JP6980185B2 - Ising model arithmetic unit - Google Patents

Description

The present invention relates to an Arithmetic logic unit that simulates an Ising model with an optical pulse.

Conventionally known von Neumann computers cannot efficiently solve combinatorial optimization problems classified as NP-complete problems. As a method for solving the combinatorial optimization problem, a method using the Ising model, which is a lattice model obtained by statistically analyzing the magnetic material as the interaction of spins arranged at each site of the lattice points, has been proposed.

Hamiltonian H, which is an energy function of the Ising model system, is known to be expressed as shown in the following equation (1).

Here, Jij is a coupling constant and indicates the interrelationship between the sites constituting the Ising model. σi and σj represent the spins of each site and take a value of 1 or -1.

When solving the combinatorial optimization problem using the Ising model, in the Hamiltonian of the above Ising model, when Jij, which is the correlation of each site, is given, the system becomes stable and the value of energy H is the highest. The optimum solution can be obtained by finding the smaller σi and σj. In recent years, a computing device capable of solving a combinatorial optimization problem such as an NP-complete problem by simulating such an Ising model using an optical pulse has attracted attention (Patent Document 1).

FIG. 1 is a diagram showing a basic configuration of an arithmetic unit of the Ising model. As shown in FIG. 1, the computing device of the Zing model is a pump optical pulse (Phase Sensitive Amplifier) 2 provided in a ring-shaped optical fiber that functions as a ring resonator 1. By injecting pump), it is configured to generate a sequence of a number of optical pulses corresponding to the number of sites in the Ising model (binarized OPO: Optical Parametric Oscillation: 0 or π-phase optical parametric oscillation). When the optical pulse train input to the ring resonator 1 makes one round and reaches PSA2 again, the pump light is input to PSA2 again to amplify the optical pulse train. The optical pulse train generated by the injection of the first pump light is a weak pulse whose phase is not determined, and its phase state is gradually determined by being amplified by PSA2 each time it orbits in the ring resonator 1. Since the PSA2 amplifies each optical pulse in a phase of 0 or π with respect to the phase of the pump light, it is determined to be in one of these phase states.

In the Ising model computing device, the spins 1 and -1 in the Ising model are implemented corresponding to the phases 0 and π of the optical pulse. The phase and amplitude of the optical pulse train are measured by the measuring unit 3 outside the ring resonator 1 for each circuit of the optical pulse, and the measurement results are input to the arithmetic unit 4 to which the coupling coefficient Jij is given in advance, and these are input to the arithmetic unit 4. Combined signal for the i-th pulse (signal to input feedback)

(Cj: Amplitude of the optical pulse at the jth site) is calculated. Further, by feedback loop control in which an external optical pulse corresponding to the coupling signal calculated by the external optical pulse input unit 5 is generated and input into the ring resonator 1, there is a phase correlation between the optical pulses constituting the optical pulse train. Can be given.

In the computing device of the Zing model, the optical pulse train is amplified in the ring resonator 1 while imparting the above-mentioned correlation, and the phases 0 and π of each optical pulse constituting the optical pulse train in the stable state are set. By measuring, the solution of the Ising model can be obtained.

International Publication No. 2015/156126 Pamphlet

In the computing device of the Zing model, when the feedback input to the optical pulse train in the ring resonator 1, that is, when the external optical pulse by the external optical pulse input unit 5 is input, the external optical pulse to be input and the light in the ring resonator 1 are input. It is necessary to synchronize the phase with the pulse train. Conventionally, the external optical pulse input unit 5 modulates an optical pulse of the same light source as the pump light that generates and amplifies an optical pulse train in the ring resonator 1 with an optical modulator to generate an external optical pulse, thereby generating the ring resonator. Phase synchronization with the optical pulse train was performed by merging with 1.

However, even if the two light pulse trains are originally generated by branching the light of the same light source, the propagation paths are different, so it is necessary to completely match the optical path lengths of the two light pulse trains, and the two light pulses. It was difficult to accurately synchronize the phases.

The present invention has been made in view of such conventional problems, and an object of the present invention is to provide a computing device for an ging model that does not require phase synchronization of light when feedback input is performed.

