Control device, quantum annealing system, control method, and program

Abstract

To obtain a solution even when three or more Kerr nonlinear parametric oscillators are interacting with each other in quantum annealing using Kerr nonlinear parametric oscillators.SOLUTION: A control device is equipped with setting means for setting the value of a pump constant, which is a constant related to the initial value of pump strength of a quantum annealing device using a Kerr nonlinear parametric oscillator, to a value determined on the basis of the maximum number of interacting Kerr nonlinear parametric oscillators, an interaction strength constant, which is a constant indicating the strength of interaction between the Kerr nonlinear parametric oscillators, and a Kerr coefficient, which is a constant representing Kerr nonlinearity, or a value greater than the above value, and execution control means for controlling the quantum annealing device on the basis of the setting by the setting means to perform quantum annealing.SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The present invention relates to a control device, a quantum annealing system, a control method, and a program. [Background technology]

[0002] One of the devices used in quantum computing is the Kerr nonlinear parametric oscillator (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2017-073106 A Summary of the Invention [Problem to be solved by the invention]

[0004] In quantum annealing using Kerr nonlinear parametric oscillators, it is preferable to be able to obtain a solution even when three or more Kerr nonlinear parametric oscillators are interacting with each other.

[0005] An example of an object of the present invention is to provide a control device, a quantum annealing system, a control 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 invention, a control device includes an execution control means for controlling a quantum annealing device equipped with the Kerr nonlinear parametric oscillator to perform quantum annealing based on an interaction number constant which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to three or more, an interaction strength constant which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant which is a constant related to the initial value of the pump strength of the Kerr nonlinear parametric oscillator and is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient or a value greater than that.

[0007] According to a second aspect of the present invention, the control device includes an execution control means for controlling a quantum annealing device including a Kerr nonlinear parametric oscillator to perform quantum annealing by starting to decrease a detuning value while keeping the pump intensity of the Kerr nonlinear parametric oscillator at 0, and then increasing the pump intensity from 0.

[0008] According to a third aspect of the present invention, a quantum annealing system comprises a quantum annealing apparatus using a Kerr nonlinear parametric oscillator, and a control device, and the control device comprises an execution control means for controlling the quantum annealing apparatus to perform quantum annealing based on an interaction number constant which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to three or more, an interaction strength constant which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant which is a constant related to the initial value of the pump strength of the Kerr nonlinear parametric oscillator and is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient or a value greater than that.

[0009] According to a fourth aspect of the present invention, a control method includes a control device that controls a quantum annealing apparatus using a Kerr nonlinear parametric oscillator to perform quantum annealing based on an interaction number constant, which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to three or more, an interaction strength constant, which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient, which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant, which is a constant related to the initial value of the pump strength of the Kerr nonlinear parametric oscillator and is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient, or a value greater than that.

[0010] According to a fifth aspect of the present invention, a control method includes a control device that controls a quantum annealing apparatus using a Kerr nonlinear parametric oscillator, controlling the quantum annealing apparatus to perform quantum annealing by starting to decrease a detuning value while keeping the pump intensity at 0, and then increasing the pump intensity from 0.

[0011] According to a sixth aspect of the present invention, the program causes a computer that controls a quantum annealing apparatus using a Kerr nonlinear parametric oscillator to set the value of a pump constant, which is a constant related to the initial value of the pump strength of the quantum annealing apparatus, to a value determined based on the maximum number of interacting Kerr nonlinear parametric oscillators, an interaction strength constant, which is a constant indicating the strength of interaction between the Kerr nonlinear parametric oscillators, and a Kerr coefficient, which is a constant representing the Kerr nonlinearity, or to a value greater than the above, and to control the quantum annealing apparatus based on the setting to perform quantum annealing.

[0012] According to a seventh aspect of the present invention, a program is provided for causing a computer that controls a quantum annealing apparatus using a Kerr nonlinear parametric oscillator to execute the following: the execution control means of the quantum annealing apparatus controls the quantum annealing apparatus to perform quantum annealing by keeping the pump intensity at 0, starting to decrease the detuning value, and then increasing the pump intensity from 0. Effect of the Invention

[0013] According to the present invention, in quantum annealing using Kerr nonlinear parametric oscillators, a solution can be obtained even when three or more Kerr nonlinear parametric oscillators are interacting with each other. [Brief description of the drawings]

[0014] [Figure 1] FIG. 1 is a diagram illustrating an example of the configuration of a quantum annealing system according to an embodiment. [Diagram 2] FIG. 1 is a diagram illustrating an example of the configuration of a quantum annealing apparatus according to an embodiment. [Diagram 3] FIG. 2 is a diagram illustrating an example of the configuration of a Kerr nonlinear parametric oscillator according to an embodiment. [Figure 4] FIG. 2 is a diagram illustrating an example of a configuration of a control device according to the embodiment. [Diagram 5] FIG. 13 is a diagram showing an example of the value of αmin during a first-order phase transition in an embodiment. [Figure 6] FIG. 11 is a diagram showing an example of the relationship between the value of α and the value of V(s) when a first-order phase transition occurs in an embodiment. [Figure 7] FIG. 11 is a diagram illustrating a first example of a relationship between p and sc in the embodiment. [Figure 8] FIG. 11 is a diagram illustrating a first example of a relationship between p and αc in the embodiment. [Figure 9] FIG. 13 is a diagram illustrating a second example of the relationship between p and sc in the embodiment. [Figure 10] FIG. 13 is a diagram illustrating a second example of the relationship between p and αc in the embodiment. [Figure 11] FIG. 11 is a diagram showing an example of the value of αmin when the Hamiltonian shown in equation (28) is used in the embodiment. [Figure 12] FIG. 11 is a diagram illustrating an example of a processing procedure when a control device according to an embodiment controls a quantum annealing device to perform quantum annealing. [Figure 13] FIG. 13 is a diagram illustrating another example of the configuration of the control device according to the embodiment. [Figure 14] FIG. 13 is a diagram illustrating another example of the configuration of the control device according to the embodiment. [Figure 15] FIG. 2 is a diagram showing another example of the configuration of a quantum annealing system according to an embodiment. [Figure 16] FIG. 4 is a diagram illustrating an example of a processing procedure in a control method according to the embodiment. [Figure 17] FIG. 11 is a diagram showing another example of the processing procedure in the control method according to the embodiment. [Figure 18] FIG. 1 is a schematic block diagram illustrating a configuration of a computer according to at least one embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] The following describes embodiments of the present invention, but the following embodiments do not limit the scope of the invention. Furthermore, not all of the combinations of features described in the embodiments are necessarily essential to the solution of the invention. In the following, circumflexed letters may be indicated by preceding them with a "^." For example, a circumflexed a will also be written as ^a.

