Optical Ising computing device

Abstract

This invention provides a large-scale, high-precision optical Ising computer that can significantly increase the number of spins, achieve optimal binary bifurcation for the problem to be solved using an arbitrary nonlinear function, and converge stably and quickly. [Solution] The system includes a pulse light source 1, an optical fiber loop 3 into which optical pulses from the pulse light source 1 are introduced, an erbium-doped optical fiber amplifier 4 provided within the optical fiber loop 3, a homodyne detection circuit 5 for detecting optical pulses from the optical fiber loop 3, a matrix-nonlinear calculation circuit 6 for digitally calculating an interaction function and a nonlinear function for binary branching for the optical pulses detected by the homodyne detection circuit 5, and an AM optical modulator 2 which receives the optical pulses from the pulse light source 1 and the information obtained from the digital calculations of the matrix-nonlinear calculation circuit 6, modulates the input optical pulses, and then injects them into the optical fiber loop 3.

Description

[Technical Field]

[0001] This invention relates to an optical Ising computing device. This application claims priority based on Japanese Patent Application No. 2024-216205, filed in Japan on December 11, 2024, the contents of which are incorporated herein by reference. [Background technology]

[0002] In recent years, there has been growing interest in Ising machines (IMs), which can quickly compute combinatorial optimization problems such as the Max Cut problem and the Traveling Salesperson Problem. An IM is a computer that focuses on the fact that these optimization problems are equivalent to the problem of finding the minimum value of the Hamiltonian of a ferromagnet, known as the Ising model in statistical mechanics. That is, by treating the direction of the spins constituting the ferromagnet as a variable that takes two values, ±1, the optimal combination of the ±1 variable can be found from the spin direction that minimizes the Hamiltonian. Specifically, a physical system that simulates spin is constructed using a binary bifurcation, and the process by which this system settles into its minimum energy state is experimentally realized, thereby entrusting the computation to natural phenomena. As a result, the solution to the optimization problem can be obtained by observing the spin when it settles into the minimum energy state.

[0003] In IM, there are a software machine by computer analysis and a computer implementing hardware. As an implementation of IM using light in hardware, a Coherent Ising Machine (CIM) using a Degenerated Optical Parametric Oscillator (DOPO) and a digital feedback circuit has been proposed (see, for example, Non-Patent Documents 1 and 2). Also, a simple CIM using an Opto-Electric Oscillator (OEO) has been proposed (see, for example, Non-Patent Document 3). In these machines, the phase (0, π) of an optical pulse is regarded as the spin (+1, -1). It has been demonstrated that CIM has excellent computing capabilities, such as being able to calculate optimization problems at high speed by taking advantage of the high speed of light.

[0004] In addition, the inventors have proposed a method of applying amplitude modulation synchronized with the repetition frequency of a pulse to an optical pulse in an optical fiber loop as a synchronization modulation technique for ultra-long-distance transmission of solitons (see, for example, Non-Patent Document 4). By using this method, the accumulation of Amplified Spontaneous Emission (ASE) noise can be constantly suppressed to a small value, and the waveform of the optical pulse can be kept clean by synchronization modulation even after interaction.

Prior Art Documents

Non-Patent Documents

[0005]

Non-Patent Document 1

Non-Patent Document 2

[0006] Since the CIMs described in these Non-Patent Documents 1 to 3 use optical oscillators such as DOPO and OEO, the upper limit of the achievable number of spins is determined by the resonator length. At present, 100,000 spins can be realized with a resonator length of 5 km, but for further scaling up, a longer resonator is required, and there is a problem that stable oscillation becomes difficult. On the other hand, even with a limited resonator length, it is possible to increase the number of spins by increasing the repetition rate of optical pulses, but there is also a problem that it is not always easy to increase the repetition frequency of DOPO and OEO.

[0007] Furthermore, solving the minimum energy problem for binary systems requires the existence of a stable binary bifurcation within the optical immersion (IM). Conventionally, this has involved using Van der Pol type binary bifurcations, i.e., third-order polynomial type bifurcations, near the oscillation threshold of DOPOs and OEOs. Specifically, it utilizes the third-order nonlinearity of DOPOs or the nonlinear characteristics of the optical modulators constituting OEOs. Consequently, in conventional CIMs, the nonlinearity used to generate binary bifurcations is limited to nonlinear functions that can be realized analogously with optical elements, resulting in limitations on computation time and accuracy.

[0008] The present invention aims to solve these problems by providing a large-scale, high-precision optical Ising computer that can significantly increase the number of spins, realize an optimal binary bifurcation for the problem to be solved using an arbitrary nonlinear function, and converge stably and quickly. [Means for solving the problem]

[0009] To achieve this objective, the first optical Ising computing apparatus according to the present invention comprises: a pulse light source; an optical fiber loop into which optical pulses from the pulse light source are introduced; an erbium-doped optical fiber amplifier provided within the optical fiber loop for compensating for losses in the optical fiber loop; a homodyne detection circuit for detecting the optical pulses from the optical fiber loop; an arithmetic circuit for performing digital calculations on the optical pulses detected by the homodyne detection circuit; and an optical modulator into which the optical pulses from the pulse light source and information obtained from the digital calculations of the arithmetic circuit are input, and the input optical pulses are modulated with the information before being incident on the optical fiber loop. Fiber optic loop The optical pulse after circling is detected by the homodyne detection circuit and input to the calculation circuit, in which the calculation circuit digitally calculates the interaction function of the optical pulse and the nonlinear function for binary branching, and then the optical modulator modulates the optical pulse from the pulse light source with the information obtained from the digital calculation, and Fiber optic loop This is characterized by superimposing and interacting with the aforementioned light pulse inside.

[0010] The second optical Ising computing apparatus according to the present invention comprises a digitally represented pulse light source, a digital memory that receives digital optical pulses from the pulse light source and software-describes the propagation of a plurality of the digital optical pulses in a long optical fiber, a digitally represented homodyne detection circuit that detects the digital optical pulses output from the digital memory, an arithmetic circuit that performs digital calculations on the digital optical pulses detected by the homodyne detection circuit, and information obtained from the digital optical pulses from the pulse light source and the digital calculations of the arithmetic circuit that are input to the input digital optical pulses The system includes a digitally represented optical modulator that modulates the optical pulse with the aforementioned information and then inputs it into the digital memory, and by digital calculation, the homodyne detection circuit detects the digital optical pulse from the digital memory and inputs it into the arithmetic circuit, in which the arithmetic circuit digitally calculates the interaction function of the digital optical pulse and the nonlinear function for binary branching, and then the optical modulator modulates the digital optical pulse from the pulse light source with the information obtained from the digital calculation and superimposes it with the digital optical pulse from the previous cycle in the digital memory before the calculation and causes it to interact.

[0011] The second optical Ising computing device according to the present invention is preferably configured by using a large-capacity digital memory instead of the optical fiber loop of the first optical Ising computing device according to the present invention, and by constructing the first optical Ising computing device according to the present invention entirely with software, thereby creating a digital simulator.

[0012] A third optical Ising computing apparatus according to the present invention comprises a CW light source, an optical fiber loop into which CW light from the CW light source is introduced, an erbium-doped optical fiber amplifier provided in the optical fiber loop for compensating for losses in the optical fiber loop, an optical filter provided in the optical fiber loop, an in-loop optical modulator operating at a modulation frequency of one integer fraction of the optical delay time in the optical fiber loop, a homodyne detection circuit for detecting optical pulses generated from the CW light circulating in the optical fiber loop from the optical fiber loop, an arithmetic circuit for performing digital calculations on the optical pulses detected by the homodyne detection circuit, and an optical modulator to which the CW light from the CW light source and information obtained from the digital calculations of the arithmetic circuit are input, and the input CW light is modulated with the information before being incident on the optical fiber loop. Fiber optic loop The optical pulse circulating is detected by the homodyne detection circuit and input to the calculation circuit, in which the calculation circuit digitally calculates the interaction function and the nonlinear function for binary branching, and then the optical modulator modulates the CW light from the CW light source with the information obtained from the digital calculation, and Fiber optic loop This is characterized by superimposing and interacting with the aforementioned light pulse inside.