前記光パルス測定部は、前記光パルス測定部と前記相互作用計算部と前記相互作用実装部とにより構成されるフィードバックループ制御が繰り返される過程で、前記複数の光パルスが安定状態に到達した後に測定した前記複数の光パルスの位相を、イジングモデルのスピンに変換することにより、イジングモデルのスピンの値を得ることを特徴とするイジングモデルの計算装置である。 In order to solve the above problems, the invention described in one embodiment pseudo-corresponds to a plurality of spins of the Rising model, and a plurality of optical pulses having the same oscillation frequency are one of the spins in the Rising model or one of the spins. A phase-sensitive amplifier that parametrically oscillates in a phase of 0 or π corresponding to -1, a ring resonator that orbits the plurality of optical pulses, and each time the plurality of optical pulses orbit around the ring resonator. An optical pulse measuring unit that measures the phase and amplitude of the plurality of optical pulses, and information indicating the phase and amplitude of the plurality of optical pulses measured by the optical pulse measuring unit are input to the coupling coefficient of the Ising model. An interaction calculation unit that calculates a feedback value based on an interaction related to a certain optical pulse, which is determined from information indicating the phase and amplitude of the plurality of optical pulses, and a ring resonator are provided. The interaction related to the certain optical pulse is implemented by modulating the transmission rate of the plurality of optical pulses propagating in the ring resonator based on the feedback value calculated by the interaction calculation unit. The interaction calculation unit includes an interaction mounting unit, and the phase and amplitude of the measured M optical pulses are c ₁ , c ₂ , c ₃ , c ₄ , c _i , c _M-1 , c _M. the relative column vector whose elements, by multiplying the matrix shown below to the coupling coefficient Ising model and calculation parameters, elements f ₁ of the resulting column _{vector, f 2, f 3, f} 4, · f i · the f _M-1, f _'M is calculated as an interaction involving light pulses with the M corresponding to the M optical pulses,

In the optical pulse measuring unit, after the plurality of optical pulses reach a stable state in the process of repeating the feedback loop control composed of the optical pulse measuring unit, the interaction calculating unit, and the interaction mounting unit. It is a calculation device of the Ising model characterized by obtaining the value of the spin of the Ising model by converting the phases of the plurality of measured optical pulses into the spins of the Ising model.

It is a figure which shows the basic structure of the arithmetic unit of the conventional Ising model. It is a figure which shows the schematic structure of the arithmetic unit of the Ising model of this embodiment. It is a figure which shows the structural example of the balanced homodyne detector. This is the processing flow in the basic configuration of the Ising model arithmetic unit.

Hereinafter, embodiments of the present invention will be described in detail.

In the Ising model computing device of the present invention, the spin directions σi and σj (± 1) of the Ising model represented by the Hamiltonian of the following equation (1) are replaced with the phase (0, π) of the optical pulse (pseudo-simulation). By doing so, the problem mapped to the Ising model can be calculated.

FIG. 2 is a diagram showing a schematic configuration of an arithmetic unit of the Ising model of the present embodiment. In FIG. 2, the computing device of the Ising model includes a ring resonator 1 composed of a ring-shaped optical fiber, a PSA (phase sensitive amplifier) 2 provided in the ring resonator 1, and an optical pulse modulator 51. , A measuring unit 3 and an arithmetic unit 41, which are branched from the ring resonator 1 and form a part of the feedback loop. In the Ising model computing device of the present embodiment, the measuring unit 3, the arithmetic unit 41, and the optical pulse modulator 51 form a feedback loop.

PSA2 pseudo-corresponds to multiple spins of the Ising model, and the phase of a pump light source (strictly speaking, local emission used for pump light pulse generation) is a sequence of multiple optical pulses having the same oscillation frequency (optical pulse sequence). It efficiently amplifies light with a phase of 0 or π. The PSA2 can be configured by using a nonlinear optical crystal such as PPLN that exhibits a second-order nonlinear optical effect, for example.

When the signal light (signal light) and the pump light (excitation light) are input, the PSA2 generates a weak pulse (idler light) having a phase of 0 or π with respect to the phase of the pump light source. In PSA2, even when only pump light is input in a state where signal light is not generated for the first time, a weak pulse can be generated as spontaneous emission light.

In PSA2, when the pump light obtained by converting the locally oscillated light (LO light) having the frequency ω to the frequency 2ω which is a double wave by the second harmonic generator is input (there is no pump light so far, just a pump). Weak noise light is generated by the parametric downward conversion process. Further, in PSA2, when the optical pulse train propagating in the ring resonator 1 is input again, the optical pulse train is signal light.

And the pump light that is perfectly phase-matched to this signal light

Is further input to PSA2, and the idler light becomes a phase-conjugated wave of the signal light Es due to OPO (optical parametric oscillation), which is a second-order nonlinear optical effect.

Occurs.

