Combinatorial Optimization Problem Processing Apparatus and Method Thereof

Abstract

A combinatorial optimization problem processing device that processes a combinatorial optimization problem of N elements in association with an Ising model, the combinatorial optimization problem processing device comprising: a 1×2 Mach-Zehnder optical modulator 10 that modulates a polarization clock pulse train; an optical interference circuit 20 that receives the polarization clock pulse train modulated by the 1×2 Mach-Zehnder optical modulator 10 and causes a predetermined interaction in the Ising model in a cycle of N pulses of the polarization clock pulse train; an optical signal processing unit 30 that transitions each pulse of the polarization clock pulse train in terms of optical power level according to the power level of each pulse of the optical signal pulse train output from the optical interference circuit 20; and a modulation signal generation unit 40 that generates a modulation signal for the 1×2 Mach-Zehnder optical modulator 10 and outputs, to the outside, a monitor signal representing a solution to the optimization problem.

Description

Technical Field

[0001] The present invention relates to a combinatorial optimization problem processing apparatus and method for deriving a solution to a combinatorial optimization problem.

Background Art

[0002] A combinatorial optimization problem is a problem of searching for a combination (solution) of parameters that maximizes (or minimizes) an evaluation index under given conditions. Combinatorial optimization problems can be applied to situations where better choices are required in various fields such as distribution and drug discovery.

[0003] For combinatorial optimization problems in the NP-hard class, as the number of elements (parameters) N of the combination increases exponentially, there is a problem that it takes an unrealistically long time to find the optimal solution by the "exhaustive search method".

[0004] It is known that solving a combinatorial optimization problem corresponds to finding the most stable energy state of an Ising model. Non-Patent Document 1 discloses a method of finding the most stable state in an Ising model by a method similar to simulated annealing, implementing it on a CMOS semiconductor chip, and simulating it to find the most stable energy state, thereby substantially solving the combinatorial optimization problem.

[0005] However, the conventional methods have a problem that it takes time to find the optimal solution. Therefore, the inventor has devised a combinatorial optimization problem processing apparatus and method that can find the optimal solution of a combinatorial optimization problem in a shorter time compared to the conventional methods so far (Patent Document 1 and Patent Document 2).

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Patent Document 2

Non-Patent Document

[0007]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0008] In Patent Documents 1 and 2, the coefficient J representing the magnitude of the interaction i:k is an important parameter that affects the property of obtaining a better (corresponding to a stable state) solution. In the region where the sum of J i:k does not exceed 1, qualitatively, the larger the absolute value of J i:k , the better the solution that can reflect the mutual relationship more strongly is expected to be obtained.

[0009] However, taking a system where N = 100, fully connected, the absolute value of J i:k is constant, and ferromagnetic and antiferromagnetic interactions are randomly assigned as an example, when the absolute value of J i:k is up to around 0.004, generally a good solution can be obtained. On the other hand, it has been found that when the absolute value of J i:k increases up to around 0.009, a phenomenon occurs where no good solution can be obtained at all.

[0010] The present invention has been made in view of the above, and an object thereof is to provide a combinatorial optimization problem processing technique capable of obtaining a good solution even in a region with a large interaction.

Means for Solving the Problems

[0011] The combinatorial optimization problem processing apparatus according to one aspect of the present invention is a combinatorial optimization problem processing apparatus that associates a combinatorial optimization problem of N elements with an Ising model and processes it. The apparatus includes a 1×2 Mach-Zehnder optical modulator that inputs and modulates a polarized clock pulse train, an Ising model operation unit that inputs the polarized clock pulse train modulated by the 1×2 Mach-Zehnder optical modulator and causes a predetermined interaction in the Ising model to occur at the period of N pulses of the polarized clock pulse train, an optical signal processing unit that inputs an optical signal pulse train output from the Ising model operation unit and the polarized clock pulse train and outputs an optical signal in which each pulse of the input polarized clock pulse train has made a transition with respect to optical power according to the power level of each pulse of the input optical signal pulse train, and a modulation signal generation unit that waveform-shapes an electrical signal obtained by photoelectrically converting the optical signal after the transition to generate a modulation signal for the 1×2 Mach-Zehnder optical modulator and outputs a monitor signal representing the solution of the optimization problem to the outside. The Ising model operation unit inputs an initialization optical pulse train having an effective peak power of half of the polarized clock pulse train and N pulses in number to create a neutral state with respect to the interaction between the elements, and repeatedly causes a predetermined interaction in the Ising model to occur at the period of N pulses of the polarized clock pulse train from the neutral state.