[0016] 1 is a diagram showing an example of the configuration of a quantum annealing system according to an embodiment. In the configuration shown in FIG. 1, the quantum annealing system 1 includes a quantum annealing device 100 and a control device 200.

[0017] The quantum annealing system 1 is a system for performing quantum annealing. Specifically, a quantum annealing device 100 performs quantum annealing under the control of a control device 200. The quantum annealing referred to here is a method for finding a solution that is represented by a combination of quantum mechanical states and that has a set objective function whose value is as small as possible. Alternatively, the quantum annealing may be set to find a solution that has a set objective function whose value is as large as possible. Quantum annealing can be seen as a method of solving combinatorial optimization problems (also called discrete optimization problems) using quantum mechanical phenomena.

[0018] 2 is a diagram showing an example of the configuration of the quantum annealing apparatus 100. In the configuration shown in FIG.

[0019] The Kerr nonlinear parametric oscillator 110 represents a variable in the problem of interest. The Kerr nonlinear parametric oscillator 110 transitions its own state from an initial state called a vacuum state to one of two coherent states under the control of the control device 200. The two coherent states correspond to the values ​​of a binary variable, and the state transition of the Kerr nonlinear parametric oscillator 110 can be considered as a solution search.

[0020] The coupler 120 causes the multiple Kerr nonlinear parametric oscillators 110 to interact with each other. In the quantum annealing apparatus 100, the coupler 120 causes the Kerr nonlinear parametric oscillators 110 to interact with each other such that, among the N Kerr nonlinear parametric oscillators 110, any p Kerr nonlinear parametric oscillators 110 interact with each other. Here, N is an integer greater than or equal to 1, and represents the number of Kerr nonlinear parametric oscillators 110 included in the quantum annealing apparatus 100.

[0021] p is a constant representing the number of Kerr nonlinear parametric oscillators 110 included in one set of interacting Kerr nonlinear parametric oscillators 110, and is an integer p≧3. It is assumed that any combination of p Kerr nonlinear parametric oscillators 110 out of N Kerr nonlinear parametric oscillators 110 can interact with each other. p is also referred to as the interaction number constant.

[0022] Fig. 3 is a diagram showing an example of the configuration of the Kerr nonlinear parametric oscillator 110. In the configuration shown in Fig. 3, the Kerr nonlinear parametric oscillator 110 includes a superconducting quantum interference device (SQUID) 111, capacitors 113 and 115, and a magnetic field generating unit 116. The superconducting quantum interference device 111 is configured to include a superconductor loop in which two Josephson junctions 112 are provided.

[0023] The magnetic field generating unit 116 is configured using a coil, and generates a magnetic field in response to a current flowing through the magnetic field generating unit 116. The magnetic field generating unit 116 and the superconducting quantum interference device 111 are magnetically coupled, and a magnetic flux is applied to the superconducting quantum interference device 111 when the magnetic field generating unit 116 generates a magnetic field.

[0024] The loop between the superconducting quantum interference device 111 and the capacitor 113 constitutes a resonant circuit 114. The resonant frequency of this resonant circuit 114 is controlled by the magnitude of the current flowing through the magnetic field generating unit 116. The inductance of the superconducting quantum interference device 111 changes periodically in response to the periodic change in the magnetic field generated by passing an AC current through the magnetic field generating unit 116, and the resonant frequency of the resonant circuit 114 changes periodically. This periodic change in the resonant frequency causes the resonant circuit 114 to parametrically resonate with the change in the magnetic field (AC magnetic field).

[0025] The generation of a magnetic field by the magnetic field generating unit 116 can also be considered as the output of an electromagnetic wave by the magnetic field generating unit 116. The parametric resonance of the resonant circuit 114 with a change in the magnetic field can also be considered as the parametric resonance of the resonant circuit 114 with the electromagnetic wave output by the magnetic field generating unit 116.

[0026] When the resonant frequency of the resonant circuit 114 is close to half the frequency of the current flowing through the magnetic field generating unit 116 and the magnitude of the current flowing through the magnetic field generating unit 116 is equal to or greater than a certain magnitude, the resonant circuit 114 parametrically oscillates due to parametric resonance. The resonant circuit 114 oscillates at a frequency half the frequency of the current flowing through the magnetic field generating unit 116.

[0027] The current flowing through the magnetic field generating unit 116 (the current that the control device 200 passes to the magnetic field generating unit 116) is understood as an input signal to the Kerr nonlinear parametric oscillator 110, and is referred to as a pump signal. The frequency of the pump signal is the frequency of the current flowing through the magnetic field generating unit 116. The amplitude of the pump signal is the amplitude of the current flowing through the magnetic field generating unit 116.

[0028] The product β=i*df / di of the amplitude of the AC component of the pump signal current (current amplitude) i amperes (A) and the change in resonant frequency f due to the current value df / di is called the pump signal strength, or pump strength. Here, "*" indicates multiplication. Since the change in resonant frequency due to the current value, df / di, is determined by the circuit structure and frequency, the pump strength β is proportional to the current amplitude of the pump signal. Therefore, the pump strength can be adjusted by adjusting the current amplitude of the pump signal.

[0029] Increasing the value of the pump strength β is also referred to as increasing the pump strength or increasing the pump strength. The oscillation of the resonant circuit 114 is also referred to as the oscillation of the Kerr nonlinear parametric oscillator 110. Let the angular frequency of the pump signal be ω p Then, the oscillation angular frequency of the Kerr nonlinear parametric oscillator 110 is ω p / 2. The occurrence of parametric oscillation is confirmed by observing that an electromagnetic wave having a frequency half that of the pump signal is output from the Kerr nonlinear parametric oscillator 110.

[0030] The difference obtained by subtracting the oscillation frequency from the resonance frequency of the Kerr nonlinear parametric oscillator 110 is called detuning. Here, if the detuning is represented by Δ, the detuning Δ is the ratio between the resonance frequency ω0 of the Kerr nonlinear parametric oscillator 110 and the oscillation angular frequency ω p Using this and 2, it is expressed as in equation (1).

