and are integers such that 1≦i,j≦N. The qubit element 110 identified by identification number i is also referred to as the i-th qubit element 110. t represents the time in one quantum annealing (one solution search using quantum annealing). Time 0 is defined as the start of quantum annealing, and time T is defined as the end of quantum annealing. Time T represents the quantum annealing time.

[0026] Δ(t) represents the detuning at time t. Detuning of a Kerr nonlinear parametric oscillator is the deviation of the oscillation frequency from the resonant frequency. a + i This indicates the creation operator at the i-th qubit element 110. a i This indicates the annihilation operator in the i-th qubit element 110.

[0027] K exhibits Kerr nonlinearity. p(t) represents the pump strength at time t. The pump strength is represented by the amplitude of the pump signal input to the qubit element 110. The pump signal is a signal that functions as a pump in parametric oscillation.

[0028] ε i indicates the qubit value set as the initial state for the i-th qubit element 110. ε i takes either the value of -1 or +1. "C(t)(ε i / 2)(a + i +a i )" is a term of the Hamiltonian for the initialization of the qubit element 110. The larger the value of the coefficient C(t), the stronger the control of the initial state setting for the qubit element 110.

[0029] The value of the coefficient C(t) is reflected, for example, in the intensity of the coherent drive signal input to the qubit element 110. The coherent drive signal is a signal for adjusting the coherent state of the qubit element 110. The control unit 200 weakens the intensity of the coherent drive signal as the value of the coefficient C(t) becomes smaller. The control unit 200 may input a coherent drive with an intensity proportional to the value of the coefficient C(t) to the qubit element 110.

[0030] "B(t)[Σ i=1 N-1 Σ j=i+1 N J ij (a + i a j +a i a + j )+Σ i=1 N h i (a + i +a i )]" is a term of the Hamiltonian indicating the optimization problem to be solved. The larger the value of the coefficient B(t), the stronger the control for exploring the estimated solution according to the optimization problem for the qubit element 110. The value of the coefficient B(t) is reflected, for example, in the coupling strength of the qubit element 110 by the coupler 120.

[0031] The coefficient J ij corresponds to the coefficient of the quadratic term (the term by the product of two binary variables) in the optimization problem. coefficient h i This corresponds to the coefficient of the linear term (a term involving one binary variable) in the optimization problem.

[0032] The observation unit 300 obtains the estimated solution obtained by quantum annealing by observing the state of the qubit element 110. The control unit 200 may set the estimated solution acquired by the observation unit 300 as the initial state of the qubit element 110, causing the quantum computing circuit 100 to perform quantum annealing again.

[0033] The control unit 200 may decrease the pump strength (the amplitude of the pump signal input to the qubit element 110) and then increase it. Alternatively, the control unit 200 may increase the pump strength from zero or a sufficiently small strength. The control method by which the control unit 200 temporarily reduces the pump strength and then increases it is also referred to as the first control method. A control method by which the control unit 200 increases the pump strength from 0 or a sufficiently low strength is also referred to as a second control method.

[0034] (Regarding the first control method) As an example of the first control method, we conducted a simulation experiment using the Hamiltonian H shown in equation (2).

[0035]

number

[0036] Equation (2) is obtained by setting the following in equation (1). The number of qubit elements 110 is N=2. Detuning Δ(t)=Γsin(πt / T), Pump strength p(t) = p1(1-Γsin(πt / T)), The coefficient of the Hamiltonian term for the initialization of the qubit element 110 is C(t) = 1 - t / T. The coefficient B(t) = t / T of the Hamiltonian term representing the optimization problem to be solved, Coefficient J 12 =-1, The coefficients h1 = -1 and h2 = 0. Γ is a constant for Γ>0. Furthermore, the Kerr nonlinearity K=1 and the initial value of the pump strength P1=4 were assumed.

[0037] Figure 2 shows an example of the time evolution of the values ​​of each parameter in the first control method. Figure 2 shows an example of the time evolution of the values ​​of each parameter when using the Hamiltonian shown in equation (2). The horizontal axis of the graph in Figure 2 represents the time in a single quantum annealing cycle. As described above, time 0 represents the start of the quantum annealing cycle, and time T represents the end of the quantum annealing cycle. The vertical axis of the graph in Figure 2 represents the parameter values.

[0038] Line L111 shows the detuning Δ(t) at each time interval t. In the example in Figure 2, the control unit 200 sets the initial value of detuning Δ(t) to 0, increases detuning Δ(t) as time progresses, and then decreases it back to 0. Line L112 shows the pump strength p(t) at each time interval t. In the example in Figure 2, the control unit 200 first decreases the pump strength p(t) from the initial value p1, and then increases it back to p1.

[0039] Line L113 shows the value of the coefficient B(t) of the Hamiltonian term representing the optimization problem to be solved, at each time t. In the example in Figure 2, the control unit 200 increases the value of the coefficient B(t) from 0 to the final value B(1). The final value B(1) may be a predetermined value. Line L114 shows the value of the coefficient C(t) of the Hamiltonian term for initializing the qubit element 110 at each time t. In the example in Figure 2, the control unit 200 decreases the value of the coefficient C(t) from its initial value C(0) to 0. The initial value C(0) of the coefficient C(t) may be a predetermined value.

[0040] Figure 3 shows a first example of the initial state of the qubit element 110 in the first control method. Figure 3 shows the initial state of the i-th qubit element 110 as ε i This shows a plot of the Wigner function when set to +1. In the graph in Figure 3, the horizontal axis (y-coordinate) represents the expectation value of the quantum state of the qubit element 110 with respect to the momentum operator p. This shows the expected value of the quantum state of the qubit element 110 with respect to the position operator x. The vertical axis (x coordinate) represents the expected value of the quantum state of the qubit element 110 with respect to the position operator x. <x>This indicates.

[0041] In this case, the initial state of the i-th qubit element 110 is |+α1> i This results in a coherent state. The subscript index "1" in "α" indicates the eigenvalue for the annihilation operator "a" of the coherent state generated under the initial Hamiltonian being considered here. Specifically, α1 = √(p1 / K), and it is written as "α1" to match the subscript "1" of "p1".

[0042] In the example in Figure 3, the function values ​​are plotted in the positive x-coordinate region, at a position relatively far from x=0. With the initial parameter settings shown in Figure 2, the pump strength is made sufficiently large for detuning, and the coefficient C(t) is made sufficiently large relative to the coefficient B(t), ε i The state of =+1 can be considered to be relatively strongly reflected as the initial state of the qubit element 110. The example in Figure 3 corresponds to an example in which the quantum state of the qubit element 110 is initialized to show the value +1 out of the two values ​​of the qubit, +1 and -1.

[0043] Expected value of position operator x <x>This can be understood as representing the qubit value indicated by the quantum state of the qubit element 110. Expected value <x>If it is a positive value, it indicates a qubit value of "+1". Expected value <x>If the value is negative, it indicates a qubit value of "-1". Expected value <x>The magnitude (absolute value) can be understood as representing the strength with which the quantum state of the qubit element 110 exhibits a qubit value.