[0012] The combinatorial optimization problem processing apparatus according to one aspect of the present invention is a combinatorial optimization problem processing apparatus that processes a combinatorial optimization problem of N elements in association with an Ising model, and includes a first phase modulation unit and a second phase modulation unit, a differential phase modulation type Mach-Zehnder optical modulator that inputs and modulates a polarization clock pulse train, an Ising model calculation unit that inputs the polarization clock pulse train modulated by the differential phase modulation type Mach-Zehnder optical modulator, causes a predetermined interaction in the Ising model to occur at the period of N pulses of the polarization clock pulse train, and outputs an external monitor signal representing a solution to the optimization problem, an N initialization optical pulses that create a neutral state with respect to the interaction between the elements and an output signal from the Ising model calculation unit as inputs, combines the initialization optical pulses with the output signal from the optical interference circuit, demultiplexes the initialization optical pulses and the optical signal pulse train, respectively, outputs one of the demultiplexed signals as a first phase modulation signal to the first phase modulation unit, outputs the other of the demultiplexed signals as a second phase modulation signal to a delay unit, a delay unit that delays the second phase modulation signal by a time greater than or equal to the pulse width of the pulses of the polarization clock pulse train and less than the pulse interval with respect to the first phase modulation signal and outputs it to the second phase modulation unit, and an optical signal processing unit that inputs the optical signal pulse train and the polarization clock pulse train output from the Ising model calculation unit, and outputs an optical signal in which each pulse of the polarization clock pulse train has undergone a transition with respect to the optical power level according to the power level of each pulse of the input optical signal pulse train, provided between any of the Ising model calculation unit and the multiplexer / demultiplexer, the multiplexer / demultiplexer and the delay unit, or the delay unit and the differential phase modulation type Mach-Zehnder optical modulator.

Advantages of the Invention

[0013] According to the present invention, it is possible to provide a combinatorial optimization problem processing technique capable of obtaining a good solution even in a region with a large interaction.

Brief Description of the Drawings

[0014]

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DETAILED DESCRIPTION OF THE INVENTION

[0015] Before describing the embodiments of the present invention, the annealing model and the combinatorial optimization problem will be briefly described.

[0016] (Annealing Model) FIG. 1 shows an example of an annealing model. The annealing model is a statistical mechanical model representing the properties of a magnetic material (such as a ferromagnetic material or an antiferromagnetic material). The annealing model is composed of lattice points that take either an up or down spin state, and reaches a stable state when the energy H considering the interaction between adjacent lattice points is minimized.

[0017] In numerical calculations using methods such as neural networks, the annealing model has a spin state σ of each lattice point i and an interaction coefficient J representing the force of interaction exerted between two spins ij and an external magnetic field coefficient h representing the force of an externally applied magnetic field i and can be expressed in terms of these. The energy H of the annealing model can be expressed by the following equation.

[0018]

Number

[0019] In the annealing model, the spin state is updated so that the energy H is minimized. By mapping the problem so that the evaluation index of the combinatorial optimization problem corresponds to the energy of this annealing model and converging the annealing model, a combination of spin states that minimizes the energy can be obtained. This means, in other words, finding a combination of parameters that minimizes the evaluation index of the original optimization problem.

[0020] In general, an optimization simulator generally referred to as an Ising model machine performs an extension that considers interactions not only between adjacent lattice points but also between all lattice points.

[0021] (Combinatorial Optimization Problem) FIG. 2 is a diagram schematically showing an example of a combinatorial optimization problem called the Max Cut 3 problem with N = 16. The circles shown in FIG. 2 represent each element of N = 16.

[0022] The Max Cut 3 problem is a problem of maximizing the total weight of the edges cut when each element is grouped into two groups. Also, "3" means the number of interactions in the Ising model.

[0023] The right diagram in FIG. 2 is a diagram schematically showing the interactions. The interactions in the right diagram show an example of receiving from three elements: the elements before and after (± 1) and the element eight before (-8). Note that the interactions of Max Cut 3 with N = 16 are not limited to this example.

[0024] Hereinafter, the combinatorial optimization problem processing apparatus according to the embodiment of the present invention will be described by an example of solving the combinatorial optimization problem shown in FIG. 2.

[0025] [First Embodiment] FIG. 3 is a diagram showing an example of the configuration of a combinatorial optimization problem processing apparatus according to the first embodiment. The combinatorial optimization problem processing apparatus 100 shown in the figure includes a 1-input 2-output Mach-Zehnder optical modulator 10 (hereinafter referred to as the Mach-Zehnder optical modulator 10), an optical interference circuit 20, an optical signal processing unit 30, and a modulation signal generation unit 40.

[0026] The Mach-Zehnder optical modulator 10 receives a polarization coherent clock pulse train (hereinafter referred to as a polarization clock pulse train). The Mach-Zehnder optical modulator 10 adjusts the fixed phase condition so that the following equation (2) holds.

[0027] [Equation]

[0028] Here, i is the number assigned to an arbitrarily determined reference pulse, and N is the problem scale. In the case of the combinatorial optimization problem in Figure 2, N=16.

[0029] Generally, due to manufacturing errors, the two output ports of a Mach-Zehnder optical modulator are A and A. - Since this deviates from the condition that the phase is equal to the phase of the output, a phase adjustment unit that can adjust the phase is provided in one or both arms of the interferometer. If equation (2) is established, the outputs from the two output ports are A and A. - The condition is met.