[0031]

number

[0032] The state of the resonant circuit 114 corresponds to the quantum state of the Kerr nonlinear parametric oscillator 110. The quantum state of the Kerr nonlinear parametric oscillator 110 is observed by measuring the phase of the electromagnetic wave output from the Kerr nonlinear parametric oscillator 110. As described above, under the control of the control device 200, the Kerr nonlinear parametric oscillator 110 transitions the quantum state of the Kerr nonlinear parametric oscillator 110 itself from an initial state called a vacuum state to one of two coherent states.

[0033] 4 is a diagram showing an example of the configuration of the control device 200. In the configuration shown in FIG. The executive control unit 210 controls the quantum annealing apparatus 100 to perform quantum annealing. In particular, the executive control unit 210 determines an interaction number constant p, an interaction strength constant J, a Kerr coefficient K, and a pump constant ξ p The quantum annealing device is controlled based on the above. The execution control unit 210 corresponds to an example of an execution control means.

[0034] As described above, the interaction number constant p is an integer constant p≧3 indicating the number of interacting Kerr nonlinear parametric oscillators 110 . The interaction strength constant J is a constant J>0 that indicates the interaction strength of the Kerr nonlinear parametric oscillator 110 .

[0035] The Kerr coefficient K is a constant, K>0, that indicates the Kerr nonlinearity of the Kerr nonlinear parametric oscillator 110 . Pump constant ξ p is a constant related to the initial value of the pump strength of the Kerr nonlinear parametric oscillator 110. p The value of is determined by the interaction number constant p, the interaction strength constant J, and the pump constant ξ p It is set based on the value of

[0036] The measurement section 220 measures the state of the Kerr nonlinear parametric oscillator 110 . The input / output unit 230 inputs and outputs signals to and from the quantum annealing apparatus 100. In particular, the input / output unit 230 outputs control parameter values ​​for the Kerr nonlinear parametric oscillator 110 and the coupler 120. In this way, the control device 200 controls the quantum annealing apparatus 100. The input / output unit 230 also receives an input of an oscillation signal of the Kerr nonlinear parametric oscillator 110. The measurement unit 220 measures the state of the Kerr nonlinear parametric oscillator 110 by measuring this oscillation signal. Specifically, as described above, the measurement unit 220 observes the quantum state in the Kerr nonlinear parametric oscillator 110 by measuring the phase of the electromagnetic wave output from the Kerr nonlinear parametric oscillator 110.

[0037] The control of the quantum annealing apparatus 100 by the control device 200 will be further described. As an example of a case where three or more Kerr nonlinear parametric oscillators 110 interact with each other, a case where the Hamiltonian H(s) is expressed as in equation (2) will be described.

[0038]

number

[0039] s is a variable whose value monotonically increases from 0 to 1 over time. The Hamiltonian is a function used as an objective function of quantum annealing. The quantum annealing system 1 transitions the state of the Kerr nonlinear parametric oscillator 110 so that the value of the Hamiltonian H(s) at each value of the variable s becomes as small as possible. N represents the number of Kerr nonlinear parametric oscillators 110 and is an integer greater than 0. Here, Δ is a constant representing the detuning, and Δ>0. (1-s)Δ represents the detuning, and when s=0, (1-s)Δ>0, and when s=1, (1-s)Δ=0.

[0040] ^a i represents the annihilation operator. ann_i It can also be written as: ^a with dagger i represents the creation operator. cre_i It can also be written as:

[0041] As described above, the Kerr coefficient K is a constant that indicates the Kerr nonlinearity, and K>0. As mentioned above, the pump constant ξ p is a constant representing the pump strength, and ξ p >0. s(ξ p / 2) represents the pump strength, and when s = 0, s(ξ p / 2)=0, s=1 when s(ξ p / 2)>0.

[0042] As described above, the interaction number constant p is a constant representing the number of Kerr nonlinear parametric oscillators 110 included in one set of interacting Kerr nonlinear parametric oscillators 110, and is an integer p≧3. As described above, the interaction strength constant J is a constant representing the strength of interaction between the Kerr nonlinear parametric oscillators 110. Here, it is assumed that any combination of p Kerr nonlinear parametric oscillators 110 interacts with each other with the same strength.

[0043] Here, it is assumed that all quantum states generated by the Kerr nonlinear parametric oscillator 110 are the same coherent state. In other words, it is assumed that the quantum state can be approximated as shown in equation (3).

[0044]

number

[0045] A × (cross) surrounded by a ○ (circle) represents a tensor product. The tensor product is also written as ○×. The term on the left side of equation (3), ``|Ψ(s)>'', represents the quantum state of the entire quantum system, and it is shown that this quantum state depends on the parameter s. The middle term in equation (3) is "〇× i=1 N |α i > i " represents the quantum state "|>" represented by each of the Kerr nonlinear parametric oscillators 110. i " is the amplitude α i This indicates that the coherent state is

[0046] The term on the right side of equation (3) "〇× i=1 N |α> i " represents the quantum state "|>" exhibited by any of the Kerr nonlinear parametric oscillators 110. i " is also a coherent state with the same amplitude α. Therefore, equation (3) indicates that the quantum states (values ​​of all quantum bits) of all the Kerr nonlinear parametric oscillators 110 are approximated to be coherent states with the same amplitude α. Here, with α being a real number, equation (4) holds true from the definition of a coherent state.

[0047]

number

[0048] "^a i " is the quantum state "|>" of the i-th Kerr nonlinear parametric oscillator 110. i " denotes an annihilation operator that acts only on ". In equation (4), the coherent state of amplitude α, |α> i " to the annihilation operator "^a i " "^a i |α> i " is "α|α> i " This represents the definition of a coherent state. Furthermore, for the Hamiltonian in equation (2), the energy function (semiclassical approximation potential) V(s) in this quantum state is expressed as equation (5).

[0049]

number

[0050] The Hamiltonian "^H(s)" of the entire quantum system is sandwiched between the quantum states "<Ψ(s)|" and "|Ψ(s)>" of the entire quantum system, "<Ψ(s)|^H(s)|Ψ(s)>", which represents the energy of the entire quantum system. Here, an approximation is made that the quantum states of all the Kerr nonlinear parametric oscillators 110 are coherent states with the same amplitude, and the approximate energy of the entire quantum system is calculated.