At this time, if the frequencies of the signal light and the idler light match, the following degenerate wave is output.

Since this output degenerate wave is a superposition of the signal light and the idler light having a phase conjugate relationship, the wave having a phase of 0 or π is efficiently amplified. In this way, in PSA2, the phase component of 0 or π in the weak optical pulse train initially generated is amplified.

The ring resonator 1 orbits a plurality of optical pulses (optical pulse trains) generated by the PSA2. The ring resonator 1 can be composed of a ring-shaped optical fiber, and the length of the optical fiber is (the number of pulses constituting the optical pulse train) × (pulse interval) equal to the time required for feedback processing. It is set to the one with the addition.

The measuring unit 3 functions as an optical pulse measuring unit that measures the phase and amplitude of the plurality of optical pulses each time a plurality of optical pulses (optical pulse trains) propagate around the ring resonator 1 (each orbit). .. Specifically, the measuring unit 3 branches the optical pulse train propagating in the ring resonator 1 and coherently measures the phase state including the amplitude thereof. In the coherent measurement, the amplitude and phase of the optical pulse train input as the light to be measured can be measured using a balanced homodyne detector.

FIG. 3 is a diagram showing a configuration example of the balanced homodyne detector 30. The balanced homodyne detector 30 can measure the amplitude and the phase state by interfering with the light constituting the optical pulse train by using the phase-synchronized light having the same frequency as the light pulse train to be measured as the reference light. The balanced homodyne detector 30 has a half mirror 31 that interferes with the light from the port 1 and the port 2 and outputs the light to the port 3 and the port 4, and a first photodetector 32 that detects the light output from the port 3. A second photodetector 33 that detects the light output from the port 4 and a difference calculation unit 34 that calculates the difference between the detection results of the first and second photodetectors 32 and 33. ..

The port 1 optical pulse train ^{_{E s e i (ωt + θ}} ) is input as the measured light, the port 2, the reference light ^E _Lo e iωt amplitude and phase are known are input. The optical pulse train input from the port 1 is branched into a component transmitted toward the port 3 in the same phase and a component whose phase is changed by π and reflected toward the port 4 in the half mirror 31. The reference light input from the port 2 is branched into a component transmitted toward the port 4 in the same phase and a component reflected toward the port 3 in the same phase in the half mirror 31.

Output light in which the in-phase component of the optical pulse train input from port 1 and the in-phase component of the reference light input from port 2 interfere with each other.

Is output from port 3, and in the first detector 32, the light intensity

An electrical signal indicating is detected.

The anti-phase component of the optical pulse train input from port 1 and the in-phase component of the reference light input from port 2 interfere with the output light.

Is output from port 4, and in the second detector 33, the light intensity

The electrical signal represented by is detected.

Further, the difference calculation unit 34 calculates the difference between the detection signal in the first detector 32 and the detection signal in the second detector 33, and _{outputs 2E LoE s} cos θ.

Therefore, since the amplitude E _{Lo of the} reference light is known, the value ± E including the cos component (sign only) and the amplitude of the phase can be obtained as the measurement result.

The value obtained as a measurement result is a signed analog value (± E), where the sign (±) indicates the phase and the analog value (E) indicates the amplitude.

Returning to FIG. 2, the arithmetic unit 41 takes the measured phase and amplitude of the optical pulse as input, and involves an optical pulse determined based on the coupling coefficient mapped to the Ising model and the phase and amplitude of other optical pulses. It functions as an interaction calculation unit that determines the interaction and calculates the phase and amplitude (coupling result of the interaction) of the optical pulse after receiving the interaction as a feedback value. As the arithmetic unit 41, for example, a digital arithmetic unit such as FPGA can be used.

Specifically, the arithmetic unit 41 first performs an operation of giving a coupling coefficient to the amplitude and phase of the optical pulse train measured by the measuring unit 3 based on the equation (2), and determines the interaction.

Above formula (2), c1, c2, c3, c4, c5 (c i) is the measurement results for each light pulse in each measurement unit 3, f1, f2, f3, f4, f5 (f i) is Each is the calculation result of the interaction. The matrix operation parameters J ₁₂ , J ₁₃ , J ₁₄ , J ₁₅ , ... J ₅₃ , J ₅₄ are coupling coefficients mapped to the Ising model and are determined according to the problem for which a solution is to be found. Ising. Although the case where the number of sites is 5 is described here as an example, the size of the square matrix to be used is determined according to the number of sites. The square matrix is the size of (number of sites) × (number of sites).