[0030] The total return time on the main path is the problem size N × the pulse interval d of the polarized clock pulse train. t The polarization clock pulse train is supplied to the Mach-Zehnder optical modulator 10 in a state where it coincides with the polarization clock pulse train A and A from the Mach-Zehnder optical modulator 10. The polarization clock pulse train is modulated by the Mach-Zehnder optical modulator 10, and A and A from the Mach-Zehnder optical modulator 10 are - The output of this signal is input to the optical interferometer 20. The return time is the time from when a specific optical pulse is ready to be modulated in the Mach-Zehnder optical modulator 10 until the electrical pulse derived from this pulse reaches the Mach-Zehnder optical modulator 10 and drives it to be modulated.

[0031] In this embodiment, each pulse i in the polarized clock pulse train corresponds to each element of the combinatorial optimization problem. Then, a set of N=16 pulses according to equation (2) can be regarded as one sequence. Specifically, i, i+N, i+2N, ... is one sequence, and (i+1), (i+1)+N, (i+1)+2N, ... is another sequence. There are N sequences in total, up to (i+(N-1)), (i+(N-1))+N, (i+(N-1))+2N, ....

[0032] Fig. 4 shows an example of a time chart for explaining the relationship between the polarized clock pulse train and each series. In Fig. 4, the polarized clock pulse train and four series of pulse trains are shown arranged vertically. Specifically, the first pulse train is the polarized clock pulse train input to, for example, A of the optical interference circuit 20 - is the polarized clock pulse train input thereto. The second pulse train is a pulse train 1bD obtained by delaying the polarized clock pulse train by one pulse of the polarized clock pulse. The third pulse train is a pulse train 0bD that does not delay the polarized clock pulse train. The fourth pulse train is a pulse train 2bD obtained by delaying the polarized clock pulse train by two pulses. The fifth pulse train is a pulse train 9bD obtained by delaying the polarized clock pulse train by nine pulses. For the purpose of easy understanding of the explanation, identification numbers -8, -7, -6,..., -1, 0, +1, +2, +3,... are assigned from the left of the polarized clock pulse train. Note that the pulse width of the polarized clock pulse train is t pw , the pulse interval is d t , and the effective peak power is P opt .

[0033] Here, pay attention to the pulse with the identification number 0 in the pulse train 1bD. The pulse with the identification number 0 is the first pulse when viewed in terms of the period of N pulses. The identification numbers of the pulses in the other pulse trains 0bD, 2bD, and 9bD at the same timing as this first pulse are +1, -1, and -8, respectively. That is, with respect to the pulse with the identification number 0, the pulse at +1 one pulse ahead, the pulse at -1 one pulse behind, and the pulse at -8 eight pulses before coincide at the same timing.

[0034] By interfering these polarized pulses with the optical interference circuit 20, an interaction Q AF represented by the following equation can be generated.

[0035]

Equation

[0036] Here, i is the serial number of the pulses constituting the polarized clock pulse train, k is the number representing the position of the pulses within N, and J i:kis a coefficient representing the magnitude of the interaction. Note that the second term within the parentheses on the right side of Equation (3) is A output from the output port of the Mach-Zehnder modulator 10 - corresponds to. Equation (3) represents an antiferromagnetic type of interaction.

[0037] In the above example, there are multiple values of k. For example, k = +1, k = -1, k = -8. These values of k correspond to the interactions shown in the right figure of FIG. 2.

[0038] The power of the polarization clock pulse train output by the optical interference circuit 20 can be expressed by the following equation.

[0039] [Number]

[0040] In this way, by inputting the output optical pulse train derived from the polarization clock pulse train from the Mach-Zehnder modulator 10 into the optical interference circuit 20, an optical signal pulse train affected by the desired interaction can be generated.

[0041] (Optical interference circuit) FIG. 5 is a diagram showing an example of the configuration of the optical interference circuit 20. The optical interference circuit 20 shown in FIG. 5 includes a first delay unit 22a, a second delay unit 22b, a third delay unit 22c, and a fourth delay unit 22d, which are a plurality of delay units, a first main path 21a, a second main path 21b, a first action path 21c, a second action path 21e, and a third action path 21f, which are a plurality of optical waveguides, and a first optical coupler 23a, a second optical coupler 23b, a third optical coupler 23c, and a fourth optical coupler 23d, which are a plurality of optical couplers.

[0042] The first delay unit 22a delays the polarization clock pulse train (A) branched from the polarization clock pulse train output by the Mach-Zehnder modulator 10 by one pulse. The first main path 21a propagates the first polarization clock pulse train 1bD obtained by delaying the polarization clock pulse train (A) by one pulse.

[0043] The second delay unit 22b delays the polarization clock pulse train (A) output from the Mach-Zehnder optical modulator 10 by the same one pulse as the first delay unit for the branched polarization clock pulse train. The second main path 21b propagates the second polarization clock pulse train 1bD obtained by delaying the polarization clock pulse train (A) by one pulse.

[0044] The first action path 21c directly propagates the third polarization clock pulse train 0bD obtained by branching the polarization clock pulse train (A - ) output from the Mach-Zehnder optical modulator 10.

[0045] The third delay unit 22c delays the polarization clock pulse train obtained by branching the polarization clock pulse train (A - ) output from the Mach-Zehnder optical modulator 10 by two pulses. The second action path 21e propagates the fourth polarization clock pulse train 2bD obtained by delaying the polarization clock pulse train (A - ) by two pulses.