[0044] The variance of the position operator x is √( <x 2 >- <x> 2 ) can be considered to represent the high probability that the qubit value will be correctly read from the quantum state of the qubit element 110. Variance √( <x 2 >- <x> 2 The larger the value of ), the higher the probability that the qubit value will be incorrectly read from the quantum state of the qubit element 110. Also, expected value <x>The smaller the magnitude (absolute value) of the qubit, the higher the probability that the qubit value will be incorrectly read from the quantum state of the qubit element 110.

[0045] Figure 4 shows a second example of the initial state of the qubit element 110 in the first control method. Figure 4 shows the initial state of the i-th qubit element 110 as ε i The plot of the Wigner function when = -1 is shown. In the graph in Figure 4, the horizontal axis (y-coordinate) represents the expectation value of the quantum state of the qubit element 110 with respect to the momentum operator p.< / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> This shows the expected value of the quantum state of the qubit element 110 with respect to the position operator x. The vertical axis (x coordinate) represents the expected value of the quantum state of the qubit element 110 with respect to the position operator x. <x>This indicates.

[0046] In this case, the initial state of the i-th qubit element 110 is |-α1> i It enters a coherent state. In the example in Figure 4, the function values ​​are plotted in the negative region of the x-coordinate, at a position relatively far from x=0. With the initial parameter settings shown in Figure 2, the pump strength is made sufficiently large for detuning, and the coefficient C(t) is made sufficiently large relative to the coefficient B(t), ε i The state =-1 can be considered to be a relatively strong reflection of the initial state of the qubit element 110. The example in Figure 4 corresponds to an example in which the quantum state of the qubit element 110 is initialized to show the value -1, out of the two values ​​of a qubit, +1 and -1.

[0047] In the first control method, Case 1: Initial state of the first qubit element 110 ε1=+1, initial state of the second qubit element 110 ε2=+1, Case 2: Initial state of the first qubit element 110 ε1=+1, initial state of the second qubit element 110 ε2=-1, Case 3: Initial state of the first qubit element 110 ε1=-1, initial state of the second qubit element 110 ε2=+1, Case 4: Initial state of the first qubit element 110 ε1=-1, initial state of the second qubit element 110 ε2=-1, For each of these, the value of the constant Γ in equation (2) was set to various values, and quantum annealing was performed at various quantum annealing times to calculate the expected value and variance of the position operator of the quantum state of the qubit element 110. Here, the quantum annealing time is represented as a dimensionless quantity normalized by the reciprocal of the Kerr coefficient. For example, if the Kerr coefficient is 1 megahertz (MHz), the quantum annealing time T=1 corresponds to 1 microsecond (μs).

[0048] (First control method, Case 1 (ε1=+1, ε2=+1)) Figure 5 shows an example of the expected value of the position operator of the quantum state of the first qubit element 110 in Case 1 using the first control method. In the graph in Figure 5, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing. <x>This indicates.

[0049] Line L211 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 as a vacuum state. Line L211 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L212 to L216.

[0050] Line L212 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L213 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L214 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L215 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L216 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0051] Figure 6 shows an example of the expected value of the position operator of the quantum state of the second qubit element 110 in Case 1 using the first control method. In the graph in Figure 6, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing. <x>This indicates.

[0052] Line L221 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L221 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L222 to L226.

[0053] Line L222 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L223 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L224 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L225 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L226 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0054] Figure 7 shows an example of the dispersion of the position operator of the quantum state of the first qubit element 110 in Case 1 using the first control method. In the graph in Figure 7, the horizontal axis represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0055] Line L231 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 as a vacuum state. Line L231 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L232 to L236.

[0056] Line L232 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L233 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L234 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.6. Line L235 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.8. Line L236 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0057] Figure 8 shows an example of the dispersion of the position operator of the quantum state of the second qubit element 110 in Case 1 using the first control method. The horizontal axis of the graph in Figure 8 represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0058] Line L241 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L241 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L242 to L246.

[0059] Line L242 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L243 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L244 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.6. Line L245 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.8. Line L246 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0060] (First control method, Case 2 (ε1=+1, ε2=-1)) Figure 9 shows an example of the expected value of the position operator of the quantum state of the first qubit element 110 in Case 2 using the first control method. In the graph in Figure 9, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing. <x>This indicates.

[0061] Line L251 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L251 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L252 to L256.

[0062] Line L252 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L253 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L254 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L255 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L256 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0063] Figure 10 shows an example of the expected value of the position operator of the quantum state of the second qubit element 110 in Case 2 using the first control method. In the graph in Figure 10, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing. <x>This indicates.

[0064] Line L261 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L261 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L262 to L266.

[0065] Line L262 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L263 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L264 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L265 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L266 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0066] Figure 11 shows an example of the dispersion of the position operator of the quantum state of the first qubit element 110 in Case 2 using the first control method. The horizontal axis of the graph in Figure 11 represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0067] Line L271 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 as a vacuum state. Line L271 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L272 to L276.

[0068] Line L272 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L273 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L274 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.6. Line L275 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.8. Line L276 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0069] Figure 12 shows an example of the dispersion of the position operator of the quantum state of the second qubit element 110 in Case 2 using the first control method. In the graph in Figure 12, the horizontal axis represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0070] Line L281 shows the variance of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 as a vacuum state. Line L281 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L282 to L286.

[0071] Line L282 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L283 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L284 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.6. Line L285 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.8. Line L286 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0072] (First control method, Case 3 (ε1=-1, ε2=+1)) Figure 13 shows an example of the expected value of the position operator of the quantum state of the first qubit element 110 in Case 3 using the first control method. In the graph in Figure 13, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing. <x>This indicates.

[0073] Line L291 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 as a vacuum state. Line L211 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L292 to L296.

[0074] Line L292 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L293 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L294 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L295 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L296 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0075] Figure 14 shows an example of the expected value of the position operator of the quantum state of the second qubit element 110 in Case 3 using the first control method. In the graph in Figure 14, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing. <x>This indicates.

[0076] Line L301 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L301 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L302 to L306.

[0077] Line L302 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L303 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L304 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L305 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L306 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0078] Figure 15 shows an example of the dispersion of the position operator of the quantum state of the first qubit element 110 in Case 3 using the first control method. In the graph in Figure 15, the horizontal axis represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0079] Line L311 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 as a vacuum state. Line L311 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L312 to L316.

[0080] Line L312 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L313 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L314 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.6. Line L315 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.8. Line L316 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0081] Figure 16 shows an example of the dispersion of the position operator of the quantum state of the second qubit element 110 in Case 3 using the first control method. In the graph in Figure 16, the horizontal axis represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0082] Line L321 shows the variance of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L321 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L322 to L326.

[0083] Line L322 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L323 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L324 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.6. Line L325 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.8. Line L326 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0084] (First control method, case 4 (ε1=-1, ε2=-1)) Figure 17 shows an example of the expected value of the position operator of the quantum state of the first qubit element 110 in Case 4 using the first control method. In the graph in Figure 17, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing. <x>This indicates.

[0085] Line L331 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L331 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L332 to L336.

[0086] Line L332 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L333 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L334 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L335 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L336 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0087] Figure 18 shows an example of the expected value of the position operator of the quantum state of the second qubit element 110 in Case 4 using the first control method. In the graph in Figure 18, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing. <x>This indicates.

[0088] Line L341 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L341 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L342 to L346.