[0051] The "(1 / N)<Ψ(s)|^H(s)|Ψ(s)>" in the first line of equation (5) represents the energy per Kerr nonlinear parametric oscillator 110. By taking the limit N→∞, it represents the energy per Kerr nonlinear parametric oscillator 110 when there are an infinite number of Kerr nonlinear parametric oscillators 110 or a very large number of Kerr nonlinear parametric oscillators 110.

[0052] In the second and third lines of equation (5), "(1-s)Δ<α|^α cre_i ^α|α>" and "(1-s)Δα 2 " represents the contribution of the detuning (1-s)Δ to the energy V(s). "(K / 2)<α|^α cre_i 2 ^α 2 |α>" and "(K / 2)α 4 " represents the contribution of the Kerr nonlinearity to the energy V(s) (the contribution of the Kerr coefficient K to the energy V(s)).

[0053] 「s(ξ p / 2)<α|^α cre_i 2 ^α 2 |α>' and 'sξ p α 2 " is the pump strength s(ξ p / 2) to the energy V(s). 「sJ(<α|^α cre_i ^α|α>) p " and "sJ(2α) p " represents the contribution of the interaction of the Kerr nonlinear parametric oscillator 110 to the energy V(s), expressed in terms of the interaction strength constant J. The second to third lines of equation (5) are calculated using equation (4). Here, α that minimizes the value of V(s) in Equation 5 is min That is, α min is expressed as equation (6).

[0054]

number

[0055] argmin is a function that outputs the argument value that minimizes the value of the expression shown to the right of it. α for each possible value of the variable s minBy calculating V(s), it is possible to calculate the base state that the Kerr nonlinear parametric oscillator 110 can generate for each value that the variable s can take. For example, when s=0, V(s) takes the minimum value 0 when α=0. Therefore, when s=0, α min = 0. When α = 0, the state of the Kerr nonlinear parametric oscillator 110 is the vacuum state, which is the initial state.

[0056] Furthermore, regardless of the value of s, when α=0, V(s)=0. If there is no nonzero value of α such that V(s)=0 for any value of 0≦s≦1, the state of the Kerr nonlinear parametric oscillator 110 will remain in the vacuum state while the value of s changes from 0 to 1 (i.e., from the beginning to the end of annealing), and no solution search will be possible.

[0057] Therefore, in order for the quantum annealing system 1 to perform quantum annealing, f(α):=V / α 2 Then, the minimum value of f(α) must be less than or equal to 0 for 0≦s≦1. Here, the α that minimizes the value of f(α) is defined as α c That is, α c is expressed as equation (7).

[0058]

number

[0059] α c satisfies equation (8).

[0060]

number

[0061] This alpha c Substituting into f(α), we obtain equation (9).

[0062]

number

[0063] In order for the quantum annealing system 1 to be able to perform a solution search by annealing, it is necessary that g(1) ≦ 0. Therefore, it is necessary to adjust the values ​​of each parameter so that g(1) ≦ 0 is satisfied. From equation (9), we can obtain equation (10) as a necessary and sufficient condition for g(1)≦0.

[0064]

number

[0065] Equation (10) can be transformed into equation (11).

[0066]

number

[0067] In order for the quantum annealing system 1 to perform a solution search by annealing, it is necessary to set the values ​​of the parameters so as to satisfy the formula (11). Therefore, the executive control unit 210 sets the pump constant ξ p The quantum annealing apparatus 100 is controlled using the above to perform quantum annealing. Here, let an appropriate value of α be α0, and rewrite J as equation (12).

[0068]

number

[0069] Based on equation (12), equation (11) can be transformed into equation (13).

[0070]

number

[0071] When Equation (13) is satisfied, there exists an s such that 0 < s ≤ 1 and g(s) = 0. Let s at this time be denoted as s c as shown. s = s c When, the value of α at which V(s) becomes minimum changes discontinuously from α = 0 where the state of the Kerr non - linear parametric oscillator 110 is the vacuum state to α = α c . This change represents a first - order phase transition. In order for the quantum annealing system 1 to perform quantum annealing based on the Hamiltonian shown in Equation (2) and to be able to perform solution search when p ≥ 3, it is impossible to avoid the first - order phase transition.

[0072] When p = 3, the value of s c , and the value of α when s = s c can be obtained analytically. c When p = 3, α c is expressed as in Equation (14).

[0073]

Equation

[0074] Substituting α in Equation (14) into f(α), Equation (15) is obtained. c

[0075]

Equation

[0076] When seeking s = s c such that g(s) = 0, it becomes as in Equation (16).

[0077]

Equation

[0078] Assuming K = Δ = α0 = 1 and ξ p = 1.5 and based on Equation (12), sc ≒0.372, and in this case α c ≒0.372. Figure 5 shows the α min 5 is a diagram showing an example of the value of s. The horizontal axis of the graph in FIG. 5 shows the value of α min Indicates the value of.

[0079] Figure 5 shows the α that minimizes the value of V(s). min The value of is calculated numerically (using SciPy's minimize_scalar) and the result is c The figure shows the area around s = s c Around α min The value of is from 0 to α c where a first-order phase transition occurs.

[0080] Fig. 6 is a diagram showing an example of the relationship between the value of α and the value of V(s) when a first-order phase transition occurs. The horizontal axis of the graph in Fig. 6 represents the value of α, and the vertical axis represents the value of V(s). Line L11 is s=s in the example of Figure 5. c -10 -3 The line L12 shows the relationship between the value of α and the value of V(s) when s=s in the example of FIG. c The line L13 shows the relationship between the value of α and the value of V(s) when s=s in the example of FIG. c +10 -3 4 shows the relationship between the value of α and the value of V(s) when

[0081] For each of lines L11, L12, and L13, the value of V(s) is minimal at α=0.0, and there is also a place where the value of V(s) is minimal between α=0.3 and 0.4. The α at which the value of V(s) is minimal between α=0.3 and 0.4 is α c is equivalent to. In the example of Figure 6, α=0 and α=α c Between α and α, there is a "mountain" where the value of V(s) is large. The quantum mechanical tunnel effect passes through this "mountain" and the value changes from α=0 to α=α c A first-order phase transition occurs.

[0082] When p≧5, it can be confirmed by numerical calculation that a first-order phase transition occurs. In addition, in the limit where p is infinite (p→∞), s c The value of , and s = s c When α c The value of can be found analytically. Based on equation (12), s = s c When α c The value of is expressed as in equation (17).