[0046] The fourth delay unit 22d delays the polarization clock pulse train obtained by branching the polarization clock pulse train (A - ) by nine pulses. The third action path 21f propagates the fifth polarization clock pulse train 9bD obtained by delaying the polarization clock pulse train (A - ) by nine pulses.

[0047] The first optical coupler 23a causes interference to add the amplitudes of the fifth polarization clock pulse train 9dD and the fourth polarization clock pulse train 2bD. The second optical coupler 23b causes interference to add the amplitude of the output optical signal of the first optical coupler 23a and the third polarization clock pulse train 0bD. The third optical coupler 23c causes interference to subtract the amplitude of the output optical signal of the second optical coupler 23b and the second polarization clock pulse train 1bD. The fourth optical coupler 23d causes interference to subtract the amplitude of the output optical signal of the third optical coupler 23c and the first polarization clock pulse train 1bD.

[0048] According to the optical interference circuit 20 described above, the interaction shown in the right figure of FIG. 2 can be generated. By changing the combination of the delay amounts of the respective first delay unit 22a to fourth delay unit 22d, it is also possible to generate an interaction by a different combination of elements.

[0049] Before generating the above interaction, an initialization optical pulse train is input to I_IN of the optical interference circuit 20 and combined with the output signal of the optical interference circuit 20 to create a neutral state with no bias in the magnitude of the mutual relationship between the elements. The initialization pulse train has N pulses, and the effective peak power P opt / 2 is a pulse train that is half of the effective peak power P opt of the polarization clock pulse. The pulse width t pw , pulse interval dt and the like are the same as those of the polarization clock pulse train.

[0050] At the first timing when the initialization optical pulse train is input, the signal level of the output optical signal of the optical interference circuit 20 is 0. Therefore, only the initialization optical pulse train is output from the optical interference circuit 20. When the initialization optical pulse train and the polarization clock pulse train are input while adjusting the timing so that the pulse peak of the modulation signal derived from any pulse of the initialization optical pulse train and the pulse peak of any pulse of the polarization clock pulse train reach the Mach-Zehnder optical modulator 10 at the same time, a neutral state where the magnitude of the mutual relationship between the elements is 0 is created.

[0051] The optical interference circuit 20 creates a neutral state where the magnitude of the mutual relationship between the elements is 0 with the initialization optical pulse train, and creates a state where a mutual relationship corresponding to the interaction in the Ising model represented by equations (3) and (4) occurs between the elements, thereby repeatedly generating a predetermined interaction in the Ising model from the neutral state at the period of the N pulses of the polarization clock pulse train. Note that the 0, 1 state of the optical pulse train observed by the monitor signal corresponds to the state where the spin of each lattice point in the Ising model is up or down.

[0052] Instead of inputting the initialization optical pulse train into the optical interference circuit 20, an optical coupler that combines the output signal of the optical interference circuit 20 and the initialization optical pulse train may be provided at the subsequent stage of the optical interference circuit 20.

[0053] (Optical signal processing unit) The optical signal processing unit 30 processes the output of the optical interference circuit 20 and inputs it to the modulation signal generation unit 40.

[0054] FIG. 6 is a diagram showing an example of the configuration of the optical signal processing unit 30. The optical signal processing unit 30 inputs the optical signal pulse train and the polarization clock pulse train output from the optical interference circuit 20, and outputs an optical signal pulse train in which each pulse of the polarization clock pulse train has undergone a transition with respect to the optical power level according to the power level of each pulse of the input optical signal pulse train. Specifically, for an optical signal pulse within the standard optical power region (between 0 and 1), the optical signal processing unit 30 uses the input power level of the standard optical power Pn = 0.5 as a demarcation point. When Pn:in < 0.5, it approaches closer to 0, and when Pn:in > 0.5, it outputs an optical signal pulse derived from an optical clock pulse train in which the optical power level has undergone a transition so as to approach closer to 1.

[0055] The optical signal processing unit 30 in FIG. 6 is cascade-connected in an appropriate number of stages in the form shown in FIG. 7. For example, in the case of a system where N = 100, fully connected, and the absolute value of J i:k is constant, and the ferromagnetic and antiferromagnetic interactions are randomly assigned, four stages of the optical signal processing unit 30 are cascade-connected.

[0056] In addition, adjust the delay due to the insertion of the optical signal processing unit 30 as a whole so as not to change the operating clock of the entire combinatorial optimization problem processing device 100, or, based on the delay due to the insertion of the optical signal processing unit 30, adjust the clock length of the entire combinatorial optimization problem processing device 100 and operate it.

[0057] By inserting the optical signal processing unit 30 after the optical interference circuit 20, it is improved so that the power level of the optical signal pulse from the solver (optical interference circuit 20) can be appropriately transitioned to the standard level of 0 or 1 within the range of the number of practical processing steps. As a result, an optical pulse pattern output corresponding to the desired "energy stable state of the icing model" can be obtained, and a good solution can be obtained even in a large interaction region where the sum of the absolute values of J i:k is close to 1 within a range not exceeding 1.