[0013] The third optical Ising computing apparatus according to the present invention is preferably configured by using a CW (Continuous Wave) light source instead of the optical pulse light source of the first optical Ising computing apparatus according to the present invention.

[0014] The first and third optical Ising computing devices according to the present invention may generate binary branching by combining a lossless loop and the calculation of a nonlinear function in the arithmetic circuit without oscillating pulses in the optical fiber loop.

[0015] The second optical Ising computing device according to the present invention may generate a binary branch by combining a lossless loop and the calculation of a nonlinear function in the arithmetic circuit without oscillating pulses in the digital memory.

[0016] Furthermore, in the first to third optical Ising computing devices according to the present invention, the homodyne detection circuit may detect the phase of the real component of the optical pulse, or it may detect the phase of the imaginary component of the optical pulse, or it may detect both the real and imaginary components of the optical pulse simultaneously. When both the real and imaginary components of the optical pulse are detected simultaneously, the Kerr effect in the optical fiber loop can be stabilized by simultaneously feeding back both of them.

[0017] Furthermore, in the first to third optical Ising computing apparatus according to the present invention, the optical modulator may include an AM optical modulator that modulates the amplitude of the optical pulse, thereby modulating the real component of the optical pulse; or the optical modulator may include an AM optical modulator that modulates the amplitude of the optical pulse and a π / 2 optical phase shifter, thereby modulating the imaginary component of the optical pulse; or the optical modulator may include an IQ optical modulator that modulates the amplitude and phase of the optical pulse, thereby simultaneously modulating the real and imaginary components of the optical pulse.

[0018] Furthermore, in the first to third optical Ising computing devices according to the present invention, it is preferable that the arithmetic circuit calculates an arbitrary nonlinear function.

[0019] Furthermore, in the first to third optical Ising computing apparatuses according to the present invention, the optical fiber loop is preferably composed of long fibers ranging from several kilometers to several hundred kilometers in length. In this case, large-scale optical calculations can be performed.

[0020] Furthermore, in the first and third optical Ising computing apparatuses according to the present invention, the optical fiber loop may consist of a porous core fiber such as a photonic crystal fiber or an anti-resonant fiber in order to suppress nonlinear optical effects in optical computing.

[0021] Furthermore, the first optical Ising computing apparatus according to the present invention may have an in-loop optical modulator inserted into the optical fiber loop, and amplitude modulation synchronized with the optical pulse may be applied by driving the in-loop optical modulator with a sinusoidal signal synchronized with the repetition of the optical pulse circulating in the optical fiber loop. In this case, the accumulation of spontaneously emitted optical noise can be suppressed and a high optical signal-to-noise ratio can be maintained.

[0022] Furthermore, in the first and third optical Ising computing devices according to the present invention, the erbium-doped optical fiber amplifier may have a gain equal to the loss compensation amount of the optical fiber loop. In this case, the gain saturation effect of the erbium-doped optical fiber amplifier can automatically stabilize the binary branching energy in the optical fiber loop.

[0023] Furthermore, the first to third optical Ising computing devices according to the present invention may feed back the feedback signal (information obtained by digital calculation) obtained by the calculation circuit from the nth optical pulse to the (n+1)th and subsequent optical pulses. [Effects of the Invention]

[0024] The optical Ising computing device according to the present invention can easily increase the number of optical pulses (spins) that can circulate around an optical fiber loop by extending the length of the optical fiber loop or increasing the repetition rate of the optical pulse, thereby enabling the calculation of larger-scale combinatorial optimization problems. Furthermore, the nonlinearity required for the generation of binary branching can be realized with an arbitrary nonlinear function using digital circuits, allowing for the realization of optimal nonlinearity depending on the problem to be solved. In addition, the pulse energy can be automatically stabilized while maintaining a high optical signal to noise ratio (OSNR) through synchronous amplitude modulation and the gain saturation effect of optical signal amplifiers such as EDFA (Erbium-doped Fiber Amplifier), enabling stable circulating over long distances.

[0025] Thus, according to the present invention, it is possible to significantly increase the number of spins, realize an optimal binary bifurcation for the problem to be solved using an arbitrary nonlinear function, and provide a large-scale, high-precision optical Ising computer that can converge more stably and quickly. [Brief explanation of the drawing]

[0026] [Figure 1] This is a block diagram showing the configurations of conventional (a) DOPO-type CIM and (b) OEO-type CIM. [Figure 2] This is a block diagram showing the configuration of an optical Ising computing apparatus according to the first embodiment of the present invention. [Figure 3] Figure 2 shows the transmission waveforms of a 10 GHz pulse train from an optical Ising computer over (a) 10,000 km (200 laps), (b) 30,000 km (600 laps), and (c) 50,000 km (1,000 laps). [Figure 4] Figure 2 shows the transmission waveforms (using synchronous amplitude modulation) of a 10 GHz pulse train from the optical Ising computer for (a) 10,000 km (200 laps), (b) 30,000 km (600 laps), (c) 50,000 km (1,000 laps), (d) 500,000 km (10,000 laps), and (e) 1,000,000 km (20,000 laps). [Figure 5] This graph shows the rise of spontaneous binary bifurcation in the optical Ising computing device of the first embodiment of the present invention, when (a) α = 1.1, β = 0, (b) α = 1.5, β = 0, and (c) α = 2.0, β = 0. [Figure 6] This graph shows the convergence of the cut-off values ​​at (a) K2000 and (b) G22 in the calculation of the 2000 × 2000 Max-cut problem using the optical Ising calculator of the first embodiment of the present invention. [Figure 7] These are α-β maps of the cut-off values ​​for (a) K2000 (left side shows the distribution of the maximum value, right side shows the distribution of the mean value) and (b) G22 (left side shows the distribution of the maximum value, right side shows the distribution of the mean value) when the tanh function is used as a nonlinear function in the optical Ising calculator of the first embodiment of the present invention. [Figure 8] These are α-β maps of the cut-off values ​​for (a) K2000 (left side shows the distribution of the maximum value, right side shows the distribution of the mean value) and (b) G22 (left side shows the distribution of the maximum value, right side shows the distribution of the mean value) when the step function is used as a nonlinear function in the optical Ising calculator of the second embodiment of the present invention. [Figure 9] These are α-β maps of the cut-off values ​​for (a) K2000 (left side shows the distribution of the maximum value, right side shows the distribution of the mean value) and (b) G22 (left side shows the distribution of the maximum value, right side shows the distribution of the mean value) when a cubic polynomial (Van der Pol type) is used as the nonlinear function in the optical Ising computing device of the third embodiment of the present invention. [Figure 10] These are α-β maps of the cut-off values ​​for (a) K2000 (left side shows the distribution of the maximum value, right side shows the distribution of the mean value) and (b) G22 (left side shows the distribution of the maximum value, right side shows the distribution of the mean value) when the cosine function is used as the nonlinear function in the optical Ising calculator of the fourth embodiment of the present invention. [Figure 11] Figures 7-10 show the results, as well as a table comparing the results obtained using DOPO and simulated annealing methods. [Figure 12] (a) A time chart for the optical Ising computer of the fifth embodiment of the present invention, in which the amplitude of the optical pulse that has propagated through the nth cycle is detected and the feedback signal obtained by the FPGA is fed back to the (n+1)th optical pulse, taking into account the processing delay in the FPGA. (b) A time chart for the optical Ising computer of the sixth embodiment of the present invention, in which the amplitude of the optical pulse that has propagated through the nth cycle is detected and the feedback signal obtained by the FPGA is fed back to the (n+2)th optical pulse, taking into account the processing delay in the FPGA. [Figure 13] This graph shows the convergence of the cut-off value in the calculation results for the 2000x2000 problem (G22) under three conditions: (a) no processing delay in the FPGA, (b) with a processing delay in the FPGA as shown in Figure 12(a) (0.25 ms), and (c) with a processing delay in the FPGA as shown in Figure 12(b) (0.5 ms). [Figure 14] This is a block diagram showing the configuration of an optical Ising computing apparatus according to the seventh embodiment of the present invention. [Figure 15]The first embodiment of the optical Ising calculator of the present invention provides a graph showing (a-1) the convergence of the cutoff value and (a-2) a histogram of the maximum cutoff value for the calculation results of a 10,000 × 10,000 problem (K10,000), and the second embodiment provides a graph showing (b-1) the convergence of the cutoff value and (b-2) a histogram of the maximum cutoff value for the calculation results of a 10,000 × 10,000 problem (K10,000) for the optical Ising calculator of the present invention provides a graph showing (b-1) the convergence of the cutoff value and (b-2) a histogram of the maximum cutoff value for the calculation results of a 10,000 × 10,000 problem (K10,000). [Figure 16] This is a block diagram showing the configuration of an optical Ising computing apparatus according to the eighth embodiment of the present invention. [Figure 17] This graph shows the calculation results for a 2000 × 2000 (K2000) problem using an optical Ising calculator according to the eighth embodiment of the present invention, specifically (a) the cycle dependence of the cutoff value, (b) the phase change of the pulse for each cycle, and (c) the change in optical power within the loop for each cycle. [Figure 18] This graph shows the rising edge of a binary bifurcation in the case of (a) no π / 2 phase change due to an optical phase shifter and (b) a π / 2 phase change, according to the optical Ising computing device of the eighth embodiment of the present invention. [Figure 19] This is a block diagram showing the configuration of an optical Ising computing apparatus according to the ninth embodiment of the present invention. [Figure 20] The following are graphs showing (a) the frequency dependence of the cutoff value and (b) an enlarged view of the rising edge of (a) in the optical Ising calculator of the ninth embodiment of the present invention for the 2000 × 2000 (K2000) problem. [Figure 21] This is a block diagram showing the configuration of an optical Ising computing apparatus according to a tenth embodiment of the present invention. [Figure 22]The graphs show (a-1) the intensity I2+Q2 and (b-1) the amplitudes I and Q of the pulse waveform after propagation of 30,000 km when a 10 ps pulse light is incident from an external source in a feedback-free state (α=0, β=0) with the optical Ising computing device of the first embodiment of the present invention, and (a-2) the intensity I2+Q2 and (b-1) the amplitudes I and Q of the pulse waveform after propagation of 30,000 km when CW light is incident in a feedback-free state (α=0, β=0) with the optical Ising computing device of the tenth embodiment of the present invention. [Figure 23] The graphs show the rising edge of the binary bifurcation of the (a-1)I component and the (b-1)Q component when a 10 ps pulse light is incident from the outside in a feedback state (α=1.5, β=0) of the optical Ising computing device of the first embodiment of the present invention, and the graphs show the rising edge of the binary bifurcation of the (a-2)I component and the (b-2)Q component when CW light is incident in a feedback state (α=1.5, β=0) of the optical Ising computing device of the tenth embodiment of the present invention. [Figure 24] This graph shows the frequency dependence of the cut-off value for the calculation results of the 2000 × 2000 (K2000) problem when (a) 10 ps pulsed light is incident from an external source using the optical Ising calculation device of the first embodiment of the present invention, and (b) CW light is incident using the optical Ising calculation device of the tenth embodiment of the present invention. [Modes for carrying out the invention]