[0089] Line L342 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L343 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L344 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L345 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L346 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0090] Figure 19 shows an example of the dispersion of the position operator of the quantum state of the first qubit element 110 in Case 4 using the first control method. The horizontal axis of the graph in Figure 19 represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0091] Line L351 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 as a vacuum state. Line L351 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L352 to L356.

[0092] Line L352 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.2. Line L353 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L354 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.6. Line L355 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.8. Line L356 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0093] Figure 20 shows an example of the dispersion of the position operator of the quantum state of the second qubit element 110 in Case 4 using the first control method. The horizontal axis of the graph in Figure 20 represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0094] Line L361 shows the variance of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 as a vacuum state. Line L361 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L362 to L366.

[0095] Line L362 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L363 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L364 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.6. Line L365 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.8. Line L366 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0096] In the experiment, the optimal solution is obtained when the values ​​of both qubits are +1. Therefore, in the examples from Figure 5 to Figure 20, it can be seen that the larger the expected value (a large positive value and large magnitude) and the smaller the variance of the position operator at the end of quantum annealing for both the first qubit element 110 and the second qubit element 110, the easier it is to obtain the optimal solution. In particular, when the expected value of the position operator at the end of quantum annealing is larger and the variance is smaller than when quantum annealing is performed with the initial state being a vacuum, it is expected that the probability of obtaining the optimal solution will be higher by setting the estimated solution as the initial value of the qubit element 110.

[0097] When we examine the experimental results (simulation results) for each case, in Case 1 (ε1=+1, ε2=+1), the expected value is larger and the variance is smaller than when the initial state is a vacuum, in all cases of Γ=0.2, Γ=0.4, and Γ=0.6. Also, when Γ=0.8, approximately T≦3×10 -1 When, and approximately T ≥ 1.5 × 10 0 In this case, the expected value is larger and the variance is smaller than when the initial state is a vacuum. Also, when Γ=1.0, T ≤ 2.5 × 10 -1 When, and approximately T ≥ 4 × 10 0 In this case, the expected value is larger and the variance is smaller than when the initial state is a vacuum.

[0098] In Case 2 (ε1=+1, ε2=-1), when Γ=0.8, T≧4×10 0 In this case, the expected value is larger and the variance is smaller than when the initial state is a vacuum. Also, when Γ=1.0, T≧2×10 0 In this case, the expected value is larger and the variance is smaller than when the initial state is a vacuum.

[0099] In Case 3 (ε1=-1, ε2=+1), when Γ=0.6, it is approximately 3 × 10 0 ≤T ≤ 1 × 10 1 In this case, the expected value is larger and the variance is smaller than when the initial state is a vacuum. Also, when Γ=0.8, it is approximately 3 × 10 0 ≤T ≤ 8 × 10 0 In this case, the expected value is larger and the variance is smaller than when the initial state is a vacuum. Also, when Γ=1.0, it is approximately 3 × 10 0 ≤T ≤ 1 × 10 1 In this case, the expected value is larger and the variance is smaller than when the initial state is a vacuum.

[0100] In case 4 (ε1=-1, ε2=-1), when Γ=0.8, it is approximately 7×10 -1 ≤T ≤ 2 × 10 0 In this case, the expected value is larger and the variance is smaller than when the initial state is a vacuum. Also, when Γ=1.0, it is approximately 7×10 -1 ≤T ≤ 1 × 10 1 In this case, the expected value is larger and the variance is smaller than when the initial state is a vacuum.

[0101] According to experimental results, for example, in the case of the Hamiltonian shown in equation (2), if Γ = 0.8, then 4 × 10 0 ≤T ≤ 2 × 10 0 Therefore, it is expected that there is a higher probability of obtaining the optimal solution than when the initial state is a vacuum. Also, if we set Γ=1.0, 4×10 0 ≤T ≤ 1 × 10 1 Therefore, it is expected that there is a higher probability of obtaining the optimal solution than when the initial state is a vacuum.

[0102] This can be interpreted as meaning that when Γ=0.8 or Γ=1.0, the desired solution can be expected to be obtained in a shorter time than when the initial state is a vacuum. Alternatively, the information processing device 1 may repeatedly perform quantum annealing while changing the settings of the constant Γ and the quantum annealing time T. Furthermore, the information processing device 1 may repeatedly perform quantum annealing while changing not only the constant Γ and the quantum annealing time T, but also the estimated solution set as the initial value of the qubit element 110.

[0103] (Regarding the second control method) As an example of a second control method, we conducted a simulation experiment using the Hamiltonian H shown in equation (3).

[0104]

number

[0105] Comparing equation (3) with equation (2), the setting of the pump strength p(t) in equation (1) is different. In equation (2), p(t) = p1(1-Γsin(πt / T)), whereas in equation (3), p(t) = (p1 / 2)(t / T). In all other respects, equation (3) is the same as equation (2). In the experiment with the second control method, the Kerr nonlinearity K=1 and the initial value of the pump strength P1=4 were also used.

[0106] Figure 21 shows an example of the time evolution of the values ​​of each parameter in the second control method. Figure 21 shows an example of the time evolution of the values ​​of each parameter when using the Hamiltonian shown in equation (3). The horizontal axis of the graph in Figure 21 represents the time in a single quantum annealing cycle. As described above, time 0 represents the start of the quantum annealing cycle, and time T represents the end of the quantum annealing cycle. The vertical axis of the graph in Figure 21 represents the parameter values.

[0107] Lines L411, L413, and L414 are the same as in Figure 2. Line L411 shows the detuning Δ(t) at each time t. Line L413 shows the value of the coefficient B(t) of the Hamiltonian term representing the optimization problem to be solved at each time t. Line L414 shows the value of the coefficient C(t) of the Hamiltonian term for the initialization of the qubit element 110 at each time t. Line L412 shows the pump strength p(t) at each time interval t. In the example in Figure 21, the control unit 200 increases the pump strength p(t) from an initial value of 0 to a final value of p1.

[0108] Figure 22 shows a first example of the initial state of the qubit element 110 in the second control method. Figure 22 shows the initial state of the i-th qubit element 110 as ε i This shows a plot of the Wigner function when set to +1. In the graph in Figure 22, the horizontal axis (y-coordinate) represents the expectation value of the quantum state of the qubit element 110 with respect to the momentum operator p.< / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> This shows the expected value of the quantum state of the qubit element 110 with respect to the position operator x. The vertical axis (x coordinate) represents the expected value of the quantum state of the qubit element 110 with respect to the position operator x. <x>This indicates.

[0109] In the example in Figure 22, the function values ​​are plotted near x=0, closer to the x>0 side. With the initial parameter settings shown in Figure 21, by setting the detuning and pump strength to small values ​​(e.g., 0) and making the coefficient C(t) sufficiently large relative to the coefficient B(t), ε i The state of =+1 can be considered to be reflected relatively weakly (weaker than in the case of control method 1) as the initial state of the qubit element 110. The example in Figure 22 corresponds to an example in which the quantum state of the qubit element 110 is initialized to show the value +1 out of the two values ​​of a qubit, +1 and -1.

