Ising Model Calculation Device

Abstract

In an Ising model calculation device for computing a generalized Ising model expressed by a Hamiltonian having a magnetic field term, the magnetic field term is applied to spins simulated by state monitoring light pulses, and a response of the obtained light pulses is determined by fitting to perform state monitoring during application of a magnetic field term.

Claims

1. An Ising model calculation device for computing a generalized Ising model expressed by a Hamiltonian having a magnetic field term, the Ising model calculation device configured to: apply a magnetic field to spins of state monitoring light pulses; measure amplitudes of the obtained state monitoring light pulses to monitor a state of the magnetic field term; and monitor an operation state of the Ising model calculation device as a coherent Ising machine.

2. The Ising model calculation device according to claim 1, wherein the magnetic field applied to the state monitoring light pulses is a magnetic field having amplitude values forming a slope dependent on time slots, and the magnetic field is applied to cross a zero point of the magnetic field.

3. The Ising model calculation device according to claim 1, wherein the magnetic field applied to the state monitoring light pulses is constant value.

4. The Ising model calculation device according to claim 1, wherein the magnetic field applied to the state monitoring light pulses is proportional to an absolute value of measured amplitudes of the state monitoring light pulses.

5. The Ising model calculation device according to claim 1, further configured to: fit a specific fitting function to the measured amplitudes of the state monitoring light pulses; and using an obtained value of a fitting parameter, select a calculation result of the Ising model calculation device as a coherent Ising machine.

6. The Ising model calculation device according to claim 1, further configured to: determine an average amplitude value of the measured amplitudes of the state monitoring light pulses; and using the average amplitude value, select a calculation result of the Ising model calculation device as a coherent Ising machine.

7. (canceled)

Description

BRIEF DESCRIPTION OF DRAWINGS

[0048] FIG. 1 is a schematic view of a related art coherent Ising machine.

[0049] FIG. 2 is a diagram illustrating a pattern of pulses of state monitoring check bits according to a first example.

[0050] FIG. 3 is a diagram illustrating other patterns 1 to 3 of pulses of the state monitoring check bits according to the first example.

[0051] FIG. 4 is a diagram for explaining a steady-state solution of amplitudes of DOPO light pulses including a magnetic field (in a case where a magnetic field term is proportional to the absolute value of the amplitude), and illustrates a relationship between a magnetic field amplitude B and a normalized pulse amplitude C.

[0052] FIG. 5 is a diagram illustrating an input of the magnetic field amplitude B of the pulses of the state monitoring check bits according to the first example, and a simulation result.

[0053] FIG. 6 is a diagram of experimental results illustrating an example of a measurement result of amplitudes of the pulses of the magnetic field check bits of the first example.

[0054] FIG. 7 is a diagram illustrating an example of a fitting function used in a second example.

[0055] FIG. 8 is a diagram illustrating a pattern of pulses of state monitoring check bits according to a third example.

[0056] FIG. 9 is a diagram illustrating other patterns 4 to 6 of pulses of the state monitoring check bits according to the third example.

[0057] FIG. 10 is a diagram illustrating other patterns 7 to 9 of pulses of the state monitoring check bits according to the third example.

[0058] FIG. 11 is a diagram of the pulse amplitudes of pattern 9 of the third example, in which odd-numbered slots and even-numbered slots are combined.

DESCRIPTION OF EMBODIMENTS

[0059] In the present invention, state monitoring during application of a magnetic field term is performed as follows. Light pulses are set as state monitoring check bits for the magnetic field term and only an external magnetic field term is applied to spins simulated by the state monitoring light pulses, to obtain a response of the obtained pulses by fitting.

[0060] When the external magnetic field is applied, it is possible to apply magnetic fields having different intensities and directions for each pulse. For example, it is also possible to alternately apply magnetic fields in opposite directions, that is, a magnetic field in a positive direction may be applied to even-numbered pulses in a time slot and a magnetic field in a negative direction may be applied to odd-numbered pulses in the time slot.

[0061] The time slot dependence of the magnetic field in the positive direction applied to the even-numbered pulses may be given a negative slope. Furthermore, the time slot dependence of the magnetic field in the negative direction applied to the odd-numbered pulses may be given a positive slope. It is also possible to reverse the odd-numbered pulses and the even-numbered pulses, and the positive direction and the opposite direction of the magnetic field.

[0062] Furthermore, if the time slot dependence of the amplitudes of the state monitoring light pulses to which the magnetic field is applied is measured and curves for even-numbered pulses or odd-numbered pulses are fitted with an activation function, it is possible to obtain information about an injection pulse phase.

[0063] When the external magnetic field is applied, it is also possible to apply magnetic fields having different intensities and directions for each pulse. The external magnetic field may be applied so that a magnetic field in a positive direction is applied to the first half of pulses in a time slot and a magnetic field in the opposite direction is applied to the latter half of pulses in the time slot. A similar application is possible when the first half and the latter half of pulses are reversed.