[0027] The embodiments of the present invention will be described below with reference to the drawings and other materials. Combinatorial optimization problems such as the Max Cut problem and the Traveling Salesperson problem involve minimizing (or maximizing -E of) the following energy function E, which is the variable u. n This is equivalent to the problem of finding combinations.

[0028]

number

[0029] The variable u in equation (1) m u n This refers to the state (+1 or -1) of the m-th and n-th spins (electric field amplitude of the light pulse), and in this invention, it refers to the electric field amplitudes of the m-th and n-th light pulses that are in the same orbit. m,n is the interaction coefficient between spins. IM is the coupling coefficient J, which represents the properties of the problem to be solved, depending on the problem to be solved. m,n This is a computational process to find the combination of u that minimizes the energy function E in equation (1), given the values ​​of u.

[0030] [Conventional Ising Machine (IM)] Figure 1 shows the configurations of the DOPO-type Ising machine (IM) proposed in Non-Patent Documents 1 and 2, and the OEO-type Ising machine (IM) proposed in Non-Patent Document 3. The conventional DOPO-type IM shown in Figure 1(a) comprises a pulse light source 51, an amplitude (AM) optical modulator [LN(LiNbO3; lithium niobate) optical modulator] 52 connected to the pulse light source 51, an optical fiber loop (optical fiber ring) 53 into which pulse light is incident via the optical modulator 52, a phase-sensitive optical amplifier (PSA: gain g > loss l) 54 provided in the optical fiber loop 53 and excited by the optical pulse whose wavelength has been converted by a wavelength converter 54a, a homodyne detection circuit 55 that detects the optical pulse from the optical fiber loop 53, and a matrix operation circuit 56 that performs digital calculations using the amplitude (real part component) of the pulse light detected by the homodyne detection circuit 55.

[0031] In DOPO, N pulses are circulating in the optical fiber ring resonator (optical fiber loop 53), and each pulse has the same amplitude and a random phase value of 0 or π. A phase-sensitive optical amplifier 54 is used in DOPO, which generates a non-linear optical effect according to the phase relationship between the pump light and the signal light, and the phase of each pulse takes only one of the values of 0 or π. Therefore, DOPO oscillates in a steady state with the interaction Hamiltonian of Equation (1) minimized. In DOPO, a pulse is branched from the optical fiber loop 53, and the phases of the N pulses are detected by homodyne detection with local light emission. All pulse amplitudes are +1 or -1, and the sign can be obtained by coherent detection of the electric field. This signal is input to the matrix operation circuit 56. The matrix operation circuit 56 consists of an A / D converter, an FPGA (Field-Programmable Gate Array), and a D / A converter. The FPGA digitally calculates the sum (combined sum) of the product of the N amplitudes u m (k) (m = 1 to N) of the k-th cycle represented by Equation (2) and J m,n previously stored in the FPGA.

[0032] [Number]

[0033] The value f n (k) of the electrical signal thus obtained calculates the spin interaction. This signal is imposed on an optical pulse using an LN modulator and multiplexed with the n-th pulse u n (k) circulating in the optical fiber loop 53 of DOPO, thereby realizing the interaction between any pulses in the optical fiber loop 53.

[0034] On the other hand, as shown in Figure 1(b), in the OEO-type IM, a continuous wave (CW) light source is used as the external light source (pulsed light source 51), and the optical pulse modulated by the AM optical modulator 52 circulates through the optical fiber loop 53. Unlike DOPO, information is carried on the intensity of the optical pulse, not the phase. That is, the amplitude of the pulse is 1 or 0, and the phases are all in phase. The photodetector 57 detects the intensity of N pulses, and by applying an offset of -1 / 2 on the output side, the signal u n (k) takes the value of +1 / 2 or -1 / 2, corresponding to spin σ = 1 or σ = -1. After calculating the interaction in the matrix operation circuit 56, a feedback gain is applied and returned to the AM optical modulator 52 to generate the signal for the next cycle. Unlike DOPO, OEO uses the modulation characteristics (cosine function) in the AM optical modulator 52 as a nonlinear function for generating a binary bifurcation.

[0035] The propagation of optical pulses in these Ising machines is governed by a nonlinear function F NL Using this, the nonlinear differential equation F can be uniformly expressed in the form of equation (3) below, or the recurrence relation equation (4) obtained by discretizing it (time Δt is normalized to 1). NL For DOPO-type IM, the equation is (5), and for OEO-type IM, it is (6). Here, α represents the linear gain (magnitude of the feedback signal), and β represents the strength of the interaction. In equations (5) and (6), the first and second terms on the right-hand side represent Van der Pol-type bifurcation (binary bifurcation), and the third term represents the interaction between pulses.