[0083]

number

[0084] Taking the log of both sides of equation (17) gives equation (18).

[0085]

number

[0086] By taking the limit p → infinity in equation (18), we obtain equation (19).

[0087]

number

[0088] From equation (19), equation (20) can be obtained.

[0089]

number

[0090] In addition, in equations (12) and (15), s = s c As a result, we obtain equation (21).

[0091]

number

[0092] Here, in the limit p → infinity, we obtain equation (22).

[0093]

number

[0094] In addition, in equation (21), "2 p s c j(K / (2 p (p-2)s c J) (p-2) / (p-4) " can be transformed into equation (23).

[0095]

number

[0096] By taking the limit p → infinity in equation (23), we obtain equation (24).

[0097]

number

[0098] From equations (21), (22), and (24), equation (25) can be obtained.

[0099]

number

[0100] The right-hand side of equation (25) "(1-s c )Δ+(K / 2)(α0 2 / K)-s c ξ p Regarding the necessary and sufficient condition for " to be 0, we obtain the condition shown in equation (26).

[0101]

number

[0102] For example, K = Δ = α0 = 1, ξ p = 1.5, then in the limit p → ∞, s c →0.6, and then α c →The result is 1. Figure 7 shows p and s c 7 is a diagram showing a first example of the relationship between p and s. The horizontal axis of the graph in FIG. 7 indicates the value of p. The vertical axis indicates the value of s c Indicates the value of. Figure 7 shows the relationship between K=Δ=α0=1 and ξ p p and s when =1.5 c This shows an example of the relationship between p and s c →It is 0.6.

[0103] Figure 8 shows the relationship between p and α c 8 is a diagram showing a first example of the relationship between p and α. The horizontal axis of the graph in FIG. 8 indicates the value of p. The vertical axis indicates the value of α c Indicates the value of. Figure 8 shows the relationship between K=Δ=α0=1 and ξ p =1.5, s=s c When p and α c This shows an example of the relationship between p and α c →It is 1.0. In the examples in Figures 7 and 8, the larger the value of p, the c and s=s c When α c The value of s also increases. c , α c Each converges to a limit value. Also, s = s c When α c The value of is positive, indicating that a first-order phase transition has occurred.

[0104] Figure 9 shows p and s c 9 is a diagram showing a second example of the relationship between p and s. The horizontal axis of the graph in FIG. 9 indicates the value of p. The vertical axis indicates the value of s c Indicates the value of. Figure 9 shows the relationship between K=Δ=1, α0=√2, and ξ p p and s when =1.5 c This shows an example of the relationship between p and s c →It is 0.8.

[0105] Figure 10 shows the relationship between p and α c 10 is a diagram showing a second example of the relationship between p and α. The horizontal axis of the graph in FIG. 10 indicates the value of p. The vertical axis indicates the value of α c Indicates the value of. Figure 10 shows the relationship between K=Δ=1, α0=√2, and ξ p =1.5, s=s c When p and α c This shows an example of the relationship between p and α c →It is √2. In the examples in Figures 9 and 10, the larger the value of p, the c and s=s c When α c The value of s also increases. c , α c Each converges to a limit value. Also, s = s c When α c The value of is positive, indicating that a first-order phase transition has occurred.

[0106] As described above, when the Hamiltonian is expressed as equation (2) and p≧3, a first-order phase transition must occur in order for the state of the Kerr nonlinear parametric oscillator 110 to change from a vacuum state to a coherent state so that a solution search can be performed. On the other hand, if a first-order phase transition occurs, the time required for annealing, in order to wait for the tunnel effect to occur, becomes exponentially longer with respect to the number of Kerr nonlinear parametric oscillators 110. From the viewpoint of shortening the time required for annealing as much as possible, it is preferable that the state of the Kerr nonlinear parametric oscillators 110 changes from the vacuum state to the coherent state without the first-order phase transition occurring.

[0107] The state of the Kerr nonlinear parametric oscillator 110 changes from the vacuum state to the coherent state without a first-order phase transition, and this change is called the α min is expressed as a continuous change, and s = s c When α c = 0. For this, s = s c It is sufficient that the detuning is 0 when where s=sc We set a Hamiltonian using a ramp function so that the detuning becomes 0 when . The ramp function R(s) is shown in equation (27).

[0108]

number

[0109] In addition, the variable s varies from -1 to 1, and one quantum annealing run (one solution search) begins when s=-1, and ends when s=1. The quantum annealing system 1 performs quantum annealing using, for example, a Hamiltonian H(s) shown in equation (28).

[0110]

number

[0111] In equation (28), R(-s)Δ denotes the detuning. The value of R(-s)Δ decreases with increasing value of s while s increases from -1 to 0, and when s = 0, R(-s)Δ = 0. While s increases from 0 to 1, R(-s)Δ = 0. In addition, in equation (28), R(s)ξ p / 2 represents the pump strength. As s increases from -1 to 0, R(s)ξ p / 2=0, and when s=0, R(s)ξ p / 2=0. As s increases from 0 to 1, R(s)ξ p The value of / 2 increases as the value of s increases.

[0112] Thus, in quantum annealing using the Hamiltonian H(s) shown in equation (28), when s = 0, both the detuning and the pump strength become 0. Under the approximation that the state of the Kerr nonlinear parametric oscillator 110 when s=0 is a coherent state, the energy function (semiclassical approximation potential) V(s) is expressed as shown in Equation (29).

[0113]

number

[0114] FIG. 11 shows the results of the Hamiltonian H(s) shown in Eq. (28) for α min The horizontal axis of the graph in FIG. 11 indicates the value of s. The vertical axis indicates the value of α min Indicates the value of. In FIG. 11, J is expressed as in equation (12), K=Δ=α0=1, ξ p For p = 3, 5, and 7, the α that minimizes the value of V(s) when p = 1.5 is min The results of numerically determining the value of α are shown for the vicinity of s = 0. Line L21 shows the relationship between the value of s and α for p = 3. min The line L22 shows the relationship between the value of s and the value of α when p=5. min The line L23 shows the relationship between the value of s and the value of α when p=7. min The relationship between the values ​​of α min The value of changes continuously from s=0.

[0115] Alternatively, the executive control unit 210 may start decreasing the detuning value while keeping the pump intensity at 0, and then increase the pump intensity from 0 before the detuning value becomes 0. This is expected to make the first-order phase transition relatively small, and to make the time required for one solution search in quantum annealing relatively short.