[0058] (Modulation signal generation unit) The modulation signal generation unit 40 forms a waveform of an electrical signal obtained by photoelectrically converting the optical signal pulse processed by the optical signal processing unit 30 to generate a modulation signal for the Mach-Zehnder optical modulator 10, and outputs a monitor signal representing the solution of the optimization problem to the outside.

[0059] The modulation signal generation unit 40 is composed of, for example, a photoelectric conversion unit, a preamplifier, a Bessel filter, a power splitter, and a post amplifier. The photoelectric conversion unit photoelectrically converts the optical signal pulse train into an electrical signal pulse train. The preamplifier amplifies the electrical signal pulse train. The Bessel filter is a type of low-pass filter that broadens the pulse width. The power splitter outputs a monitor signal obtained by tapping the pulse train output by the Bessel filter to the outside. The output signal of the power splitter is amplified by the post amplifier and connected to the modulation terminal of the Mach-Zehnder optical modulator 10.

[0060] Synchronizing with the timing when the first pulse of the initialization optical pulse train reaches the modulation terminal of the Mach-Zehnder optical modulator 10, a polarization clock pulse train is input to the Mach-Zehnder optical modulator 10. At this time, the timing of the pulses constituting the polarization clock pulse train is adjusted to be approximately at the center of the pulse width range of the initialization pulse signal broadened by the Bessel filter. This adjustment of the mutual timing may be performed either on the polarization clock pulse train or on the initialization optical pulse train.

[0061] When a polarization clock pulse train is input to the Mach-Zehnder optical modulator 10 at such a timing, a neutral state (symmetric state) with a magnitude of the mutual correlation of elements corresponding to each of the series of N = 16 pulses, where the magnitude is 0, is generated. Then, due to "fluctuations" such as noise, the above interaction occurs naturally and spontaneously in the optical interference circuit 20, resulting in a phenomenon where the symmetry is broken and a stable state in the case of being regarded as an Ising model is created.

[0062] In this way, by reading the stable state in the case of being regarded as an Ising model that appears due to an emergent phenomenon beyond the so-called reductionist understanding, the solution to the combinatorial optimization problem can be obtained.

[0063] [Second Embodiment] FIG. 8 is a diagram showing an example of the configuration of a combinatorial optimization problem processing apparatus according to the second embodiment. The combinatorial optimization problem processing apparatus 200 shown in the figure includes a differential phase modulation type Mach-Zehnder optical modulator 60, an optical interference circuit 20, an optical signal processing unit 30, a multiplexer / demultiplexer 70, and a delay unit 80. Since the optical interference circuit 20 and the optical signal processing unit 30 are the same as those in the first embodiment, the description here is omitted.

[0064] The differential phase modulation type Mach-Zehnder optical modulator 60 takes a polarization clock pulse train as an input. The differential phase modulation type Mach-Zehnder optical modulator 60 adjusts the fixed phase condition so that the formula (2) shown in the first embodiment holds. The polarization clock pulse trains of A and A modulated by the differential phase modulation type Mach-Zehnder optical modulator 60 and output from two output ports are input to the optical interference circuit 20. - The polarization clock pulse trains of A and A modulated by the differential phase modulation type Mach-Zehnder optical modulator 60 and output from two output ports are input to the optical interference circuit 20.

[0065] The differential phase modulation type Mach-Zehnder optical modulator 60 includes a first phase modulation section and a second phase modulation section, and is the same as the Mach-Zehnder interference type optical intensity modulation section MZ-1 described in Patent No. 5632330. Fig. 9 shows an example of the configuration of the differential phase modulation type Mach-Zehnder optical modulator 60. As shown in Fig. 9, the differential phase modulation type Mach-Zehnder optical modulator 60 includes two multimode interference sections (MMI) 63, 64, a first phase modulation section 61, and a second phase modulation section 62.

[0066] Under the phase condition in the basic state of the differential phase modulation type Mach-Zehnder optical modulator 60, the polarization clock pulse train input to the MMI 63 is output to one of the outputs of the MMI 64 (A - ). At this time, when a modulation signal that exactly π-shifts the previous phase condition is input to the first phase modulation section 61, it switches to the state of being output to one of the outputs of the MMI 64 (A), and the differential phase modulation type Mach-Zehnder optical modulator 60 becomes an open state. This open state is restored to the state of being output to one of the outputs of the MMI 64 (A - ) by inputting a modulation signal that exactly returns the phase condition to the second phase modulation section 62, and the differential phase modulation type Mach-Zehnder optical modulator 60 returns to the closed state.

[0067] That is, when a modulation signal is input to the first phase modulation section 61, the differential phase modulation type Mach-Zehnder optical modulator 60 becomes an open state, and when a modulation signal is input to the second phase modulation section 62, it becomes a closed state. The configuration and operation of the differential phase modulation type Mach-Zehnder optical modulator 60 are described in Patent No. 5632330. Here, further explanation is omitted.

[0068] The optical interference circuit 20 takes the polarization clock pulse train modulated by the differential phase modulation type Mach-Zehnder optical modulator 60 as an input, causes a predetermined interaction in the idling model in the period of N pulses of the polarization clock pulse train, and outputs an external monitor signal representing the solution of the above combination optimization problem. The signal output from the terminal not denoted as OUT of the fourth optical coupler 23d in Fig. 7 is the monitor signal. The monitor signal represents the solution of the optimization problem.