[0036]

number

[0037] The amplitude of the optical pulse orbiting DOPO or OEO repeats according to equation (3) or (4), and the nonlinear function F NLThe signal splits into either a positive or negative equilibrium point (stable amplitude value) given by = 0. If the optical pulse splits into a positive amplitude value, its spin is set to +1; if it splits into a negative amplitude value, its spin is set to -1. In this case, in both DOPO and OEO IMs, when the feedback gain is set near the oscillation threshold, the system attempts to oscillate under the condition that the energy in equation (1) is minimized. Therefore, by detecting the phase or intensity of each pulse when stable oscillation is reached, the desired variable u can be obtained. n A combination can be obtained.

[0038] Thus, conventional optical pulse oscillators (IMs) utilize the oscillation of optical pulses. Therefore, the upper limit of the number of optical pulses that can be realized is determined by the resonator length, and a long resonator that can obtain stable oscillation is required for large-scale calculations. For this to work, the gain of the DOPO becomes extremely large, which is impractical. Furthermore, increasing the repetition frequency is not easy. In contrast, the present invention can obtain the phase (amplitude +1, -1) of the optical pulse with the minimum energy without causing oscillation within the optical fiber loop. This is because, even without using an optical oscillator, if a mechanism for stable binary branching exists in the target system, it is sufficient for the calculation process.

[0039] Furthermore, in conventional IMs, the nonlinearity for the generation of binary bifurcation is limited to cubic polynomials (Van der Pol type), as shown in equations (5) and (6). A cubic polynomial is merely a linear term with a cubic term perturbatively added, and its nonlinearity is not necessarily strong. In this invention, we considered that if we could artificially create a more steep nonlinearity than the Van der Pol type, we could easily create a situation in which stable binary bifurcation is likely to occur.

[0040] [First Embodiment] Figure 2 shows the configuration of an optical Ising computing device according to the first embodiment of the present invention. This device includes a pulse light source 1 that generates pulsed light, an AM optical modulator 2 connected to the pulse light source 1, an optical fiber loop 3 including a core made of silica silicon or the like into which pulsed light is incident via the AM optical modulator 2, an EDFA (erbium-doped optical fiber amplifier, gain g = loss l) 4 provided within the optical fiber loop 3 to compensate for the loss of the optical fiber loop 3, an in-loop AM optical modulator 2', a homodyne detection circuit 5 that detects optical pulses from the optical fiber loop 3, a matrix / nonlinear calculation circuit 6 that performs digital calculations on the pulsed light detected by the homodyne detection circuit 5, a synthesizer 7 that controls the in-loop AM optical modulator 2' with an output clock signal, and an optical delay circuit 8. The matrix / nonlinear calculation circuit 6 is composed of an A / D converter, an FPGA circuit, and a D / A converter. Furthermore, an external feedback circuit is configured by the AM optical modulator 2, the homodyne detection circuit 5, the matrix / nonlinear calculation circuit 6, etc.

[0041] The optical Ising computer shown in Figure 2 does not oscillate in the EDFA4 within the optical fiber loop 3, and the gain and loss are balanced within the optical fiber loop 3. In other words, there is no pulse oscillation within this optical fiber loop 3, and it is a lossless circular transmission path. The optical fiber loop length is, for example, 50 km, and the cumulative dispersion within the optical fiber loop 3 is made zero by dispersion management or fiber Bragg grating.

[0042] The optical Ising computer shown in Figure 2 is the cosine component u, which is the real part of the electric field amplitude of the optical pulse propagated through the optical fiber loop 3. m[k] is detected by the homodyne detection circuit 5, converted to digital by the A / D converter of the matrix / nonlinear arithmetic circuit 6, and then input to the FPGA circuit. Homodyne detection in the homodyne detection circuit 5 is achieved by injecting the pulse propagating through the optical fiber loop 3 and the pulse from the pulse light source 1 into a balanced detector (Balanced PD (B-PD)) not shown. This local emission is input to the homodyne detection circuit 5 in synchronization with the circulating pulse by the optical delay circuit 8 from the same pulse light source 1 as the signal light pulse. This is a self-homodyne-like method, and since the same pulse light source 1 can be used, stable detection is possible.

[0043] In the matrix-nonlinear operation circuit 6 of Figure 2, the interaction function is, i.e., the matrix J shown in equation (7). m,n and u m The product with [k] (corresponding to equation (2)) and the nonlinear operation related to equation (8), which includes the operation for binary branching, are calculated (corresponding to equations (5) and (6)).

[0044]

number

[0045] Here, α is a parameter representing the gain (corresponding to α in equations (5) and (6)), and β is a parameter representing the strength of the interaction. In this method, the FPGA circuit within the external feedback circuit digitally provides the nonlinearity, which makes it possible to introduce various nonlinear functions that were previously impossible. Next, the nonlinear function F in equation (8) is calculated. NL After converting the signal to an analog signal using D / A conversion, the AM optical modulator 2 modulates the output optical pulse u0 from the pulse light source 1 with the amplitude of the analog signal, and the modulated pulse is injected into the loop (optical fiber loop 3). This becomes the k+1th optical pulse. As a result, u n [k] and u n+1The relationship for [k] is given by equation (9). In this case, if the gain α of the external feedback circuit is made greater than 1, the entire system becomes a hybrid bifurcation machine due to the linear optical fiber loop 3 and the gain of the feedback circuit.

[0046]

number

[0047] A key feature of the optical Ising computing device in the first embodiment of the present invention is that, instead of using oscillators such as the IM of conventional DOPOs or OEOs for analog nonlinear operation, digital nonlinearity is introduced into the feedback electrical circuit (external feedback circuit). Importantly, this configuration enables the generation of stable binary bifurcations. Furthermore, a key feature of this digital nonlinearity is that any nonlinear function can be prepared, enabling the realization of an optimal binary bifurcation for the system.

[0048] Furthermore, the optical Ising computing apparatus of the first embodiment of the present invention can increase the size N of the optimization problem by making the optical fiber loop length sufficiently long (several kilometers to several hundred kilometers) and the pulse interval sufficiently narrow. Therefore, the long-distance coherent transmission technology of ultra-high-speed optical pulse signals using a circular transmission path can be directly utilized for large-capacity computing. For example, if an optical pulse of 10 GHz is repeatedly transmitted through a circular loop of 50 km, the size N = 2.5 × 10⁻⁶. 6 Because individual pulses can propagate, it becomes possible to compute extremely large optimization problems, such as 2.5 million x 2.5 million.

[0049] In DOPO, noise accumulation associated with optical fiber loop circulation is inherently low. However, in the loop transmission of pulses using EDFA, Amplified Spontaneous Emission (ASE) noise accumulates with repeated loops, causing the OSNR to gradually deteriorate. Therefore, as shown in Figure 2, an in-loop AM optical modulator 2' is inserted into the optical fiber loop 3, and noise within the optical fiber loop 3 is removed by amplitude modulation synchronized with the pulse repetition frequency. Here, the in-loop optical modulator 2' is driven by the output clock signal (sine wave signal) of the synthesizer 7. The repetition frequency of the pulse light source 1 is synchronized with this synthesizer, thereby enabling amplitude modulation synchronized with the pulse repetition frequency to be applied to the optical pulse in the optical fiber loop 3. This synchronous modulation technique introduces the synchronous modulation for ultra-long-distance soliton transmission proposed by the inventor, as described in Non-Patent Literature 4. It is important that this method keeps ASE accumulation at a constant low value, and that the waveform of the optical pulse remains clean even after interaction due to synchronous modulation.