[0110] Figure 23 shows a second example of the initial state of the qubit element 110 in the second control method. Figure 23 shows the initial state of the i-th qubit element 110 as ε i The plot of the Wigner function when = -1 is shown. In the graph in Figure 23, the horizontal axis (y-coordinate) represents the expectation value of the quantum state of the qubit element 110 with respect to the momentum operator p.< / x> This shows the expected value of the quantum state of the qubit element 110 with respect to the position operator x. The vertical axis (x coordinate) represents the expected value of the quantum state of the qubit element 110 with respect to the position operator x. <x>This indicates.

[0111] In the example in Figure 23, the function values ​​are plotted near x=0, closer to the x<0 side. With the initial parameter settings shown in Figure 21, the detuning and pump strength are set to small values ​​(e.g., 0), and the coefficient C(t) is made sufficiently large relative to the coefficient B(t), ε i The state =-1 can be considered to be reflected relatively weakly (weaker than in the case of control method 1) as the initial state of the qubit element 110. The example in Figure 23 corresponds to an example in which the quantum state of the qubit element 110 is initialized to show the value -1, one of the two values ​​of a qubit, +1 and -1.

[0112] In the second control method as well, for each of the above cases 1 to 4, the value of the constant Γ in equation (3) was set in various ways, and quantum annealing was performed at various quantum annealing times to calculate the expected value and variance of the position operator of the quantum state of the qubit element 110.

[0113] (Second control method, Case 1 (ε1=+1, ε2=+1)) Figure 24 shows an example of the expected value of the position operator of the quantum state of the first qubit element 110 in Case 1 using the second control method. In the graph in Figure 24, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing. <x>This indicates.

[0114] Line L511 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L511 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L512 to L516.

[0115] Line L512 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L513 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L514 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L515 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L516 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0116] Figure 25 shows an example of the expected value of the position operator of the quantum state of the second qubit element 110 in Case 1 using the second control method. In the graph in Figure 25, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing. <x>This indicates.

[0117] Line L521 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L521 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L522 to L526.

[0118] Line L522 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L523 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L524 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L525 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L526 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0119] Figure 26 shows an example of the dispersion of the position operator of the quantum state of the first qubit element 110 in Case 1 using the second control method. In the graph in Figure 26, the horizontal axis represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0120] Line L531 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 as a vacuum state. Line L531 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L532 to L536.

[0121] Line L532 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L533 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L534 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.6. Line L535 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.8. Line L536 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0122] Figure 27 shows an example of the dispersion of the position operator of the quantum state of the second qubit element 110 in Case 1 using the second control method. In the graph in Figure 27, the horizontal axis represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0123] Line L541 shows the variance of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L541 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L542 to L546.

[0124] Line L542 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L543 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L544 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.6. Line L545 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.8. Line L546 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0125] (Second control method, Case 2 (ε1=+1, ε2=-1)) Figure 28 shows an example of the expected value of the position operator of the quantum state of the first qubit element 110 in Case 2 using the second control method. In the graph in Figure 28, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing. <x>This indicates.

[0126] Line L551 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L551 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L552 to L556.

[0127] Line L552 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L553 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L554 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L555 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L556 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0128] Figure 29 shows an example of the expected value of the position operator of the quantum state of the second qubit element 110 in Case 2 using the second control method. In the graph in Figure 29, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing. <x>This indicates.

[0129] Line L561 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L561 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L562 to L566.

[0130] Line L562 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L563 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L564 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L565 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L566 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0131] Figure 30 shows an example of the dispersion of the position operator of the quantum state of the first qubit element 110 in Case 2 using the second control method. In the graph of Figure 30, the horizontal axis represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0132] Line L571 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 as a vacuum state. Line L571 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L572 to L576.

[0133] Line L572 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L573 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L574 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.6. Line L575 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.8. Line L576 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0134] Figure 31 shows an example of the dispersion of the position operator of the quantum state of the second qubit element 110 in Case 2 using the second control method. The horizontal axis of the graph in Figure 31 represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0135] Line L581 shows the variance of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L581 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L582 to L586.

[0136] Line L582 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L583 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L584 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.6. Line L585 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.8. Line L586 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0137] (Second control method, Case 3 (ε1=-1, ε2=+1)) Figure 32 shows an example of the expected value of the position operator of the quantum state of the first qubit element 110 in Case 3 using the second control method. In the graph in Figure 32, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing. <x>This indicates.

[0138] Line L591 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L511 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L592 to L596.

[0139] Line L592 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L593 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L594 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L595 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L596 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0140] Figure 33 shows an example of the expected value of the position operator of the quantum state of the second qubit element 110 in Case 3 using the second control method. In the graph in Figure 33, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing. <x>This indicates.

[0141] Line L601 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L601 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L602 to L606.

[0142] Line L602 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.2. Line L603 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.4. Line L604 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.6. Line L605 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=0.8. Line L606 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, for each quantum annealing time, when Γ=1.0.

[0143] Figure 34 shows an example of the dispersion of the position operator of the quantum state of the first qubit element 110 in Case 3 using the second control method. In the graph in Figure 34, the horizontal axis represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) is shown.

[0144] Line L611 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when quantum annealing is performed with the initial state of both the first qubit element 110 and the second qubit element 110 being the vacuum state. Line L611 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, which is indicated by lines L612 to L616.

[0145] Line L612 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.2. Line L613 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.4. Line L614 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.6. Line L615 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.8. Line L616 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 1.0.

[0146] FIG. 35 is a diagram showing an example of the variance of the position operator of the quantum state of the second qubit element 110 in case 3 with the second control method. [[ID=#23]]The horizontal axis of the graph in FIG. 35 indicates the quantum annealing time. The vertical axis is the variance √(<x 2 >- <x> 2 ) indicates.

[0147] Line L621 shows the variance of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L621 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L622 to L626.

[0148] Line L622 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L623 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L624 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.6. Line L625 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.8. Line L626 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0149] (Second control method, case 4 (ε1=-1, ε2=-1)) Figure 36 shows an example of the expected value of the position operator of the quantum state of the first qubit element 110 in Case 4 using the second control method. In the graph in Figure 36, the horizontal axis represents the quantum annealing time. The vertical axis represents the expected value of the position operator x of the quantum state of the first qubit element 110 at the end of quantum annealing. <x>is shown.

[0150] Line L631 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when quantum annealing is performed with the initial state of both the first qubit element 110 and the second qubit element 110 being the vacuum state. Line L631 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, which is indicated by lines L632 to L636.

[0151] Line L632 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.2. Line L633 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.4. Line L634 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.6. Line L635 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.8. Line L636 shows the expected value of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 1.0.

[0152] FIG. 37 is a diagram showing an example of the expected value of the position operator of the quantum state of the second qubit element 110 in case 4 with the second control method. The horizontal axis of the graph in FIG. 37 indicates the quantum annealing time. The vertical axis indicates the expected value of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing <x>is shown.

[0153] Line L641 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing for each quantum annealing time when quantum annealing is performed with the initial state of both the first qubit element 110 and the second qubit element 110 being the vacuum state. Line L641 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, which is indicated by lines L642 to L646.

[0154] Line L642 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.2. Line L643 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.4. Line L644 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.6. Line L645 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 0.8. Line L646 shows the expected value of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing for each quantum annealing time when Γ = 1.0.

[0155] FIG. 38 is a diagram showing an example of the variance of the position operator of the quantum state of the first qubit element 110 in case 4 with the second control method. The horizontal axis of the graph in FIG. 38 indicates the quantum annealing time. The vertical axis is the variance √(<x 2 >- <x> 2 ) indicates.