[0064] When an external magnetic field is applied, it is also possible to apply magnetic fields having different intensities and directions for each pulse. The external magnetic field may be alternately applied, so that the magnetic field is applied to even-numbered pulses in a time slot but is not applied to odd-numbered pulses in the time slot. A similar application is possible when the even numbers and odd numbers are reversed.

[0065] Thus, advantageously, in an apparatus for computing an Ising model composed of a magnetic field term and an inter-spin interaction term, it is possible to evaluate whether the magnetic field term is applied to a desired state.

[0066] It is possible to check whether the external magnetic field is applied as desired by the following method. For example, amplitudes of light pulses of state monitoring check bits of even-numbered and odd-numbered magnetic field terms in a time slot of time-division light pulses are measured. The measurement data points are fitted by a fitting function, to confirm the following items (1) to (4) in accordance with fitting parameters of the fitting function.

[0067] Specifically, the fitting parameters reflect the following four items (1) to (4) and determine these items.

[0068] (1) Is the orientation (sign) of the phase of the magnetic field correct?

The sign of saturation amplitude reflects a sign of the injection pulse phase, and the absolute value of the saturation amplitude reflects a state of the DOPO oscillation.

[0069] (2) How much does the phase of the magnetic field deviate from 0/π?

The sign of saturation amplitude reflects a sign of the injection pulse phase, and the absolute value of the saturation amplitude reflects a state of the DOPO oscillation.

[0070] (3) Does the center point of the magnetic field deviate (for example, a bias deviation of a modulator)?

The bias on the horizontal axis reflects the bias at the zero point of the injection pulse phase.

[0071] (4) Is there imbalance between positive and negative in the injected magnetic field or the measurement system?

[0072] The bias on the vertical axis reflects the imbalance between positive and negative of the amplitudes of the injection pulses, the imbalance between positive and negative of the measurement system, and the like.

[0073] These items may be optionally selected to monitor the state of the magnetic field term.

[0074] The check bit pattern that may include at least a part of these pieces of information may have various forms, as described in the examples below.

[0075] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

First Example

[0076] FIG. 2 is a diagram illustrating a pattern of amplitudes of pulses including state monitoring check bits according to a first example. In FIG. 2, the horizontal axis expresses time, time slots are set in the order of circulating light pulses, and sections of both the check bits and the calculation bits are illustrated, and the vertical axis expresses the amplitudes of pulses in which, for example, the optical phase 0 is positive and π is negative. Here, a case of a magnetic field in which the pulses of even-numbered slots have a negative slope, and the pulses of odd-numbered slots have a positive slope is illustrated.

[0077] The slopes of the pulses indicate an increasing or a decreasing trend of the amplitude values of the pulses when the time slot number increases (time slot dependence), and the check bit section on the left side in FIG. 2 corresponds to the slopes indicated by dotted lines connecting the leading ends of the pulses in the even-numbered or odd-numbered time slots.

[0078] It is important to alternate the magnetic field in the order of the even/odd numbers of the time slots so that this slope and the amplitude of the magnetic field changes from positive to negative or from negative to positive. A feedback signal for the check bits may be proportional to the absolute value of the measured amplitude (f.sub.i=B.sub.i|C.sub.i|).

[0079] FIGS. 3(a) to 3(c) illustrate other patterns 1 to 3 of pulses of the state monitoring check bits according to the first example. Only portions of the state monitoring check bits are illustrated, and portions of the calculation bits are not illustrated. All of these patterns can be used to check whether the external magnetic field is applied as desired by confirming the above items (1) to (4) of the fitting parameters by a fitting function method described below. Either of the patterns may be assigned to odd-numbered slots or even-numbered slots.

[0080] FIG. 4 is a diagram for explaining a steady-state solution of amplitudes of DOPO light pulses including a magnetic field (in a case where a magnetic field term is proportional to the absolute value of the amplitude) and illustrates a relationship between a magnetic field amplitude B (horizontal axis) and a normalized pulse amplitude C (vertical axis).

[0081] According to NPL 2, an equation describing the time evolution of the normalized amplitude of the DOPO light pulse is expressed by Equation (8) below.

[00002]$\begin{array}{cc}\frac{d}{\mathrm{dt}}{c}_j=\left[-1+p-\left(c_j^2+s_j^2\right)\right]c_j+\underset{l=1,l\ne j}{\overset{N}{.Math.}}{\xi }_{\mathrm{jl}}{c}_l& \left(8\right)\end{array}$

[0082] If Equation (8) is simplified to determine a steady-state solution,

For c>0

c=√{square root over (−1+p+B)}

For c<0

c=−√{square root over (−1+p−B)}

[0083] is obtained and the diagram of the relationship between the magnetic field amplitude B and the normalized pulse amplitude C in FIG. 4 is obtained.

[0084] Consequently, if state monitoring check bits of a magnetic field term having the magnetic field amplitude B illustrated in FIG. 5(a) (32 pulses in total, even-numbered pulses having a negative slope, and odd-numbered pulses having a positive slope) are used as input, a simulation result as illustrated in FIG. 5(b) can be obtained.