[0050] Furthermore, the optical Ising computing device of the first embodiment of the present invention uses passive pulse cycling without oscillation, similar to the conventional DOPO and OEO IMs shown in Figure 1, enabling stable operation. When the feedback signal increases, the power within the optical fiber loop 3 increases steadily, but the gain saturation of the EDFA4 reduces the gain, suppressing the increase in power within the optical fiber loop 3. Conversely, when the power within the optical fiber loop 3 decreases, the gain of the EDFA4 increases, suppressing the decrease in power within the optical fiber loop 3. In this way, the gain saturation of the EDFA4 plays a role in stabilizing the energy within the optical fiber loop 3, thereby automatically stabilizing the binary branch energy. In contrast, this slow gain saturation mechanism of the EDFA4 is not present in the conventional DOPO and OEO IMs shown in Figure 1, making automatic stabilization of binary branching difficult in these devices. Moreover, the optical Ising computing device of the first embodiment of the present invention can quickly transition from a noisy state to a stable binary branch state by adjusting the magnitude of α. Furthermore, regarding gain adjustments such as those in quantum annealing, gradually increasing α and β from 0 with each cycle allows convergence to a higher cutoff value compared to the case where α and β are constant. However, this may increase the number of cycles required for convergence, so it is necessary to appropriately change α and β.

[0051] Computer analysis of this device was performed based on the circuit transmission of optical pulses with a repetition rate of 10 GHz and a width of 10 ps. Specifically, a Gaussian pulse train with a repetition rate of 10 GHz and a pulse width of 10 ps was transmitted in a 50 km loop. The photodetector bandwidth was assumed to be 40 GHz, and the A / D conversion was assumed to be 160 GSa / s. First, in order to observe the waveform changes of the pulses associated with circuit transmission, the propagation of the pulses was analyzed without feedback gain or interaction (i.e., α=β=0). For the propagation analysis, the split-step Fourier method was used to calculate the nonlinear Schrödinger equation (10) below.

[0052]

number

[0053] Here, β2 is the dispersion value of the optical fiber, γ is the nonlinear optical coefficient, and l is the loss. The circulating transmission line is a 50 km long distributed managed transmission line consisting of 33.3 km of SLA (Super Large Area Fiber) and 16.7 km of IDF (Inverse Dispersion Fiber), and was circulated at a transmission power of -10 dBm. The dispersion of the fibers is 20 ps / nm / km (SLA) and -40 ps / nm / km (IDF), and the effective core cross-sectional area of ​​each is A eff = 110 μm 2 , 30 μm 2 The fiber loss is assumed to be 0.2 dB / km, and the gain of EDFA4 is calculated considering gain saturation: g = g0 / (1 + P / P sat ), P sat = (P p It is calculated using + 1) / 2. Here, g0 is the small-signal gain, P is the input optical power, P sat is saturation power, P p This is the excitation light power, and the small-signal gain is set to 0.2 dB / km × 50 km = 10 dB to compensate for fiber loss. The noise figure (NF) of the EDFA4 is set to 4 dB, and a 1 nm bandwidth optical filter is inserted at the output of the EDFA4.

[0054] Figure 3 shows the waveform changes when a Gaussian pulse train with a repetition rate of 10 GHz and a pulse width of 10 ps is transmitted in a 50 km loop. From Figure 3, it can be seen that the deterioration of OSNR and waveform distortion increase with increasing propagation distance. At a transmission distance of about 10,000 km, which corresponds to the distance across the Pacific Ocean, the waveform is roughly maintained, as shown in Figure 3(a). However, as the distance increases, as shown in Figures 3(b) and (c), the propagation waveform begins to become distorted, pulse drops occur, and it becomes unusable as an IM. Therefore, an in-loop AM optical modulator 2' was inserted into the optical fiber loop 3, and 10 GHz intensity modulation (modulation degree: 0.1) was applied in synchronization with the circulating signal to suppress OSNR deterioration. The results are shown in Figures 4(a) to (e). As shown in Figure 4, fluctuations in the pulse height due to ASE noise remain, but the deterioration of waveform distortion is suppressed. Furthermore, noise accumulation is minimal even during non-pulse periods, and as shown in Figure 4(e), a pulse waveform with a good signal-to-noise ratio (S / N) is obtained even after propagation of 1,000,000 km.

[0055] Next, we show the analysis results when digital nonlinear feedback is introduced into the circulating system of the 50 km optical fiber loop 3 shown in Figure 3. In this embodiment, the tanh function shown in equation (11) is defined in the FPGA circuit as a nonlinear function for matrix calculation of the interaction in the digital feedback circuit and for generating binary branching.

[0056]

number

[0057] Here, the noise ζn required to cause a binary bifurcation is defined as F. NLThis is added to the above. γ is a coefficient representing the strength of the noise. Noise ζn can be artificially generated in the FPGA circuit, but in reality, the ASE noise from the EDFA included in the loop functions as noise ζn, so there is no need to specifically provide γζn in the FPGA circuit. As described above, using this nonlinear function makes it easy to create a situation in which stable binary bifurcation is likely to occur due to a much steeper nonlinearity than that of Van der Pol type polynomials. Also, since the tanh function is a function of up to ±1, for example, in the AM optical modulator 52 in Figure 1, the maximum magnitude of the optical field u0 is fed back to the optical fiber loop 53. The reason why the interaction term is also included in the tanh function is that the presence of this term affects the binary bifurcation itself, and the lowest energy can be achieved for the system as a whole.

[0058] First, setting β = 0, we investigated whether spontaneous binary bifurcation occurs in the optical Ising computing device of the first embodiment of the present invention (occurrence of random binary bifurcation of ±A (amplitude) at 50%:50%) by computer analysis. The results are shown in Figure 5. We investigated how the binary bifurcation develops by starting a circulating pulse from ASE noise and changing α. Figures 5(a) to (c) show the rise time of the binary bifurcation corresponding to α = 1.1, 1.5, and 2.0, respectively. As shown in Figure 5(a), at α = 1.1, it takes a relatively long time for binary bifurcation to occur. On the other hand, as shown in Figure 5(b), at α = 1.5, the binary bifurcation rises faster than in Figure 5(a), and as shown in Figure 5(c), at α = 2.0, the binary bifurcation rises instantaneously. Thus, it was confirmed that the magnitude of the binary bifurcation is proportional to α, and that the binary bifurcation rises slowly when the gain is low and rapidly when the gain is high. As the feedback optical signal increases, the power in the optical fiber loop 3 increases, but the power does not increase linearly. At a certain power level, the gain of the EDFA decreases and settles at a constant value at a slightly higher power level. From the above, it can be seen that a stable binary branch basically exists in the optical Ising calculation device of the first embodiment of the present invention.

[0059] Next, a computational analysis of the Max Cut problem in quantum annealing was performed using the optical Ising computing apparatus of the first embodiment of the present invention. For the Max Cut problem, two types of graphs called K2000 and G22 were prepared, and the Max Cut value was determined by numerical analysis of this apparatus. The Max Cut value is the problem of finding the way to divide a graph into two groups by cutting the edges connecting the vertices, such that the sum of the weights of the edges to be cut is maximized. K2000 is a graph in which each vertex is connected to all 1999 other vertices with a weight of +1 or -1, and its matrix J m,n This is given by a 2000x2000 symmetric matrix where the diagonal elements (m = n: 2000 elements) are 0 and the off-diagonal elements (m ≠ n: 2000×2000 - 2000 = 3,998,000 elements) randomly take values ​​of +1 or -1. On the other hand, G22 is a simple graph where each vertex is connected to only 19 of the other 1999 vertices, and their weights are all given as 1. That is, its matrix J m,n This is a 2000 × 2000 symmetric matrix where 2000 diagonal elements (m = n) are 0, 3998000 off-diagonal elements (m ≠ n), which is 1% of the total, are 1, and the remaining off-diagonal elements are 0.

[0060] An example of how the cut-off value converges with each loop during this calculation is shown in Figures 6(a)K2000 and (b)G22. Since the simulation includes ASE noise from the EDFA, the digital noise coefficient in the FPGA circuit was set to γ ​​= 0. The light source pulse width was set to 10 ps, ​​the repetition frequency to 10 GHz, and the power to -10 dBm. An AM optical modulator was inserted after the EDFA for synchronous amplitude modulation. The propagation time within the optical fiber loop 3 is 0.25 ms per 50 km loop, and converges approximately at 10,000 km, requiring a calculation time of 50 ms for convergence. The dips in the cut-off values ​​in Figures 6(a) and (b) are caused by nonlinear phase rotation due to the Kerr effect within the optical fiber loop 3.