[0069] Similar to the first embodiment, an optical signal processing unit 30 is inserted after the optical interference circuit 20. The optical signal processing unit 30 inputs an optical signal pulse train and outputs an optical signal pulse train that has undergone a transition according to the power level of each pulse in the input optical signal pulse train. In the example of FIG. 8, the optical signal processing unit 30 is inserted between the optical interference circuit 20 and the optical multiplexer / demultiplexer 70. However, the optical signal processing unit 30 may be inserted between the optical multiplexer / demultiplexer 70 and the delay unit 80, or between the delay unit 80 and the differential phase modulation type Mach-Zehnder optical modulator 60.

[0070] The optical multiplexer / demultiplexer 70 inputs N initialization optical pulses that create a neutral state with respect to the interaction between elements and the optical signal pulse train from the optical interference circuit 20, and provides two demultiplexed outputs for any of the above inputs. One of the optical signal pulses demultiplexed by the optical multiplexer / demultiplexer 70 is input as a drive signal to the first phase modulation unit 61 of the differential phase modulation type Mach-Zehnder optical modulator 60, and the other optical signal pulse is input to the delay unit 80. The optical signal pulse delayed in the delay unit 80 is output as a drive signal to the second phase modulation unit 62 of the differential phase modulation type Mach-Zehnder optical modulator 60.

[0071] FIG. 10 is a diagram showing the relationship between N initialization optical pulses, a first phase modulation signal, a second phase modulation signal, and a polarization clock pulse train. Note that FIG. 10 shows only the timing of each signal and the amplitude has no meaning.

[0072] The first phase modulation signal switches to the polarization clock pulse train after the N initialization optical pulses. Therefore, the first phase modulation after the 17th (i = 17) coincides with the timing of the polarization clock pulse.

[0073] The second phase modulation signal via the delay unit 80 has a timing that is delayed by a delay time d with respect to the first phase modulation signal. The delay time d is a time that is equal to or greater than the pulse width of the pulses in the polarization clock pulse train and is sufficiently narrower than the pulse interval.

[0074] When a first phase-modulated signal and a second phase-modulated signal that are shifted by a delay time d are input, the differential phase-modulation type Mach-Zehnder optical modulator 60 is in an open state for the duration of the delay time d. By inputting a polarization clock pulse train in accordance with the timing of this open state, the polarization clock pulse train outputs a differential phase-modulation output corresponding to the power of the feedback signal and the initialization signal from the differential phase-modulation type Mach-Zehnder optical modulator 60 to the optical interference circuit 20.

[0075] When a polarization clock pulse train is input to the optical interference circuit 20 at such timing, a neutral state (symmetrical state) where the magnitude of the relationship of each element is 0 is generated for each series of N = 16 pulses. Thereafter, by causing the above-described interaction to occur in the optical interference circuit 20, a phenomenon occurs in which symmetry is broken and a stable state of the Ising model is created. In this way, by reading the state corresponding to the Ising model in the stable state that appears due to an emergence phenomenon that goes beyond a so-called reductionist understanding, the solution to the combinatorial optimization problem can be obtained.

[0076] [Third Embodiment] The third embodiment is a combinatorial optimization problem processing apparatus including a functional circuit unit 22 of FIG. 11 instead of the optical interference circuit 20 of the first and second embodiments. Since other components are the same as those of the first embodiment or the second embodiment, the overall configuration diagram of the combinatorial optimization problem processing apparatus of the third embodiment is omitted.

[0077] The functional circuit unit 22 shown in FIG. 11 is configured by an optical interference circuit 20 using an FPGA and a Mach-Zehnder optical modulator. The functional circuit unit 22 shown in the figure includes photoelectric AD converters 220 and 221, an FPGA 222, a DA converter 223, and a Mach-Zehnder optical modulator (MZM) 224.

[0078] The photoelectric AD converter 220 AD-converts an electrical pulse signal obtained by photoelectrically converting a polarization clock pulse train (A - ), and the photoelectric AD converter 221 AD-converts an electrical pulse signal obtained by photoelectrically converting the polarization clock pulse train (A).

[0079] The FPGA 222 digitally processes the calculation of the above interaction (Figure 2). The output signal of the FPGA 222 is DA-converted and connected to the modulation signal terminal of the Mach-Zehnder optical modulator 224.

[0080] The Mach-Zehnder optical modulator 224 intensity-modulates the coherent local oscillation clock pulse light with the output signal of the FPGA 222. The coherent local oscillation clock pulse light can be provided as a pulse train obtained by branching a polarization clock pulse train with a directional coupler (not shown).

[0081] The OUT terminal corresponds to the OUT terminal of the optical interference circuit 20. Thus, the optical interference circuit can also be constituted by a semiconductor integrated circuit such as an FPGA. Here, the optical interference circuit 20 and the functional circuit section 22 are also referred to as an Ising model calculation section.

[0082] [Comparison Simulation] An example of the numerical calculation simulation by the combined optimization problem processing apparatus of Patent Documents 1 and 2 is shown in FIGS. 12 to 15.