[0156] Line L651 shows the variance of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 as a vacuum state. Line L651 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L652 to L656.

[0157] Line L652 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L653 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L654 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=0.6. Line L655 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.8. Line L656 shows the dispersion of the position operator of the quantum state of the first qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0158] Figure 39 shows an example of the dispersion of the position operator of the quantum state of the second qubit element 110 in Case 4 using the second control method. In the graph in Figure 39, the horizontal axis represents the quantum annealing time. The vertical axis represents the variance of the position operator x of the quantum state of the second qubit element 110 at the end of quantum annealing (√( <x 2 >- <x> 2 ) indicates.

[0159] Line L661 shows the variance of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per unit of quantum annealing time, when quantum annealing is performed with the initial state of both the first and second qubit elements 110 being a vacuum state. Line L661 is shown for comparison with the case where an estimated solution is set as the initial state of the qubit element 110, as shown by lines L662 to L666.

[0160] Line L662 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.2. Line L663 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.4. Line L664 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.6. Line L665 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, for the case Γ=0.8. Line L666 shows the dispersion of the position operator of the quantum state of the second qubit element 110 at the end of quantum annealing, per quantum annealing time, when Γ=1.0.

[0161] Similar to the experiment of the first control method, in the experiment of the second control method, the optimal solution is obtained when the values of both two qubits are +1. Therefore, in the examples from FIG. 24 to FIG. 39, it can be considered that for both the first qubit element 110 and the second qubit element 110, the larger the expected value of the position operator at the end of quantum annealing (the larger the positive value) and the smaller the variance, the easier it is to obtain the optimal solution. In particular, when the initial state is the vacuum state and quantum annealing is performed, compared with the case where the expected value of the position operator at the end of quantum annealing is larger and the variance is smaller, it is expected that by setting the estimated solution as the initial value of the qubit element 110, the possibility of obtaining the optimal solution will be higher.

[0162] Referring to the experimental results (simulation results) for each case, in Case 1 (ε1 = +1, ε2 = +1), for any value of Γ, approximately when T ≥ 5×10 -1 the expected value is larger and the variance is smaller than when the initial state is the vacuum state.

[0163] In Case 2 (ε1 = +1, ε2 = -1), when Γ = 0.8, approximately when 7.5×10 0 ≤ T ≤ 1.5×10 1 the expected value is larger and the variance is smaller than when the initial state is the vacuum state. Also, in the case of Γ = 1.0, approximately when T ≥ 7×10 0 and except in the vicinity of T = 1.5×10 1 the expected value is larger and the variance is smaller than when the initial state is the vacuum state.

[0164] In Case 3 (ε1 = -1, ε2 = +1), for the first qubit element 110, at any quantum annealing time, the expected value is equal to or smaller than that when the initial state is the vacuum state, or the variance is equal to or larger than that when the initial state is the vacuum state. In Case 4 (ε1 = -1, ε2 = -1), the expected value is smaller than that when the initial state is the vacuum state.

[0165] According to the experimental results, for example, in the case of the Hamiltonian shown in Equation (3), in Case 1 and Case 2, there may be a case where it is expected that an optimal solution can be obtained with a higher probability than when the initial state is the vacuum state by setting the constant Γ and the quantum annealing time T. Therefore, the information processing apparatus 1 may repeat quantum annealing while changing the setting of the constant Γ, the setting of the quantum annealing time T, and the estimated solution set as the initial value of the quantum bit element 110.

[0166] FIG. 40 is a diagram showing a first example of the procedure of the process performed by the information processing apparatus 1. In the process of FIG. 40, the control unit 200 acquires an estimated solution to be set as the initial value of the quantum bit element 110 (step S101). As described above for the information processing apparatus 1, the estimated solution set by the control unit 200 as the initial value of the quantum bit element 110 is not limited to a specific one.

[0167] Next, the control unit 200 initializes the quantum state of the quantum bit element 110 so as to set the obtained estimated solution as the initial value of the quantum bit element 110 (step S102). Next, the control unit 200 controls the quantum computing circuit 100 to execute quantum annealing (one solution search by quantum annealing) (step S103).

[0168] Next, the observation unit 300 acquires a candidate solution by reading the quantum state of the quantum bit element 110 at the end of quantum annealing (step S104). In FIG. 40, for convenience of explanation, the estimated solution set as the initial state of the quantum bit element 110 is referred to as "estimated solution", and the estimated solution obtained by quantum annealing is referred to as "candidate solution" to distinguish the two. Next, the control unit 200 determines whether or not the end condition for repeated execution of quantum annealing is satisfied (step S105).

[0169] The termination conditions here are not limited to any particular set. For example, the termination condition here may be that the loop from step S101 to S105 has been executed a predetermined number of times or more. Alternatively, the termination condition here may be that a candidate solution has been obtained in which the value of an evaluation function, such as a Hamiltonian representing the optimization problem to be solved, is better than a predetermined threshold.

[0170] If the control unit 200 determines that the termination condition is not met in step S105 (step S105: NO), the process returns to step S101. On the other hand, if the control unit 200 determines that the termination condition is met in step S105 (step S105: NO), the information processing device 1 outputs candidate solutions obtained by quantum annealing (step S106).

[0171] The method by which the information processing device 1 outputs the estimated solution is not limited to a specific method. For example, the information processing device 1 may have a display screen to display the estimated solution. Alternatively, the information processing device may have communication means to transmit the estimated solution to another device. Furthermore, the number of candidate solutions output by the information processing device 1 is not limited to a specific number. For example, the information processing device 1 may output only those candidate solutions whose evaluation function value is better than a predetermined threshold. Alternatively, the information processing device 1 may output all of the candidate solutions obtained. After step S106, the information processing device 1 terminates the process shown in Figure 40.

[0172] Figure 41 shows a second example of the processing procedure performed by the information processing device 1. Steps S201 to S205 in Figure 41 are the same as steps S101 to S105 in Figure 40. In Figure 41, for the sake of explanation, the estimated solution set as the initial state of the qubit element 110 is referred to as the "estimated solution," and the estimated solution obtained by quantum annealing is referred to as the "candidate solution," thus distinguishing between the two.

[0173] If it is determined in step S205 that the termination condition is not met (step S205: NO), the control unit 200 determines whether the obtained latest candidate solution is the same as the estimated solution set as the initial state of the qubit element 110 in the quantum annealing at that time (step S221).

[0174] If the control unit 200 determines that the obtained candidate solution is different from the estimated solution (step S211: NO), it sets the obtained candidate solution as the estimated solution to be set as the initial value of the qubit element 110 when it performs the next process in step S202 (step S221). After step S221, the process returns to step S202.

[0175] On the other hand, if in step S221 it is determined that the obtained candidate solution is the same as the estimated solution (step S211: YES), the control unit 200 changes at least one of the following: detuning, pump strength, or estimated solution settings (step S231). For example, the control unit 200 may change the value of the constant Γ for adjusting detuning and pump strength, as illustrated in equations (2) and (3). After step S231, the process returns to step S202.

[0176] On the other hand, if the control unit 200 determines in step S205 that the termination condition is met (step S205: YES), the information processing device 1 outputs candidate solutions obtained by quantum annealing (step S241). Step S241 is the same as step S106 in Figure 40. After step S241, the information processing device 1 terminates the process shown in Figure 41.