[0061] Next, the distribution of cutoff values ​​is plotted as contour lines (α-β maps) while varying α and β, as shown in Figures 7(a)K2000 and (b)G22. The left figure in Figures 7(a) and (b) shows the maximum value of the cutoff value after 100 trials, and the right figure shows the distribution of the mean value. The × symbols in the figures indicate that cases where convergence did not occur in 100 trials are included. In K2000 shown in Figure 7(a), the maximum value of 32983 (marked with a circle in the figure) is obtained when (α,β) = (0.05, 0.04), and in G22 shown in Figure 7(b), the maximum value of 13304 (marked with a circle in the figure) is obtained when (α,β) = (0.5, 0.15).

[0062] [Second Embodiment] In the optical Ising computing device of the second embodiment of the present invention, the step function f(u) of equation (12) is used as the nonlinear function for generating a binary branch in the digital feedback circuit. n A nonlinear function using [k]) was defined in an FPGA circuit.

[0063]

number

[0064] This function f(u n [k]) is u n The function takes values ​​of ±1 / 2 around [k]=0. Furthermore, as η approaches infinity, it becomes a step function with an amplitude of ±1 / 2, which can provide an even more abrupt nonlinear function than the tanh function type. The α-β maps when using this step function are shown in Figures 8(a)K2000 and (b)G22. In Figure 8(a)K2000, the maximum value of 32898 (marked with a circle in the figure) is obtained when (α,β) = (-0.05, 0.03), and in Figure 8(b)G22, the maximum value of 13314 (marked with a circle in the figure) is obtained when (α,β) = (0.5, 0.13).

[0065] [Third Embodiment] In the optical Ising computing device of the third embodiment of the present invention, a Van der Pol type cubic polynomial (equation (5)) is defined in the FPGA circuit as a nonlinear function for generating binary branching in the digital feedback circuit. This is the same nonlinear function as the DOPO type IM shown in Figure 1(a), and the same function can be realized in this device without using an optical oscillator like DOPO. The α-β maps when using the cubic polynomial are shown in Figures 9(a) K2000 and (b) G22. In K2000 in Figure 9(a), the maximum value of 32725 (marked with a circle in the figure) is obtained when (α,β) = (0.7, 0.01), and in G22 in Figure 9(b), the maximum value of 13269 (marked with a circle in the figure) is obtained when (α,β) = (0.9, 0.06).

[0066] [Fourth Embodiment] In the optical Ising computing device of the fourth embodiment of the present invention, a cosine function (equation (6)) is defined in the FPGA circuit as a nonlinear function for generating binary branching in the digital feedback circuit. This is the same nonlinear function as the OEO-type IM shown in Figure 1(b), and the same function can be realized in this device without using an optoelectronic oscillator like the OEO. The α-β maps when using the cosine function are shown in Figures 10(a) K2000 and (b) G22. In K2000 in Figure 10(a), the maximum value of 32713 (marked with a circle in the figure) is obtained when (α,β) = (0, 0.03), and in G22 in Figure 10(b), the maximum value of 13290 (marked with a circle in the figure) is obtained when (α,β) = (0.6, 0.1), (0.6, 0.11), and (0.7, 0.09).

[0067] Figure 11 shows a table summarizing the results of these four embodiments. For comparison, Figure 11 also shows the experimental results of the DOPO-type IM described in Non-Patent Document 2, and the numerical calculation results of the simulated annealing method described in the same document. These results show that the tanh function yields high cutoff values ​​for both the K2000 and G22 problems, and the average values ​​for K2000 and G22 are superior to those of the DOPO-type IM. The tanh function is difficult to realize in the prior art, and these results demonstrate the usefulness of the present invention.

[0068] [Fifth Embodiment] In Figure 2, assuming that the time required for calculations in the FPGA circuit can be ignored, the amplitude of the optical pulse that has propagated through the nth loop can be detected, and the feedback signal obtained from the FPGA circuit can be directly fed back to the nth optical pulse using this detection. However, if the processing takes a long time, it becomes difficult to feed the feedback back to the nth optical pulse. In the optical Ising computing device of the fifth embodiment of the present invention, considering the processing time in the FPGA circuit, the processing time in the FPGA circuit is set to the time it takes for the optical pulse to complete one revolution around the optical fiber loop (0.25 ms if the optical fiber loop length is 50 km), and the feedback signal is fed back to the (n+1)th optical pulse. This time chart is shown in Figure 12(a).

[0069] [Sixth Embodiment] In the optical Ising computing device of the sixth embodiment of the present invention, the processing time in the FPGA circuit was set to the time it takes for an optical pulse to complete two revolutions of the optical fiber loop (0.5 ms if the optical fiber loop length is 50 km), and the feedback signal was fed back to the (n+2)th optical pulse. This time chart is shown in Figure 12(b).

[0070] The 2000×2000 problem (G22) was calculated using the optical Ising computing apparatus of the fifth and sixth embodiments of the present invention, and a comparison was made with the case where processing time can be ignored. Figure 13 shows a comparison of the calculation results for G22 (α = 0.5, β = 0.15). The dashed line in the figure represents the result when processing time can be ignored. As the processing delay increases, the frequency of feedback is halved, so it can be seen that the optical Ising computing apparatus of the sixth embodiment of the present invention shown in Figure 12(b) tends to converge more slowly than the optical Ising computing apparatus of the fifth embodiment of the present invention shown in Figure 12(a). From this, it can be said that in order to obtain quick results, it is desirable to configure the system with the shortest optical fiber loop length corresponding to the size N of the optimization problem.

[0071] [Seventh Embodiment] The seventh embodiment of the optical Ising computing apparatus of the present invention, in addition to circulating the optical pulse in the optical Ising computing apparatus of the first embodiment of the present invention, circulates the optical pulse in a hollow core fiber such as a photonic crystal fiber or an anti-resonant fiber instead of circulating it in the optical fiber loop 3. Alternatively, if the spin number is small, the optical pulse may be circulated in an optical fiber loop of short-length fibers, which are ordinary optical fibers shortened. In hollow core fibers and short-length fibers, nonlinear optical effects are suppressed, so the periodic dips in the cutoff value that occurred in the optical Ising computing apparatus of the first embodiment of the present invention do not occur, and the pulse can be stably focused to the maximum cutoff value. Furthermore, since hollow core fibers are ideally a vacuum and do not have loss, dispersion, or nonlinear optical effects, the pulse propagates over long distances without distortion. For this reason, the EDFA 4 and the in-loop AM optical modulator 2' for synchronous modulation are unnecessary. Also, since there is no ASE noise, the noise necessary to cause binary bifurcation is generated digitally by the FPGA circuit as shown in equation (11).

[0072] Furthermore, as in the optical Ising computing apparatus of the first embodiment of the present invention, instead of the optical fiber loop 3 that circulates the optical pulse, a digital memory 6' may be used to digitally represent the optical pulse and to describe the propagation of multiple optical pulses in a long optical fiber in software, as shown in Figure 14. The optical pulse is input to the digital memory 6' instead of the optical fiber loop 3, and the real part component of the electric field amplitude of the digital optical pulse output from the digital memory 6' is detected by the homodyne detection circuit 5. In the arithmetic circuit 6, after digitally calculating the interaction function and the nonlinear function for binary branching, the AM optical modulator 2 modulates the digital optical pulse from the pulse light source 1 with the information obtained from the digital calculation, and superimposes it with the digital optical pulse from the previous cycle stored in the digital memory 6' before the calculation to cause interaction. The entire configuration of the optical Ising computing apparatus shown in Figure 14 may be constructed in software and used as a digital simulator.