[0083] FIGS. 12 and 13 are an example of the numerical calculation simulation when the absolute value of J i:k is near 0.004. FIG. 12 is a graph of the change of the output optical signal peak power with respect to the step, where the vertical axis is the normalized output optical signal peak power and the horizontal axis is the solution search step. FIG. 13 is a graph showing the appearance frequency focusing on the Ising energy of the search solution.

[0084] FIGS. 14 and 15 are an example of the numerical calculation simulation when the absolute value of J i:k is near 0.009. FIG. 14 is a graph of the change of the output optical signal peak power with respect to the step, where the vertical axis is the normalized output optical signal peak power and the horizontal axis is the solution search step. FIG. 15 is a graph showing the appearance frequency focusing on the Ising energy of the search solution.

[0085] J i:kWhen the absolute value of J is near 0.004, an expected signal output can be obtained, and as shown by the appearance frequency focusing on the Ising energy of the search solution in FIG. 13, generally good solutions can be obtained. However, when i:k the absolute value of J is near 0.009, the normalized peak power of the optical pulse assumed for each Ising lattice point no longer transitions to the 1 and 0 levels assumed for the up and down of the Ising spin. As a result, as shown by the appearance frequency focusing on the Ising energy of the search solution in FIG. 15, no good solutions can be obtained at all.

[0086] Subsequently, an example of the numerical calculation simulation by the combinatorial optimization problem processing apparatus 100 of the present embodiment is shown in FIGS. 16 and 17.

[0087] FIGS. 16 and 17 are an example of the numerical calculation simulation when the absolute value of J i:k is near 0.009. FIG. 16 is a graph of the change with respect to the step of the output optical signal peak power, where the vertical axis is the normalized output optical signal peak power and the horizontal axis is the solution search step. FIG. 17 is a graph representing the appearance frequency focusing on the Ising energy of the search solution.

[0088] As shown in FIG. 16, even when the absolute value of J i:k is near 0.009, in the present embodiment, the normalized peak power of the optical pulse assumed for each Ising lattice point transitions to the 1 and 0 levels assumed for the up and down of the Ising spin. At the same time, as shown by the appearance frequency focusing on the Ising energy of the search solution in FIG. 17, better solutions can be obtained than the solutions obtained when the absolute value of J i:k is near 0.004 according to Patent Documents 1 and 2.

[0089] As described above, according to the present embodiment, by providing an optical signal processing unit 30 that transitions each pulse of the polarization clock pulse train with respect to the optical power level according to the power level of each pulse of the optical signal pulse train output from the optical interference circuit 20 after the optical interference circuit 20 of the combinatorial optimization problem processing apparatuses 100 and 200, an optical pulse pattern output corresponding to the energy stable state of a desired Ising model can be obtained, and the coefficient J i:k representing the magnitude of the interaction can be made close to 1 within a range where the sum of the absolute values does not exceed 1, and it becomes possible to obtain a good solution even in a region where the interaction is large.

[0090] The present invention is not limited to the above-described embodiment, and can be modified within the scope of the gist thereof. Although the Max Cut 3 problem with N = 16 is exemplified as the combinatorial optimization problem, the present invention is not limited to this example. The present invention can be applied to any problem as long as the combinatorial optimization problem can be mapped so as to correspond to the energy of the Ising model. Also, the interaction of the Max Cut 3 problem with N = 16 is not limited to the above example.

Explanation of Reference Numerals

[0091] 100, 200 Combinatorial optimization problem processing apparatus 10 1-input 2-output Mach-Zehnder optical modulator 20 Optical interference circuit 30 Optical signal processing unit 40 Modulation signal generation unit 60 Differential phase modulation type Mach-Zehnder optical modulator 70 Optical multiplexer / demultiplexer 80 Delay unit

Claims

1. A combinatorial optimization problem processing apparatus that associates a combinatorial optimization problem of N elements with an Ising model and processes it, a 1×2 Mach-Zehnder optical modulator that inputs and modulates a polarized clock pulse train, an Ising model arithmetic unit that inputs the polarized clock pulse train modulated by the 1×2 Mach-Zehnder optical modulator and causes a predetermined interaction in the Ising model to occur at the period of N pulses of the polarized clock pulse train, an optical signal processing unit that inputs the optical signal pulse train and the polarized clock pulse train output from the Ising model arithmetic unit, and outputs an optical signal in which each pulse of the input polarized clock pulse train has transitioned with respect to the optical power level according to the power level of each pulse of the input optical signal pulse train, a modulation signal generation unit that waveform-shapes an electrical signal obtained by photoelectrically converting the optical signal after transition to generate a modulation signal for the 1×2 Mach-Zehnder optical modulator, and outputs a monitor signal representing the solution of the optimization problem to the outside, The Ising model arithmetic unit inputs an initialization optical pulse train having an effective peak power of 1 / 2 of the polarized clock pulse train and a number of pulses of N, creates a neutral state with respect to the interaction between the elements, and repeatedly causes a predetermined interaction in the Ising model to occur at the period of N pulses of the polarized clock pulse train Combinatorial optimization problem processing apparatus.