[0177] As described above, the quantum computing circuit 100 includes a qubit element 110 using a parametric oscillator with Kerr nonlinearity. The control unit 200 initializes the quantum state of the qubit element 110 to one of the two values ​​of the qubit using a coherent drive signal, and then controls the quantum computing circuit to increase the detuning of the qubit element.

[0178] According to the information processing device 1, when performing a solution search using a k-parametric oscillator, if an estimated solution (a candidate solution) has been obtained, the obtained estimated solution can be reflected in the solution search. Specifically, the information processing device 1 can initialize the quantum state of the qubit element 110 using the k-parametric oscillator to indicate the qubit value in the estimated solution, and perform a solution search by quantum annealing. As a result, it is expected that the information processing device 1 will be able to more easily obtain desired solutions, such as the optimal solution, depending on the estimated solution set as the initial state of the qubit element 110.

[0179] The ease with which a desired solution can be obtained can be understood as the short time required to obtain the desired solution. Here, the time required to obtain the desired solution can refer to either the time required for one quantum annealing (one solution search using quantum annealing) or the time required for repeated quantum annealing executions. When the desired solution, such as the optimal solution, is relatively easy to obtain, it is expected that the probability of obtaining the desired solution, such as the optimal solution, is relatively high even if the time required for one quantum annealing is relatively short, and that the time required for repeated quantum annealing executions until the desired solution, such as the optimal solution, is relatively short.

[0180] Furthermore, the control unit 200 initializes the quantum state of the qubit element 110 using a coherent drive signal, and then controls the quantum computing circuit 100 to detune the qubit element 110 from larger to smaller, and to detune the amplitude of the pump signal from smaller to larger.

[0181] According to the information processing device 1, the amplitude of the pump signal at the start of quantum annealing can be set to a relatively large value, and the qubit values ​​in the estimated solution can be reflected relatively strongly as the initial state of the qubit element 110. According to the information processing device 1, in this respect, it is expected that it will be easier to obtain the desired solution, such as the optimal solution, especially when the estimated solution is close to the desired solution, such as the optimal solution.

[0182] Furthermore, the control unit 200 initializes the quantum state of the qubit element 110 using a coherent drive signal, then controls the quantum computing circuit 100 to increase and then decrease the detuning of the qubit element 110, thereby increasing the amplitude of the pump signal.

[0183] According to the information processing device 1, the amplitude of the pump signal at the start of quantum annealing can be set to a relatively small value, such as 0, and the qubit value in the estimated solution can be reflected relatively weakly as the initial state of the qubit element 110. In this respect, according to the information processing device 1, even when the estimated solution is somewhat far from the desired solution, such as the optimal solution, it is expected that the desired solution, such as the optimal solution, will be relatively easier to obtain.

[0184] Furthermore, if the estimated solution obtained by the quantum state initialization of the qubit element 110 and the solution search controlled by the quantum computing circuit 100 differs from the estimated solution set for the qubit element 110 during the quantum state initialization of the qubit element 110, the control unit 200 initializes the quantum state of the qubit element 110 so that the estimated solution obtained during the solution search becomes the initial value, and performs the solution search again under the control of the quantum computing circuit 100.

[0185] According to the information processing device 1, it is expected that the probability of obtaining a desired solution, such as the optimal solution, will increase. Specifically, according to the information processing device 1, by repeatedly changing the estimated solution set as the initial state of the qubit element 110 and performing a solution search by quantum annealing, it is expected that the probability of setting an estimated solution that makes it easier to obtain a desired solution, such as the optimal solution, will increase.

[0186] Furthermore, if the estimated solution obtained by initializing the quantum state of the qubit element 110 and searching for a solution by controlling the quantum computing circuit 100 is equal to the estimated solution set for the qubit element 110 during the initialization of the quantum state of the qubit element 110, the control unit 200 changes at least one of the following: the maximum value of detuning, the minimum value of the pump signal amplitude, or the estimated solution set as the initial state of the quantum state of the qubit element 110, and then performs the initialization of the quantum state of the qubit element 110 and the search for a solution by controlling the quantum computing circuit 100 again.

[0187] According to the information processing device 1, it is expected that the probability of obtaining a desired solution, such as the optimal solution, will increase. Specifically, according to the information processing device 1, by repeatedly performing a solution search by quantum annealing while changing at least one of the maximum value of detuning, the minimum value of the pump signal amplitude, or the estimated solution set as the initial state of the quantum state of the qubit element 110, it is expected that the probability of setting the detuning, pump signal, and estimated solution in a way that makes it easier to obtain a desired solution, such as the optimal solution, will increase.

[0188] <Second Embodiment> Figure 42 shows an example of the configuration of an information processing device according to at least one embodiment. In the configuration shown in Figure 42, the information processing device 610 comprises a quantum computing circuit 611 and a control unit 613. The quantum computing circuit 611 comprises a qubit element 612.

[0189] In this configuration, the qubit element 612 is a qubit element that uses a parametric oscillator with Kerr nonlinearity. The control unit 613 initializes the quantum state of the qubit element 612 to one of the two values ​​of the qubit using a coherent drive signal, and then controls the quantum computing circuit 611 to increase the detuning of the qubit element 612. The control unit 613 is an example of a control means.

[0190] According to the information processing device 610, when performing a solution search using a k-parametric oscillator, if candidate solutions have been obtained, these obtained candidate solutions can be reflected in the solution search. Specifically, the information processing device 610 can initialize the quantum state of the qubit element 612 using the k-parametric oscillator to indicate the qubit value in the candidate solution, and then perform a solution search by quantum annealing. As a result, it is expected that the information processing device 610 will be able to more easily obtain desired solutions, such as the optimal solution, depending on the candidate solution set as the initial state of the qubit element 612.

[0191] <Third Embodiment> Figure 43 shows an example of the configuration of a control device according to at least one embodiment. In the configuration shown in Figure 43, the control device 620 includes a control unit 621.

[0192] In this configuration, the control unit 621 initializes the quantum state of a quantum computing circuit equipped with a qubit element using a parametric oscillator having Kerr nonlinearity to one of the two values ​​of the qubit using a coherent drive signal, and then controls the quantum computing circuit to increase the detuning of the qubit element. The control unit 621 is an example of a control means.

[0193] According to the control device 620, when performing a solution search using a k-parametric oscillator, if candidate solutions have been obtained, these obtained candidate solutions can be reflected in the solution search. Specifically, the control device 620 can initialize the quantum state of the qubit element using the k-parametric oscillator to indicate the qubit value in the candidate solution, and then perform a solution search by quantum annealing. As a result, it is expected that the control device 620 will be able to more easily obtain desired solutions, such as the optimal solution, depending on the candidate solution set as the initial state of the qubit element.

[0194] <Fourth Embodiment> Figure 44 shows an example of a processing procedure in an information processing method according to at least one embodiment. The information processing method shown in Figure 44 includes controlling a quantum computing circuit (step S611).

[0195] In controlling the quantum computing circuit (step S611), a computer controlling a quantum computing circuit equipped with a qubit element having Kerr nonlinearity initializes the quantum state of the qubit element to represent one of the two values ​​of the qubit using a coherent drive signal, and then controls the quantum computing circuit to increase the detuning of the qubit element.