[0073] The capacity of the digital memory 6' for realizing the propagation delay corresponding to the orbit time of the optical fiber loop 3 (in the optical Ising computing device of the first to sixth embodiments of the present invention, the propagation distance is L = 50 km) is such that the speed of light in the fiber is v = 2 × 10 8 Assuming a sampling interval of m / s, a sampling interval of Δt = 2 ps, and an amplitude resolution of N = 64 bits, the estimated speed is (L / v / Δt) × N = 125 Mbit × 64 = 8 Gbit / s.

[0074] Figures 15(a-1) and 15(a-2) show the calculation results (100 trials) for a 10,000 × 10,000 problem (K10,000) using the optical Ising computing device of the seventh embodiment of the present invention. These results were obtained using a digital simulator in which the configuration of the optical Ising computing device was entirely constructed using software. For comparison, Figures 15(b-1) and 15(b-2) show the calculation results (50 trials) using the optical Ising computing device (fiber propagation) of the first embodiment of the present invention. Figures 15(a-1) and 15(b-1) show the convergence of the maximum cut value with increasing rotation, while Figures 15(a-2) and 15(b-2) show histograms of the maximum cut value. It was confirmed that both embodiments converged to roughly the same maximum cut value. Furthermore, in Figure 15(b-1), similar to Figure 6, a periodic dip is observed due to nonlinear phase rotation caused by the Kerr effect in the optical fiber loop 3. However, in Figure 15(a-1), it was confirmed that no dip occurs because the Kerr effect is absent.

[0075] [Eighth Embodiment] As shown in Figure 16, the optical Ising calculator of the eighth embodiment of the present invention has a π / 2 optical phase shifter 9 inserted after the AM optical modulator 2 of the optical Ising calculator of the first embodiment of the present invention shown in Figure 2. Furthermore, the homodyne detection circuit 5 detects the imaginary component (sin component, Q channel) of the electric field amplitude, rather than the real component (cos component, I channel). Originally, the electric field amplitude of an optical pulse is given by a complex number I + iQ, so there is a cos component, i.e., the I component, and a sin component, i.e., the Q component, which is shifted in phase by 90 degrees, and both can be obtained simultaneously by homodyne detection. In the optical Ising calculators of the first to seventh embodiments of the present invention, the nonlinear function F NL All calculations are performed using only the I component. Leakage to the Q component is ignored and left as is, and only the I component is fed back. On the other hand, in the optical Ising computing device of the eighth embodiment of the present invention, the I component is set to zero, and a binary branch is generated by the Q component with a phase shift of 90 degrees.

[0076] Here, the Q component of the electric field of the light pulse is u0u Q , n [k] is defined as follows: A light pulse propagating through a fiber loop is homodyne detected, and the Q component of its electric field is u0u Q , m [k] is converted to digital and then input to the FPGA circuit. Then F NL All calculations are performed using only the Q component. That is, the calculation of the binary bifurcation based on phase information is performed using real numbers with the value of the Q component. In this case, the nonlinear interaction is the same as the calculation of the binary bifurcation of the I component. Here, what is important in order to generate a binary bifurcation based on the Q component is that when this interaction information is fed back, the amplitude of the externally supplied optical pulse is amplitude-modulated by a real number Q, and then coupled to the optical loop after undergoing a phase change of exp[iπ / 2] by the optical phase shifter 9. This is because this operation results in iQ (=e iπ / 2 This is because Q) is calculated, and a phase shift of π / 2 is maintained for the I channel. This makes binary bifurcation possible for the Q channel only.

[0077] In this case, the nonlinear function F of the Q channel Q , n [k] is given by equation (13) below.

number

number

[0078] Figures 17(a) to (c) show the cycle dependence of the cutoff value for the K2000 problem in the Q channel obtained in this way, the phase change of the pulse for each cycle, and the change in optical power within the loop for each cycle, respectively. α = 0.05 and β = 0.04 are set. Even in this case, the cutoff value can be calculated, but a periodic dip in the binary branching due to the nonlinear optical effect in the optical fiber is observed at pulse phases of 0 and π. This is due to the fact that in the Q component, the state sinφ=0 occurs at phase rotations φ=0 and ±π. Here, the nonlinear effect of the Q component is originally shifted in phase by π / 2 compared to the I component, and this is further shifted by exp[iπ / 2] and fed back, so the instability due to the nonlinear effect appears at phases of 0 and π.

[0079] In the optical Ising computing device of the eighth embodiment of the present invention, the binary branching is a binary branching of the imaginary part, so the feedback signal to the loop needs to be multiplied by exp[iπ / 2]. If this is simply fed back to the optical loop as the feedback signal of the real part without a phase shift of π / 2, binary branching does not occur. This is shown in Figures 18(a) and (b). Here, Figure 18(a) shows the case without a phase shift of π / 2, and Figure 18(b) shows the case with a phase shift of π / 2. To see the stability of only the binary branching, α=1.5 and β=0 are set. From these, it can be seen that binary branching of the Q component does not occur unless the phase shift is shifted by π / 2 in the feedback.

[0080] [Ninth Embodiment] As shown in Figure 19, the optical Ising computer of the ninth embodiment of the present invention replaces the AM optical modulator 2 and optical phase shifter 9 of the optical Ising computer of the eighth embodiment of the present invention with an IQ optical modulator 10. Furthermore, the homodyne detection circuit 5 simultaneously detects the real component (cos component, i.e., I channel) and the imaginary component (sin component, i.e., Q channel) of the electric field amplitude. In the optical Ising computer of the eighth embodiment of the present invention, the I channel component and the Q channel component can be independently generated as binary branches. Since the optical electric field is given as a complex quantity, it is considered that a binary branch exists in which the I channel and Q channel coexist. In the optical Ising computer of the ninth embodiment of the present invention, the I channel signal and the Q channel signal obtained by homodyne detection are made to interact nonlinearly (both are calculated simultaneously) to generate a complex binary branch of the entire optical electric field. What is important here is that since the I channel information needs to be fed back to the real part and the Q channel information to the imaginary part, it is essential to use the IQ optical modulator 10 used in coherent communication. Another important point is that, due to the Kerr effect in optical fibers, the I channel influences the Q channel, and the Q channel influences the I channel, resulting in a binary branching process through their interaction. If the Kerr effect were absent, the I channel and Q channel would not interact, and two independent binary branches would occur simultaneously.

[0081] Here, the I component of the electric field of the light pulse is u0u I , n [k], the Q component is u0u Q , n [k] is defined as the nonlinear function of the I channel and Q channel. I,n [k] and F Q,n Let [k] be F I,n [k] and F Q,n [k] is given by equation (15) below and equation (13) above, respectively.

[0082]

number

number

[0083] In the optical Ising computing apparatus of the ninth embodiment of the present invention, when calculating the I channel and the Q channel, there are two maximum cutoff values ​​that exist simultaneously and independently, so the maximum cutoff value D is defined as shown in the following equations (17) and (18).

[0084] 1: Amplitude u of the I channel I (spin x) I ) defined by:

number

number

[0085] The overall picture of the loop trajectory dependence of the cut-off value of the K2000 problem obtained in this way is shown in Figure 20(a), and an enlarged view of its rising point is shown in Figure 20(b). As shown in Figures 20(a) and (b), the cut-off value D I and D QA slight difference is observed. However, both show high cutoff values. The slight difference is due to the difference in noise characteristics (pseudorandom numbers) of the I channel and Q channel between the initial state and each subsequent cycle. Also, for reference, Figure 20(b) shows the calculation results when only the Q channel is fed back using the optical Ising calculation device of the 8th embodiment of the present invention. The dip in the cutoff value that occurred when only the I channel (1st embodiment, Figure 6) and only the Q channel (8th embodiment, Figure 17(a)) were fed back has disappeared in the optical Ising calculation device of the 9th embodiment of the present invention. In other words, it is shown that if only the binary branching of either the I channel or the Q channel is used, leakage occurs from the I channel to the Q channel or from the Q channel to the I channel due to the Kerr effect, causing a dip in the maximum cutoff value. In contrast, by using the binary branching of the I channel and the Q channel simultaneously, as in the optical Ising calculation device of the 9th embodiment of the present invention, energy is transferred between the two channels, and the overall power (I 2 +Q 2 Since ) is kept constant, no dips appear in the cutoff value, and the solution can converge stably in the maximum cutoff problem. Therefore, this method using the IQ optical modulator 10 is an important technique for stabilizing the Kerr effect when constructing an optical Ising computing device.