For the above interaction, for example, assuming that the number of sites (the number of optical pulses constituting the light pulse train) is N, the calculation unit 41 performs a matrix calculation by the following equation (3) to determine the interaction. Can be done.

As shown in the above equations (2) and (3), the arithmetic unit 41 generates a column vector whose element is the measurement result in the measuring unit 3, and performs an operation of multiplying the generated column vector by a matrix. Interactions can be determined.

The arithmetic unit 41 further performs a calculation according to equation (4) shown below, to obtain the number of turns of the (n + 1) coupling a result of the interaction for each light pulse in the c _'i (n) as a feedback value.

In the above equation (4), c'i (n) is the coupling result of the interaction for the i-th optical pulse in the optical resonator circumference (n), and c is the cos component of the i-th optical pulse. , R are coefficients for converting to transmittance. In the formula (4), the second term is obtained by dividing the fi obtained based on the above formulas (2) and (3) for calculating the interaction by the measurement result c _{i of the measuring instrument 3.} By substituting the obtained fi divided by ci into the above equation (4), a calculation result c'i (n) which is a feedback value is obtained.

The optical pulse modulator 51 modulates the amplitude and phase of the optical pulse propagating in the ring resonator 1 by using the calculation result c'i (n) calculated by the arithmetic unit 41 to generate an optical pulse. It functions as an interaction mounter that implements the magnitude and sign of the involved interactions. In the present embodiment, the optical pulse modulator 51 is provided in the ring resonator 1 and feeds back to the optical pulse train by modulating the amplitude and phase of the optical pulse propagating in the ring resonator 1. Since it is not necessary to input an external optical pulse for feedback, it is not necessary to perform phase synchronization of the light.

In practice, the optical pulse modulator 51 is input with the operation result c _'i (n) in the arithmetic unit 41, modulates the transmittance of the optical pulse train in the ring resonator 1 as follows.

The optical pulse modulator 51 can be configured by using a push-pull modulator or the like composed of a 2-arm Mach zender. In the case of a push-pull modulator, the response function of its optoelectric field is

It is represented by. Where A is the maximum transmittance of the modulator,

And φ is the bias of the modulator. Therefore, the actual modulation amount T in the optical pulse modulator 51 using the push-pull modulator is set to θ << | π / 2 |, where φ is the bias of the modulator.

Will be. Especially when θ << π / 2,

Will be.

According to the above equations (5) and (6), if the number of sites is relatively small, the number of bonds is relatively small, or the coupling coefficient Jij is set relatively small, the input is performed according to the equation (6). It can be seen that it is possible to give feedback to each optical pulse almost ideally because the modulation can be applied almost linearly to the light pulse. Therefore, when a push-pull modulator composed of a 2-arm Mach zender is used as the optical pulse modulator 51, it can be said that it is preferable to deal with the problem that the number of sites and the number of bonds are relatively small.

In this way, by giving the optical pulse modulator 51 an input according to the calculation result of the arithmetic unit 41, it is possible to feed back the pseudo interaction to the optical pulse train in the ring resonator 1.

When the optical pulse train modulated by the optical pulse modulator 51 is input to PSA2 again, the input optical pulse train is amplified. With the above configuration, the Ising model computing device guides the optical pulse train to a stable state according to the problem while repeating amplification and feedback.

FIG. 3 is a processing flow in the basic configuration of the Ising model arithmetic unit. As shown in FIG. 3, in the Ising model computing device, when the pump light is first injected into the PSA2, a weak noise light pulse train is generated (S1), and the generated noise light pulse train is the ring resonator 1. Propagate around the inside. A part of the optical pulse train propagating in the ring resonator 1 is branched, and the amplitude and phase thereof are measured by the measuring unit 3 (S2).

When the measurement result of the optical pulse train is obtained, the interaction is calculated by the matrix in which the coupling coefficient corresponding to the problem to be solved is mapped in the arithmetic unit 41, and the feedback value is calculated based on the calculated interaction. (S4). When a feedback value is input, the optical pulse modulator 51 gives feedback to the optical pulse train by modulating the optical pulse train in the ring resonator 1 (S5).

The optical pulse train after the feedback is input to the PSA2 again, amplified by the pump light synchronized with the optical pulse train (S6), and propagates in the ring resonator 1 again. After being amplified by the PSA2, the optical pulse train propagating again in the ring resonator 1 is repeatedly subjected to coherent measurement, matrix calculation, and feedback according to the calculation result.