[0196] According to the information processing method shown in Figure 44, when performing a solution search using a k-parametric oscillator, if candidate solutions have been obtained, these obtained candidate solutions can be reflected in the solution search. Specifically, in the information processing method shown in Figure 44, the quantum state of the qubit element using the k-parametric oscillator is initialized to indicate the qubit value in the candidate solution, and a solution search can be performed by quantum annealing. As a result, it is expected that the information processing method shown in Figure 44 will make it easier to obtain desired solutions, such as the optimal solution, depending on the candidate solution set as the initial state of the qubit element.

[0197] Figure 45 shows an example of a computer configuration according to at least one embodiment. As shown in Figure 45, the computer 700 comprises a CPU 710, a main memory 720, an auxiliary memory 730, an interface 740, and a non-volatile recording medium 750.

[0198] One or more of the above-mentioned control unit 200, control unit 613, and control device 620, or a part thereof, may be implemented in the computer 700. In that case, the operation of each of the above-mentioned processing units is stored in the auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, expands it in the main memory device 720, and executes the above-mentioned processing according to the program. The CPU 710 also reserves memory areas in the main memory device 720 corresponding to each of the above-mentioned storage units according to the program. Communication between each device and other devices is performed by the interface 740 having a communication function and performing communication according to the control of the CPU 710. The interface 740 also has a port for the non-volatile recording medium 750 and reads information from the non-volatile recording medium 750 and writes information to the non-volatile recording medium 750.

[0199] When the control unit 200 is implemented in the computer 700, its operation is stored in auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main memory 720, and executes the above processing according to the program.

[0200] Furthermore, the CPU 710 reserves memory in the main memory 720 for the control unit 200 to process according to the program. Communication between the control unit 200 and other devices is performed by the interface 740 having a communication function and operating according to the control of the CPU 710. Interaction between the control unit 200 and the user is performed by the interface 740 having input and output devices, presenting information to the user via the output device and accepting user operations via the input device according to the control of the CPU 710.

[0201] When the control unit 613 is implemented in the computer 700, its operation is stored in auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from auxiliary storage device 730, loads it into main memory device 720, and executes the above process according to the program.

[0202] Furthermore, the CPU 710 reserves memory in the main memory 720 for the control unit 613 to process according to the program. Communication between the control unit 613 and other devices is performed by the interface 740 having a communication function and operating according to the control of the CPU 710. Interaction between the control unit 613 and the user is performed by the interface 740 having input and output devices, presenting information to the user via the output device and accepting user operations via the input device according to the control of the CPU 710.

[0203] When the control device 620 is implemented in the computer 700, the operation of the control unit 621 is stored in auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main memory device 720, and executes the above process according to the program.

[0204] Furthermore, the CPU 710 reserves memory in the main memory 720 for the control device 620 to process according to the program. Communication between the control device 620 and other devices is performed by the interface 740 having a communication function and operating according to the control of the CPU 710. Interaction between the control device 620 and the user is performed by the interface 740 having input and output devices, presenting information to the user via the output device and accepting user operations via the input device according to the control of the CPU 710.

[0205] One or more of the above-mentioned programs may be recorded on the non-volatile recording medium 750. In this case, the interface 740 may read the program from the non-volatile recording medium 750. The CPU 710 may then either directly execute the program read by the interface 740, or temporarily save it in the main memory 720 or auxiliary memory 730 before executing it.

[0206] Alternatively, a program for executing all or part of the processing performed by the control unit 200, control unit 613, and control device 620 may be recorded on a computer-readable recording medium, and the processing of each unit may be performed by having the computer system read and execute the program recorded on this recording medium. The term "computer system" here includes hardware such as the OS (Operating System) and peripheral devices. Furthermore, "computer-readable recording media" refers to portable media such as flexible disks, magneto-optical disks, ROMs (Read Only Memory), CD-ROMs (Compact Disc Read Only Memory), and storage devices such as hard disks built into computer systems. The above-mentioned program may be intended to implement only a part of the functions described above, and may also be able to implement the above-mentioned functions in combination with programs already recorded in the computer system.

[0207] Although the present disclosure has been described above with reference to embodiments, the present disclosure is not limited to the embodiments described above. Various modifications to the structure and details of the present disclosure are possible, as can be understood by those skilled in the art within the scope of the present disclosure. Furthermore, the embodiments described above may be combined with other embodiments as appropriate.

[0208] Some or all of the above embodiments may also be described as follows, but are not limited to the following:

[0209] (Note 1) Equipped with a quantum computing circuit and control means, The quantum computing circuit comprises a qubit element using a parametric oscillator having Kerr nonlinearity, The control means initializes the quantum state of the qubit element using a coherent drive signal to show one of the two values ​​of the qubit, and then controls the quantum computing circuit to increase the detuning of the qubit element. Information processing device.

[0210] (Note 2) The control means initializes the quantum state of the qubit element using the coherent drive signal, and then controls the quantum computing circuit to increase and then decrease the detuning of the qubit element, and to decrease and then increase the amplitude of the pump signal. The information processing device described in Appendix 1.

[0211] (Note 3) The control means initializes the quantum state of the qubit element using the coherent drive signal, then controls the quantum computing circuit to increase and then decrease the detuning of the qubit element, and to increase the amplitude of the pump signal. The information processing device described in Appendix 1.

[0212] (Note 4) If the solution obtained by the quantum state search performed by the quantum computing circuit after the quantum state of the qubit element is initialized differs from the solution set for the qubit element during the quantum state initialization, the control means initializes the quantum state of the qubit element so that the solution obtained during the solution search becomes the initial value, and performs the solution search again by controlling the quantum computing circuit. An information processing device described in any one of the appendices 1 to 3.

[0213] (Note 5) If the solution obtained by initializing the quantum state of the qubit element and searching for a solution by controlling the quantum computing circuit is equal to the solution set for the qubit element during the initialization of the quantum state of the qubit element, the control means changes at least one of the following: the maximum value of the detuning, the minimum value of the amplitude of the pump signal, or the solution set as the initial state of the quantum state of the qubit element, and then performs the initialization of the quantum state of the qubit element and the search for a solution by controlling the quantum computing circuit again. An information processing device described in any one of the appendices 1 to 4.

[0214] (Note 6) A control means for controlling a quantum computing circuit equipped with a qubit element using a parametric oscillator having Kerr nonlinearity, after initializing the quantum state of the qubit element to represent one of the two values ​​of the qubit using a coherent drive signal, thereby increasing the detuning of the qubit element. A control device equipped with the following features.

[0215] (Note 7) The control means initializes the quantum state of the qubit element using the coherent drive signal, and then controls the quantum computing circuit to increase and then decrease the detuning of the qubit element, and to decrease and then increase the amplitude of the pump signal. The control device described in Appendix 6.

[0216] (Note 8) The control means initializes the quantum state of the qubit element using the coherent drive signal, then controls the quantum computing circuit to increase and then decrease the detuning of the qubit element, and to increase the amplitude of the pump signal. The control device described in Appendix 6.