[0116] Moreover, equation (11) can be approximated as equation (30).

[0117]

number

[0118] The execution control unit 210 is set to satisfy the formula (30). p The quantum annealing apparatus 100 may be controlled to perform quantum annealing based on the above. Here, when the value of p is large, (p-4) / (p-2) in equation (11) can be approximated to 1. In addition, (1 / 2) of Eq. (30) p ) 2 / (p-4) is 1 / 2 2p / (p-4) When the value of p is large, 2p / (p-4) can be approximated by 2, and (1 / 2 p ) 2 / (p-4) can be approximated by 1 / 4.

[0119] Also, when the value of p is large, (1 / (p-2))1 / (p-4) can be approximated by 1. In addition, the exponent of K in Equation 11 is (p-2) / (p-4), and can be approximated by 1 when the value of p is large. Therefore, as described above, equation (11) can be approximated as equation (30).

[0120] FIG. 12 is a diagram showing an example of a processing procedure when the control device 200 controls the quantum annealing device 100 to perform quantum annealing. In the process of FIG. 12, the executive control unit 210 performs initial settings for controlling the quantum annealing device 100 to perform quantum annealing, such as setting the value of a variable s to −1 (step S11).

[0121] Next, executive control unit 210 changes the value of detuning in response to the change in the value of variable s (step S12). After starting to change the detuning value, executive controller 210 may increase the pump intensity. Executive controller 210 may increase the pump intensity after the detuning value reaches 0. Alternatively, executive controller 210 may increase the pump intensity before the detuning value reaches 0.

[0122] After the time for one solution search in quantum annealing has elapsed, the measurement unit 220 measures the state of the Kerr nonlinear parametric oscillator (step S14), whereby the control device 200 obtains a solution for one solution search in quantum annealing. After step S14, the control device 200 ends the process of FIG.

[0123] As described above, the executive control unit 210 determines the interaction number constant p, the interaction strength constant J, the Kerr coefficient K, and the pump constant ξ p The quantum annealing apparatus is controlled based on the above. The interaction number constant p is an integer constant of p≧3 indicating the number of interacting Kerr nonlinear parametric oscillators 110. The interaction strength constant J is a constant J>0 indicating the strength of the interaction of the Kerr nonlinear parametric oscillators 110. The Kerr coefficient K is a constant K>0 indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator 110. The pump constant ξ p is a constant related to the initial value of the pump strength of the Kerr nonlinear parametric oscillator 110. p The value of is determined by the interaction number constant p, the interaction strength constant J, and the pump constant ξ p It is set based on the value of

[0124] According to the control device 200, even when three or more Kerr nonlinear parametric oscillators 110 are interacting with each other, the state of the Kerr nonlinear parametric oscillators 110 can be transitioned from a vacuum state to a coherent state, thereby obtaining a solution in quantum annealing.

[0125] In addition, the pump constant ξ p The value of is set based on the interaction number constant p, the Kerr coefficient K, and the interaction strength constant J so as to satisfy the above formula (11). According to the control device 200, even when three or more Kerr nonlinear parametric oscillators 110 are interacting with each other, the state of the Kerr nonlinear parametric oscillators 110 can be transitioned from a vacuum state to a coherent state, thereby obtaining a solution in quantum annealing.

[0126] In addition, the pump constant ξ p The value of is set based on the interaction number constant p, the Kerr coefficient K, and the interaction strength constant J so as to satisfy the above formula (30). According to the control device 200, even when three or more Kerr nonlinear parametric oscillators 110 are interacting with each other, the state of the Kerr nonlinear parametric oscillators 110 can be transitioned from a vacuum state to a coherent state, thereby obtaining a solution in quantum annealing.

[0127] Furthermore, executive control unit 210 starts decreasing the detuning value while keeping the pump intensity at zero, and then increases the pump intensity from zero. According to the control device 200, by starting to decrease the detuning value before increasing the pump intensity, it is expected that a first-order phase transition in the state of the Kerr nonlinear parametric oscillator 110 will not occur or the magnitude of the first-order phase transition will be relatively small.

[0128] Furthermore, the executive control unit 210 increases the pump intensity from zero after setting the detuning value to zero. According to the control device 200, after the detuning value is set to 0, the pump intensity is increased from 0. It is expected that a first-order phase transition in the state of the Kerr nonlinear parametric oscillator 110 will occur.

[0129] 13 is a diagram showing another example of the configuration of the control device according to the embodiment. In the configuration shown in FIG. In such a configuration, the execution control unit 611 controls the quantum annealing device equipped with a Kerr nonlinear parametric oscillator to perform quantum annealing based on an interaction number constant, which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to three or more, an interaction strength constant, which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient, which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant, which is a constant related to the initial value of the pump strength of the Kerr nonlinear parametric oscillator, which is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient, or a value larger than that.

[0130] The execution control unit 611 corresponds to an example of an execution control means. According to the control device 610, even when three or more Kerr nonlinear parametric oscillators are interacting with each other, the state of the Kerr nonlinear parametric oscillators can be transitioned from a vacuum state to a coherent state, thereby obtaining a solution in quantum annealing.

[0131] 14 is a diagram showing another example of the configuration of the control device according to the embodiment. In the configuration shown in FIG. In this configuration, the executive control unit 621 controls the quantum annealing device equipped with a Kerr nonlinear parametric oscillator to perform quantum annealing by starting to decrease the detuning value while keeping the pump intensity of the Kerr nonlinear parametric oscillator at 0, and then increasing the pump intensity from 0.

[0132] The execution control unit 621 corresponds to an example of an execution control means. By starting to decrease the detuning value before increasing the pump intensity, the controller 620 is expected to avoid a first order phase transition in the state of the Kerr nonlinear parametric oscillator, or to have a relatively small magnitude of the first order phase transition, thereby allowing the controller 620 to expect a relatively short quantum annealing time.

[0133] Fig. 15 is a diagram showing another example of the configuration of a quantum annealing system according to an embodiment. A quantum annealing system 630 in the configuration shown in Fig. 15 includes a quantum annealing device 631 and a control device 632. The control device 632 includes an execution control unit 633. In such a configuration, the execution control unit 633 controls the quantum annealing device equipped with a Kerr nonlinear parametric oscillator to perform quantum annealing based on an interaction number constant, which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to three or more, an interaction strength constant, which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient, which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant, which is a constant related to the initial value of the pump strength of the Kerr nonlinear parametric oscillator, which is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient, or a value larger than that.