When such amplification and feedback for the optical pulse train are repeated a predetermined number of times (S3), the state of the optical pulse train becomes stable. It was given by replacing 0 or π, which is the phase state of the measurement result obtained by the measuring unit 3 when the stable state was reached, with the spin σ state (± 1) of the Ising model and demapping it to the problem to be solved. You will get a solution to the problem.

In the computing device of the Ising model of the present embodiment, an optical pulse modulator 51 is provided in the ring resonator 1 in which the optical pulse train orbits propagates, and the modulation amount is electrically input to the optical pulse modulator 51. Since the optical pulse train can be directly optical-modulated and input back, it is not necessary to use an external optical pulse input for the feedback input. Therefore, the phase synchronization of light at the time of feedback input becomes unnecessary.

The calculation device of the Ising model described in the above embodiment has been described by taking as an example the case where the PSA is composed of a nonlinear optical crystal such as PPLN that exhibits a second-order nonlinear optical effect, but the third-order nonlinear optics. It may be a configuration that exerts an effect.

1 Ring resonator 2 PSA (Phase sensitive amplifier)
3 Measuring unit 4, 41 Computing unit 5 External optical pulse input unit 51 Optical pulse modulator 30 Balanced homodyne detector 31 Half mirror 32 First photodetector 33 Second photodetector 34 Difference calculation unit

Claims (5)

A phase-sensitive amplifier that pseudo-corresponds to multiple spins of the Ising model and parametrically oscillates multiple optical pulses having the same oscillation frequency in a phase of 0 or π corresponding to 1 or -1 of the spins in the Ising model. ,
A ring resonator that orbits the plurality of optical pulses and
An optical pulse measuring unit that measures the phase and amplitude of the plurality of optical pulses each time the plurality of optical pulses propagate around the ring resonator.
It is determined from the coupling coefficient of the Ising model and the information indicating the phase and amplitude of the plurality of optical pulses by inputting the information indicating the phase and amplitude of the plurality of optical pulses measured by the optical pulse measuring unit. The interaction calculation unit, which calculates the feedback value based on the interaction related to the optical pulse,
The present invention is performed by modulating the transmittance of the plurality of optical pulses provided in the ring resonator and propagating orbiting in the ring resonator based on the feedback value calculated by the interaction calculation unit. It is equipped with an interaction mounting part that mounts the interaction related to the optical pulse.
In the interaction calculation unit, the phase and amplitude of the measured M optical pulses are for a column vector whose elements _{are c 1} , c ₂ , c ₃ , c ₄ , · c _i · c _M-1 , and c _M. , The elements of the column vector f ₁ , f ₂ , f ₃ , f ₄ , f _i · f _M-1 , f ′ _M is calculated as an interaction involving M optical pulses corresponding to the M optical pulses.

In the optical pulse measuring unit, after the plurality of optical pulses reach a stable state in the process of repeating the feedback loop control composed of the optical pulse measuring unit, the interaction calculating unit, and the interaction mounting unit. A computer for an Ising model, characterized in that a value of the spin of the Ising model is obtained by converting the measured phases of the plurality of optical pulses into the spin of the Ising model. _{The interaction calculation unit divides fi i} obtained in the calculated interaction by c _{i , and uses the cos component c i} of the i-th optical pulse and the number N of the plurality of optical pulses to fi /. seeking ci, using the coefficient R for converting the transmittance, by the following equation, the phase and amplitude c after each light pulse in the optical resonator circulation number (n) is subjected to interaction _'i (n ) a computing device Ising model according to claim 1, characterized in that calculated as the feedback value.

In the phase-sensitive amplifier, pump light having a frequency of 2ω was input, a weak noise optical pulse train having a frequency of ω was generated by optical parametric oscillation, and the optical pulse train propagating in the ring resonator was input again. The ging model according to claim 1 or 2, wherein a pump light having a frequency of 2ω, which is perfectly phase-matched, is input to the optical pulse train, and the optical pulse train is amplified in a phase of 0 or π. Computing device. The optical pulse measuring unit measures the phase and amplitude of an optical pulse by homodyne detection by a balanced homodyne detector using locally oscillated light for generating the pump light input to the phase sensitive amplifier as a reference light. The isging model computing device according to claim 3, wherein the device is characterized by the above-mentioned. The interaction mounting unit superimposes on a certain optical pulse by modulating the phase and amplitude of the locally oscillated light for generating the pump light input to the phase sensitive amplifier as the plurality of optical pulses. The computing device of the Ising model according to claim 3 or 4, wherein a light pulse to be combined is generated.

Images