[0217] (Note 9) If the solution obtained by the quantum state search performed by the quantum computing circuit after the quantum state of the qubit element is initialized differs from the solution set for the qubit element during the quantum state initialization, the control means initializes the quantum state of the qubit element so that the solution obtained during the solution search becomes the initial value, and performs the solution search again by controlling the quantum computing circuit. A control device as described in any one of the appendices 6 to 8.

[0218] (Note 10) If the solution obtained by initializing the quantum state of the qubit element and searching for a solution by controlling the quantum computing circuit is equal to the solution set for the qubit element during the initialization of the quantum state of the qubit element, the control means changes at least one of the following: the maximum value of the detuning, the minimum value of the amplitude of the pump signal, or the solution set as the initial state of the quantum state of the qubit element, and then performs the initialization of the quantum state of the qubit element and the search for a solution by controlling the quantum computing circuit again. A control device as described in any one of the appendices 6 to 9.

[0219] (Note 11) A computer that controls a quantum computing circuit equipped with qubit elements using qubit elements with Kerr nonlinearity, After initializing the quantum state of the qubit element to represent one of the two values ​​of the qubit using a coherent drive signal, the quantum computing circuit is controlled to increase the detuning of the qubit element. Information processing methods that include the following.

[0220] (Note 12) The computer initializes the quantum state of the qubit element using the coherent drive signal, and then controls the quantum computing circuit to detune the qubit element from larger to smaller, and to detune the amplitude of the pump signal from smaller to larger. The information processing method described in Appendix 11, including the above.

[0221] (Note 13) The computer initializes the quantum state of the qubit element using the coherent drive signal, and then controls the quantum computing circuit to increase and then decrease the detuning of the qubit element, thereby increasing the amplitude of the pump signal. The information processing method described in Appendix 11, including the above.

[0222] (Note 14) If the computer initializes the quantum state of the qubit element and the solution obtained by the solution search controlled by the quantum computing circuit differs from the solution set for the qubit element during the initialization of the quantum state of the qubit element, the computer initializes the quantum state of the qubit element so that the solution obtained in the solution search becomes the initial value, and then performs the solution search controlled by the quantum computing circuit again. An information processing method described in any one of the appendices 11 to 13, including the above.

[0223] (Note 15) If the computer initializes the quantum state of the qubit element and the solution obtained by the solution search controlled by the quantum computing circuit is equal to the solution set for the qubit element during the initialization of the quantum state of the qubit element, then the computer changes at least one of the following: the maximum value of the detuning, the minimum value of the pump signal amplitude, or the solution set as the initial state of the quantum state of the qubit element, and then performs the initialization of the quantum state of the qubit element and the solution search controlled by the quantum computing circuit again. An information processing method described in any one of the appendices 11 to 14, including the above.

[0224] (Note 16) A computer that controls a quantum computing circuit equipped with qubit elements using qubit elements with Kerr nonlinearity, After initializing the quantum state of the qubit element using a coherent drive signal to represent one of the two values ​​of the qubit, the quantum computing circuit is controlled to increase the detuning of the qubit element. A program that executes the command.

[0225] (Note 17) To the aforementioned computer, After initializing the quantum state of the qubit element using the coherent drive signal, the quantum computing circuit is controlled to increase and then decrease the detuning of the qubit element, and to decrease and then increase the amplitude of the pump signal. The program described in Appendix 16 that executes this program.

[0226] (Note 18) To the aforementioned computer, After initializing the quantum state of the qubit element using the coherent drive signal, the quantum computing circuit is controlled to increase and then decrease the detuning of the qubit element, thereby increasing the amplitude of the pump signal. The program described in Appendix 16 that executes this program.

[0227] (Note 19) To the aforementioned computer, If the solution obtained by initializing the quantum state of the qubit element and searching for a solution by controlling the quantum computing circuit differs from the solution set for the qubit element during the initialization of the quantum state of the qubit element, the quantum state of the qubit element is initialized so that the solution obtained in the search for a solution becomes the initial value, and the search for a solution by controlling the quantum computing circuit is performed again. The program described in one of the appendices 16 to 18 that will execute the above.

[0228] (Note 20) To the aforementioned computer, If the solution obtained by initializing the quantum state of the qubit element and searching for a solution by controlling the quantum computing circuit is equal to the solution set for the qubit element during the initialization of the quantum state of the qubit element, then at least one of the following is changed: the maximum value of the detuning, the minimum value of the amplitude of the pump signal, or the solution set as the initial state of the quantum state of the qubit element, and the initialization of the quantum state of the qubit element and the search for a solution by controlling the quantum computing circuit are repeated. The program described in one of the appendices 16 to 19 that will execute the above. [Explanation of Symbols]

[0229] 1,610 Information Processing Device 100, 611 Quantum calculation circuit 110,612 qubit element 120 Combiner 200, 613, 621 Control Unit 300 Observation Unit 620 Control Unit< / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x> < / x>

Claims

1. Equipped with a quantum computing circuit and control means, The quantum computing circuit comprises a qubit element using a parametric oscillator having Kerr nonlinearity, The control means initializes the quantum state of the qubit element using a coherent drive signal to show one of the two values ​​of the qubit, and then controls the quantum computing circuit to increase the detuning of the qubit element. Information processing device.

2. The control means initializes the quantum state of the qubit element using the coherent drive signal, and then controls the quantum computing circuit to increase and then decrease the detuning of the qubit element, and to decrease and then increase the amplitude of the pump signal. The information processing apparatus according to claim 1.

3. The control means initializes the quantum state of the qubit element using the coherent drive signal, then controls the quantum computing circuit to increase and then decrease the detuning of the qubit element, and to increase the amplitude of the pump signal. The information processing apparatus according to claim 1.

4. If the solution obtained by the quantum state search performed by the quantum computing circuit after the quantum state of the qubit element is initialized differs from the solution set for the qubit element during the quantum state initialization, the control means initializes the quantum state of the qubit element so that the solution obtained during the solution search becomes the initial value, and performs the solution search again by controlling the quantum computing circuit. The information processing apparatus according to claim 1.

5. If the solution obtained by initializing the quantum state of the qubit element and searching for a solution by controlling the quantum computing circuit is equal to the solution set for the qubit element during the initialization of the quantum state of the qubit element, the control means changes at least one of the following: the maximum value of the detuning, the minimum value of the amplitude of the pump signal, or the solution set as the initial state of the quantum state of the qubit element, and then performs the initialization of the quantum state of the qubit element and the search for a solution by controlling the quantum computing circuit again. The information processing apparatus according to claim 1.

6. A control means for controlling a quantum computing circuit equipped with a qubit element using a parametric oscillator having Kerr nonlinearity, after initializing the quantum state of the qubit element to represent one of the two values ​​of the qubit using a coherent drive signal, thereby increasing the detuning of the qubit element. A control device equipped with the following features.

7. A computer that controls a quantum computing circuit equipped with qubit elements using qubit elements with Kerr nonlinearity, After initializing the quantum state of the qubit element to represent one of the two values ​​of the qubit using a coherent drive signal, the quantum computing circuit is controlled to increase the detuning of the qubit element. Information processing methods that include the following.

8. A computer that controls a quantum computing circuit equipped with qubit elements using qubit elements with Kerr nonlinearity, After initializing the quantum state of the qubit element using a coherent drive signal to represent one of the two values ​​of the qubit, the quantum computing circuit is controlled to increase the detuning of the qubit element. A program that executes the command.

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