2. A combinatorial optimization problem processing apparatus that associates a combinatorial optimization problem of N elements with an Ising model and processes it, a differential phase modulation type Mach-Zehnder optical modulator that includes a first phase modulation unit and a second phase modulation unit, inputs a polarized clock pulse train, and modulates it, an Ising model arithmetic unit that inputs the polarized clock pulse train modulated by the differential phase modulation type Mach-Zehnder optical modulator, causes a predetermined interaction in the Ising model to occur at the period of N pulses of the polarized clock pulse train, and outputs a monitor signal representing the solution of the optimization problem to the outside, The N initialization optical pulses that create a neutral state with respect to the interaction between the elements and the optical signal pulse train output from the Ising model calculation unit are input, the initialization optical pulses are combined with the optical signal pulse train, and the initialization optical pulses and the optical signal pulse train are each demultiplexed. One of the demultiplexed signals is output as a first phase modulation signal to the first phase modulation unit, and the other demultiplexed signal is output as a second phase modulation signal to a delay unit. A multiplexer / demultiplexer that includes a delay unit that delays the second phase modulation signal by a time that is equal to or greater than the pulse width of the pulses of the polarization clock pulse train and less than the pulse interval with respect to the first phase modulation signal and outputs it to the second phase modulation unit. An optical signal processing unit that inputs the optical signal pulse train output from the Ising model calculation unit and the polarization clock pulse train either between the Ising model calculation unit and the multiplexer / demultiplexer, between the multiplexer / demultiplexer and the delay unit, or between the delay unit and the differential phase modulation type Mach-Zehnder optical modulator, and outputs an optical signal in which each pulse of the polarization clock pulse train has made a transition with respect to the optical power level according to the power level of each pulse of the input optical signal pulse train. A combinatorial optimization problem processing device.

3. The combinatorial optimization problem processing device according to claim 1 or 2, Let i be the serial number of the pulses constituting the polarized clock pulse train, j be the number representing the position of the pulses within N, and J be the coefficient representing the magnitude of a predetermined interaction in the Ising model. ｉ：ｋ When this is the case, the predetermined interaction in the Ising model can be expressed by the following equation: [Number 5] The power of the polarization clock pulse train output by the Ising model calculation unit can be expressed by the following formula 【Number 6】 A combinatorial optimization problem processing device.

4. A combinatorial optimization problem processing method executed by a combinatorial optimization problem processing device that associates and processes a combinatorial optimization problem of N elements with an Ising model, modulating a polarization clock pulse train with a 1×2 Mach-Zehnder optical modulator, inputting the polarization clock pulse train modulated by the 1×2 Mach-Zehnder optical modulator to an Ising model calculation unit to cause a predetermined interaction in the Ising model to occur at the period of N pulses of the polarization clock pulse train, transitioning each pulse of the polarization clock pulse train with respect to the optical power level according to the power level of each pulse of the optical signal pulse train output from the Ising model calculation unit, shaping the electrical signal obtained by photoelectrically converting the optical signal after the transition to generate a modulation signal for the 1×2 Mach-Zehnder optical modulator, and outputting a monitor signal representing the solution of the optimization problem to the outside. The annealing model calculation unit inputs an initialization optical pulse train with an effective peak power equal to half of the polarization clock pulse train and a number of pulses of N, creates a neutral state for the interaction between the elements, and repeats a predetermined interaction in the annealing model from the neutral state at a period of N pulses of the polarization clock pulse train to cause it to occur. Combinatorial optimization problem processing method.

5. A combinatorial optimization problem processing method executed by a combinatorial optimization problem processing apparatus that associates and processes a combinatorial optimization problem of N elements with an annealing model, A differential phase modulation type Mach-Zehnder optical modulator including a first phase modulation unit and a second phase modulation unit modulates a polarization clock pulse train, The polarization clock pulse train modulated by the differential phase modulation type Mach-Zehnder optical modulator is input to an annealing model calculation unit, a predetermined interaction in the annealing model is caused to occur at a period of N pulses of the polarization clock pulse train, and a monitor signal representing a solution to the optimization problem is output to the outside. The N initialization optical pulses that create a neutral state for the interaction between the elements and the optical signal pulse train output from the annealing model calculation unit are input to a multiplexer / demultiplexer, the initialization optical pulses are combined with the optical signal pulse train, and the initialization optical pulses and the optical signal pulse train are each demultiplexed. One of the demultiplexed signals is output as a first phase modulation signal to the first phase modulation unit, and the other demultiplexed signal is output as a second phase modulation signal to a delay unit. The delay unit delays the second phase modulation signal by a time that is equal to or greater than the pulse width of the pulses of the polarization clock pulse train and less than the pulse interval with respect to the first phase modulation signal and outputs it to the second phase modulation unit. In any one of between the annealing model calculation unit and the multiplexer / demultiplexer, between the multiplexer / demultiplexer and the delay unit, or between the delay unit and the differential phase modulation type Mach-Zehnder optical modulator, each pulse of the polarization clock pulse train is transitioned with respect to the optical power level according to the power level of each pulse of the optical signal pulse train output from the annealing model calculation unit. Combinatorial optimization problem processing method.

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