[0134] The execution control unit 633 corresponds to an example of an execution control means. According to the quantum annealing system 630, even when three or more Kerr nonlinear parametric oscillators are interacting with each other, the state of the Kerr nonlinear parametric oscillators can be transitioned from a vacuum state to a coherent state, and a solution in quantum annealing can be obtained.

[0135] Fig. 16 is a diagram showing an example of a procedure of a process in a control method according to the embodiment. The control method shown in Fig. 16 includes controlling the execution of quantum annealing (step S611). In controlling the execution of quantum annealing (step S611), the quantum annealing device is controlled to perform quantum annealing based on an interaction number constant, which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to three or more, an interaction strength constant, which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient, which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant, which is a constant related to the initial value of the pump strength of the Kerr nonlinear parametric oscillator, which is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient, or a value larger than that.

[0136] According to the control method shown in FIG. 16, even when three or more Kerr nonlinear parametric oscillators are interacting with each other, the state of the Kerr nonlinear parametric oscillators can be transitioned from the vacuum state to a coherent state, and a solution in quantum annealing can be obtained.

[0137] Fig. 17 is a diagram showing another example of the procedure of the process in the control method according to the embodiment. The control method shown in Fig. 17 includes controlling the execution of quantum annealing (step S621). In controlling the execution of quantum annealing (step S621), a control device that controls a quantum annealing apparatus using a Kerr nonlinear parametric oscillator controls the quantum annealing apparatus to perform quantum annealing by starting to decrease the detuning value while keeping the pump intensity at 0, and then increasing the pump intensity from 0.

[0138] 17, by starting to decrease the detuning value before increasing the pump intensity, it is expected that the first-order phase transition of the state of the Kerr nonlinear parametric oscillator will not occur or the magnitude of the first-order phase transition will be relatively small, which is expected to result in a relatively short time required for quantum annealing in the control device 620.

[0139] FIG. 18 is a schematic block diagram illustrating a configuration of a computer according to at least one embodiment. In the configuration shown in FIG. 18, a computer 700 includes a CPU 710, a main memory device 720, an auxiliary memory device 730, an interface 740, and a non-volatile recording medium 750.

[0140] Any one or more of the control device 200, the control device 610, and the control device 620, or a part of them, may be implemented in the computer 700. In this 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, develops it in the main storage device 720, and executes the above-mentioned processing according to the program. The CPU 710 also secures a storage area corresponding to each of the above-mentioned storage units in the main storage device 720 according to the program. Communication between each device and other devices is executed 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.

[0141] When the control device 200 is implemented in a computer 700, the operations of the execution control unit 210 and the measurement unit 220 are stored in the form of a program in the auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-mentioned processing according to the program.

[0142] Furthermore, the CPU 710 allocates a storage area in the main storage device 720 for the control device 200 to perform processing according to the program. The input / output unit 230 inputs and outputs signals by the interface 740 inputting and outputting signals between the control device 200 and other devices. The interface 740 has an input device and an output device, and the control device 200 interacts with the user by presenting information to the user via the output device under the control of the CPU 710 and accepting user operations via the input device.

[0143] When the control device 610 is implemented in the computer 700, the operation of the execution control unit 611 is stored in the form of a program in the auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it in the main storage device 720, and executes the above-mentioned processing in accordance with the program.

[0144] Furthermore, the CPU 710 allocates a storage area in the main storage device 720 for the control device 610 to perform processing according to the program. Input and output of signals between the control device 610 and other devices is performed by the interface 740 inputting and outputting signals between the control device 610 and other devices. Interaction between the control device 610 and a user is performed by the interface 740 having an input device and an output device, presenting information to the user via the output device under the control of the CPU 710, and accepting user operations via the input device.

[0145] When the control device 620 is implemented in the computer 700, the operation of the execution control unit 611 is stored in the form of a program in the auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-mentioned processing in accordance with the program.

[0146] Furthermore, the CPU 710 allocates a storage area in the main memory 720 for the control device 620 to perform processing according to the program. Input and output of signals between the control device 620 and other devices is performed by the interface 740 inputting and outputting signals between the control device 620 and other devices. Interaction between the control device 620 and a user is performed by the interface 740 having an input device and an output device, presenting information to the user via the output device under the control of the CPU 710, and accepting user operations via the input device.

[0147] Any one or more of the above-mentioned programs may be recorded in non-volatile recording medium 750. In this case, interface 740 may read the program from non-volatile recording medium 750. Then, CPU 710 may directly execute the program read by interface 740, or may temporarily store the program in main storage device 720 or auxiliary storage device 730 and execute it.

[0148] Note that the programs for executing all or part of the processes performed by the control devices 200, 610, and 620 may be recorded on a computer-readable recording medium, and the programs recorded on the recording medium may be read into a computer system and executed to perform the processes of each part. Note that the term "computer system" as used herein includes the OS (Operating System) and hardware such as peripheral devices. Furthermore, the term "computer-readable recording medium" refers to portable media such as flexible disks, optical magnetic disks, ROMs (Read Only Memory), and CD-ROMs (Compact Disc Read Only Memory), as well as storage devices such as hard disks built into computer systems. The above-mentioned program may be for realizing part of the above-mentioned functions, or may be capable of realizing the above-mentioned functions in combination with a program already recorded in the computer system.

[0149] Although an embodiment of the present invention has been described in detail above with reference to the drawings, the specific configuration is not limited to this embodiment, and designs that do not deviate from the gist of the present invention are also included.

[0150] A part or all of the above-described embodiments can be described as, but is not limited to, the following supplementary notes.

[0151] (Appendix 1) an execution control means for controlling a quantum annealing device including the Kerr nonlinear parametric oscillator to perform quantum annealing based on an interaction number constant which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to 3 or more, an interaction strength constant which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant which is a constant related to an initial value of pump strength of the Kerr nonlinear parametric oscillator and is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient or a value larger than that; A control device comprising:

[0152] (Appendix 2) The value of the pump constant is based on the interaction number constant p, the Kerr coefficient K, and the interaction strength constant J.

number

[0153] (Appendix 3) The value of the pump constant is based on the Kerr coefficient K, the interaction strength constant J, and the maximum number p of interacting Kerr nonlinear parametric oscillators.

number

[0154] (Appendix 4) the executive control means starts decreasing the detuning value while keeping the pump intensity at 0, and then increases the pump intensity from 0; 4. The control device according to claim 1 ,

[0155] (Appendix 5) the executive control means sets the detuning value to 0 and then increases the pump strength from 0; 5. The control device according to claim 4.