[0085] FIG. 6 illustrates an example (experimental results) of a measurement result of amplitudes of actual magnetic field check bits.

[0086] The fitting function illustrated in FIG. 7 according to a second example described below (an example of a Softsign function is illustrated as the fitting function in FIG. 7) is applied and fitted to measurement points of the experimental results to determine fitting parameters (α, β, and γ in FIG. 7). Thus, it is possible to evaluate whether the magnetic field term is applied to a desired state in a generalized Ising model calculation device.

[0087] It is noted that the Softsign function is an example, and any function corresponding to a function (activation function) described in NPL 3 can be applied as the fitting function.

Second Example

[0088] The following information can be obtained from the fitting parameters determined by the fitting function of the second example illustrated in FIG. 7.

[0089] For example, if the fitting function illustrated in FIG. 7 is fitted to experimental data of an amplitude measurement of even-numbered and odd-numbered magnetic field check bits to determine the fitting parameters α, β, and γ, the following information can be obtained.

[0090] The fitting parameters α, β, and γ respectively reflect the following items. α: Saturation amplitude.fwdarw. The sign of α reflects the sign of the injection pulse phase, and the absolute value of a reflects the state of the DOPO oscillation.

[0091] Consequently, it is possible to confirm [0092] whether the orientation (sign) of the phase of the magnetic field is correct (fitting parameter α), and [0093] how much the phase of the magnetic field deviates from 0/π (fitting parameter α). β: Bias on the horizontal axis.fwdarw.β reflects the bias at the zero point of the injection pulse phase.

[0094] Consequently, [0095] whether the center point of the magnetic field deviates (for example, a bias deviation of the modulator) (fitting parameter β) [0096] can be confirmed. [0097] γ: Bias on the vertical axis.fwdarw.γ reflects the imbalance between positive and negative of the amplitude of the injection pulse, the imbalance between positive and negative of the measurement system, and the like.

[0098] Consequently, [0099] whether there is imbalance between positive and negative in the injected magnetic field or the measurement system (fitting parameter γ) can be confirmed.

[0100] These items may be optionally selected to monitor the state of the magnetic field term.

Third Example

[0101] FIG. 8 is a diagram illustrating a pattern of state monitoring check bits according to a third example. In FIG. 8, the left half illustrates a check bit section, and the right half illustrates a calculation bit section.

[0102] The check bit pattern that may include at least a part of the pieces of information described in the second example may have various forms. The state monitoring check bits of the third example in FIG. 8 are characterized in that a constant magnetic field is applied to the check bits.

[0103] The feedback signal for the check bits may be a constant (f.sub.i=B.sub.i). FIGS. 9(a), 9(b), and 9(c) illustrate other patterns 4, 5, and 6 of the state monitoring check bits according to the third example. Pattern 6 in FIG. 9(c) is a combination of patterns 4 and 5 in FIGS. 9(a) and 9(b).

[0104] In this case, it is possible to determine that [0105] if the sign of the magnetic field check bit portion is correct, both positive and negative orientations of the phase of the magnetic field are OK (acquisition of information about item (1) of the fitting parameter), [0106] if the amplitude exceeds a certain value, phase shift is OK (acquisition of information about item (2) of the fitting parameter), [0107] it is not possible to obtain information about item (3) of the fitting parameter, and [0108] if there is imbalance between positive and negative of the signal or the measurement system, heights of the positive portion and the negative portion are different. (acquisition of information about item (4) of the fitting parameter).

[0109] These items may be optionally selected to monitor the state of the magnetic field term. FIGS. 10(a), 10(b), and 10(c) illustrate still other patterns 7, 8, and 9 of the state monitoring check bits according to the third example. Pattern 9 in FIG. 10(c) is a combination of patterns 7 and 8 in FIGS. 10(a) and 10(b) in even-numbered slots and odd-numbered slots.

[0110] In FIG. 11, the pattern 9 of FIG. 10(c) is expressed as the pulse amplitude C with respect to the time slots on the horizontal axis.

[0111] In this case, it is possible to determine that [0112] if the sign of the magnetic field check bit portion is correct, both positive and negative orientations of the magnetic field are OK (acquisition of information about item (1) of the fitting parameter), [0113] if the amplitude exceeds a certain value, phase shift is OK (acquisition of information about item (2) of the fitting parameter), and [0114] it is not possible to obtain information about item (3) of the fitting parameter. [0115] in the case of pattern 9, if there is imbalance between positive and negative of the signal or the measurement system, heights of the positive portion and the negative portion are different. (acquisition of information about item (4) of the fitting parameter). These items may be optionally selected to monitor the state of the magnetic field term.

INDUSTRIAL APPLICABILITY

[0116] As described above, in the present invention, it is possible to implement, in a generalized Ising model composed of a magnetic field term and an inter-spin interaction term, an Ising model calculation device capable of monitoring a state of the magnetic field term and checking the accuracy of a solution.