[0156] (Appendix 6) An execution control means for controlling a quantum annealing device including the Kerr nonlinear parametric oscillator to perform quantum annealing, so that the pump intensity of the Kerr nonlinear parametric oscillator is kept at 0, the detuning value is started to be decreased, and then the pump intensity is increased from 0. A control device comprising:

[0157] (Appendix 7) The present invention includes a quantum annealing device using a Kerr nonlinear parametric oscillator and a control device, The control device includes: an execution control means for controlling the quantum annealing device to perform quantum annealing based on an interaction number constant which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to 3 or more, an interaction strength constant which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant which is a constant related to an initial value of the pump strength of the Kerr nonlinear parametric oscillator and is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient or a value larger than that; Equipped Quantum annealing system.

[0158] (Appendix 8) A control device for controlling a quantum annealing device using a Kerr nonlinear parametric oscillator, The quantum annealing device is controlled to perform quantum annealing based on an interaction number constant which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to 3 or more, an interaction strength constant which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant which is a constant related to an initial value of pump strength of the Kerr nonlinear parametric oscillator and is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient or a value larger than that. The control method includes:

[0159] (Appendix 9) A control device that controls a quantum annealing device using a Kerr nonlinear parametric oscillator starts decreasing the detuning value while keeping the pump intensity at 0, and then controls the quantum annealing device to perform quantum annealing so that the pump intensity is increased from 0. The control method includes:

[0160] (Appendix 10) The computer that controls the quantum annealing device using the Kerr nonlinear parametric oscillator Setting the value of a pump constant, which is a constant related to the initial value of pump strength of the quantum annealing apparatus, to a value determined based on the maximum number of interacting Kerr nonlinear parametric oscillators, an interaction strength constant, which is a constant indicating the strength of interaction between the Kerr nonlinear parametric oscillators, and a Kerr coefficient, which is a constant representing the Kerr nonlinearity, or a value larger than the value; Controlling the quantum annealing apparatus based on the setting to perform quantum annealing; A program for executing.

[0161] (Appendix 11) The computer that controls the quantum annealing device using the Kerr nonlinear parametric oscillator Controlling the quantum annealing apparatus to perform quantum annealing such that the pump intensity is kept at 0, the detuning value is started to decrease, and then the pump intensity is increased from 0; A program for executing the above. [Explanation of symbols]

[0162] 1,630 Quantum Annealing System 100, 631 Quantum annealing device 110 Kerr Nonlinear Parametric Oscillator 120 Combiner 200, 610, 620, 632 Control device 210, 611, 621, 633 Executive control unit 220 Measuring section 230 Input / output section

Claims

1. an execution control means for controlling a quantum annealing device including the Kerr nonlinear parametric oscillator to perform quantum annealing based on an interaction number constant which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to three or more, an interaction strength constant which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant which is a constant related to an initial value of a pump strength of the Kerr nonlinear parametric oscillator and is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient or a value larger than that; A control device comprising:

2. The value of the pump constant is based on the interaction number constant p, the Kerr coefficient K, and the interaction strength constant J. [0010] is set to a value of or greater than The control device according to claim 1 .

3. The value of the pump constant is based on the Kerr coefficient K, the interaction strength constant J, and the maximum number p of interacting Kerr nonlinear parametric oscillators. [0025] is set to a value of or greater than The control device according to claim 1 .

4. the executive control means starts decreasing the detuning value while keeping the pump intensity at 0, and then increases the pump intensity from 0; A control device according to any one of claims 1 to 3.

5. An execution control means for controlling a quantum annealing device including the Kerr nonlinear parametric oscillator to perform quantum annealing, so that the pump intensity of the Kerr nonlinear parametric oscillator is kept at 0, the detuning value is started to be decreased, and then the pump intensity is increased from 0. A control device comprising:

6. The present invention includes a quantum annealing device using a Kerr nonlinear parametric oscillator and a control device, The control device includes: an execution control means for controlling the quantum annealing device to perform quantum annealing based on an interaction number constant which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to three or more, an interaction strength constant which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant which is a constant related to an initial value of the pump strength of the Kerr nonlinear parametric oscillator and is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient or a value larger than that; Equipped Quantum annealing system.

7. A control device for controlling a quantum annealing device using a Kerr nonlinear parametric oscillator, The quantum annealing device is controlled to perform quantum annealing based on an interaction number constant which is a constant indicating the number of interacting Kerr nonlinear parametric oscillators and is set to three or more, an interaction strength constant which is a constant indicating the strength of the interaction of the Kerr nonlinear parametric oscillators, a Kerr coefficient which is a constant indicating the Kerr nonlinearity of the Kerr nonlinear parametric oscillator, and a pump constant which is a constant related to an initial value of pump strength of the Kerr nonlinear parametric oscillator and is set to a value determined based on the interaction number constant, the interaction strength constant, and the Kerr coefficient or a value larger than that. The control method includes:

8. A control device that controls a quantum annealing device using a Kerr nonlinear parametric oscillator starts decreasing a detuning value while keeping the pump intensity at 0, and then controls the quantum annealing device to perform quantum annealing so that the pump intensity is increased from 0. The control method includes:

9. The computer that controls the quantum annealing device using the Kerr nonlinear parametric oscillator Setting the value of a pump constant, which is a constant related to the initial value of pump strength of the quantum annealing apparatus, to a value determined based on the maximum number of interacting Kerr nonlinear parametric oscillators, an interaction strength constant, which is a constant indicating the strength of interaction between the Kerr nonlinear parametric oscillators, and a Kerr coefficient, which is a constant representing the Kerr nonlinearity, or a value larger than the value; Controlling the quantum annealing apparatus based on the setting to perform quantum annealing; A program for executing.

10. The computer that controls the quantum annealing device using the Kerr nonlinear parametric oscillator Controlling the quantum annealing apparatus to perform quantum annealing such that the pump intensity is kept at 0, the detuning value is started to decrease, and then the pump intensity is increased from 0; A program for executing.

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