[0086] [Tenth Embodiment] As shown in Figure 21, the optical Ising computer in the tenth embodiment of the present invention uses a CW (Continuous Wave) light source 11 instead of the pulse light source 1 in the optical Ising computer in the first embodiment of the present invention. Homodyne detection is performed using the optical pulse output from the optical fiber loop 3 and the CW light source 11. This is equivalent to the configuration of a commercially available digital coherent communication system. In addition, the optical Ising computer in the seventh to ninth embodiments of the present invention may also replace the pulse light source 1 with the CW (Continuous Wave) light source 11. The repetition frequency f of AM synchronous modulation in the optical fiber loop 3. mIf the optical fiber loop length is l, its refractive index is n, and the speed of light in a vacuum is c, then f m It is given by =qc / (nl), where q is the number of pulses (spins) in the optical fiber loop 3, and the number of interacting pulses. Therefore, by introducing an in-loop optical modulator 2' that operates at a modulation frequency that is an integer fraction of the optical delay time of the optical fiber loop 3 into the optical fiber loop 3, even if CW light is initially injected into the optical fiber loop 3, pulses are formed due to the waveform shaping effect of the modulator, and eventually converge to an optical pulse determined by the optical filter 12 in the optical fiber loop 3. In other words, even with a CW input, steady-state pulses of about 10 to 20 ps can easily circulate in the optical fiber loop 3.

[0087] Here, in order to observe the waveform change in the optical fiber loop 3, we compared the waveform change in the optical fiber loop 3 when a 10 ps pulse light was incident from the outside using the optical Ising computing device of the first embodiment of the present invention, and when CW light was incident using the optical Ising computing device of the tenth embodiment of the present invention, under conditions without feedback (α=0, β=0). The results are shown in Figures 22(a) and (b), respectively. Figures 22(a) and (b) show the intensity I of the pulse waveform after propagation of 30,000 km. 2 +Q 2 The top image shows the amplitudes I and Q, while the bottom image shows the amplitudes I and Q. Here, the modulation depth of the in-loop AM optical modulator 2' is set to 30%, and the bandwidth of the optical filter 12 is set to 125 GHz. Both converge to a 14 ps pulse as they circulate and propagate steadily within the optical fiber loop 3, and it can be used as an optical Ising calculator even with CW light incidence.

[0088] Next, with α=1.5 and β=0, Figure 23 shows the results of comparing the rise time of the binary branching in pulsed light incidence (first embodiment) and CW light incidence (tenth embodiment). Figures 23(a-1) and 23(b-1) correspond to the binary branching of the I and Q components when a 10 ps pulse light is incident from the outside, respectively, while Figures 23(a-2) and 23(b-2) correspond to the binary branching of the I and Q components when CW light is incident, respectively. The binary branching of the Q component occurs automatically through the Kerr effect, but no feedback of the Q signal is performed. In all cases, the modulation index is set to 30% and the filter bandwidth to 125 GHz. As can be seen from Figures 23(a-2) and 23(b-2), the rise time of the binary branching is slightly slower with CW light incidence than with pulsed light incidence (see Figures 23(a-1) and (b-1)). This is because, when CW light is incident, the formation of pulses as spin is slow, and therefore the rise time of the binary bifurcation is delayed.

[0089] Next, Figure 24 shows the change in the cutoff value of the 2000×2000 (K2000) problem against the propagation distance (number of orbits) when pulsed light is incident and when continuous wave (CW) light is incident. Figure 24(a) shows the case of pulsed light incident, and Figure 24(b) shows the case of CW light incident. It can be seen that the rise of the cutoff value is faster and larger in Figure 24(a) than in Figure 24(b). This is because, in the case of CW light incident, the formation of pulses as spins is slower, so the calculation takes longer. However, when the calculation for CW light incident is continued and the propagation distance is doubled to 60,000 km (1200 orbits), it can be seen that it converges to the same maximum cutoff value as in Figure 24(a) for pulsed light incident. This shows that, although the calculation takes longer (approximately twice as long) compared to pulsed light input, the optical Ising calculation device also functions with CW light incident. The optical Ising computing apparatus of the tenth embodiment of the present invention is characterized by its simplicity because it does not require the use of a complex and expensive pulsed light source. [Industrial applicability]

[0090] As described in detail above, the present invention eliminates the need for an optical oscillator and enables the realization of an optical Ising computing device with a simple configuration. Therefore, it is easy to extend the length of the optical fiber loop or increase the repetition rate of the optical pulses. As a result, the number of optical pulses (spins) that can circulate in the optical fiber loop can be easily increased, enabling the calculation of larger-scale combinatorial optimization problems. Furthermore, since optimal nonlinear feedback calculations can be realized according to the problem to be solved, it is possible to converge the calculation of combinatorial optimization problems more quickly. In addition, due to synchronous amplitude modulation and the gain saturation effect of EDFA, the pulse energy can be automatically stabilized while maintaining a high OSNR, enabling stable circulating over long distances. As a result, a larger-scale and more accurate Ising machine can be provided. [Explanation of Symbols]

[0091] 1. Pulsed light source 2 AM Optical Modulator 2' Loop-based AM optical modulator 3 Optical fiber loops 4. Erbium-doped optical fiber amplifier (EDFA) 5. Homodyne detection circuit 6. Matrix and Nonlinear Arithmetic Circuits (Arithmetic Circuits) 6' Digital Memory 7 Synthesizers 8. Optical delay circuit 9 Optical phase shifter 10 IQ Optical Modulators 11 CW light source 12 Light Filters 51. Pulsed light source 52 (AM) Optical Modulator 53 Fiber optic loops 54 Phase-sensitive optical amplifier 55 Homodyne detection circuit 56 Matrix calculation circuit 57 Photodetector

Claims

1. A pulsed light source, A fiber optic loop into which optical pulses from the pulsed light source are introduced, An erbium-doped optical fiber amplifier is provided within the optical fiber loop to compensate for the loss of the optical fiber loop, A homodyne detection circuit for detecting the optical pulse from the optical fiber loop, A calculation circuit that performs digital calculations on the optical pulse detected by the homodyne detection circuit, The system includes an optical modulator that receives the optical pulses from the pulsed light source and information obtained from the digital calculations of the calculation circuit, modulates the input optical pulses with the information, and then injects them into the optical fiber loop. The optical pulse after circulating through the optical fiber loop is detected by the homodyne detection circuit and input to the calculation circuit. The calculation circuit then digitally calculates the interaction function of the optical pulse and the nonlinear function for binary branching. The optical modulator then modulates the optical pulse from the pulse light source using the information obtained from the digital calculation, and superimposes and interacts with the optical pulse in the optical fiber loop. A distinctive optical Ising computing device.

2. A digitally represented pulsed light source, A digital optical pulse is input from the pulse light source, and a digital memory is used to describe the propagation of multiple such digital optical pulses in a long optical fiber using software. A digitally represented homodyne detection circuit is used to detect the digital optical pulse output from the digital memory, A calculation circuit that performs digital calculations on the digital optical pulse detected by the homodyne detection circuit, The system includes a digitally represented optical modulator that receives the digital optical pulses from the pulse light source and information obtained from the digital calculations of the calculation circuit, modulates the input digital optical pulses with the information, and then inputs them into the digital memory. By performing digital calculations, the digital optical pulse from the digital memory is detected by the homodyne detection circuit and input to the arithmetic circuit. In the arithmetic circuit, the interaction function and the nonlinear function for binary branching of the digital optical pulse are digitally calculated. Then, in the optical modulator, the digital optical pulse from the pulse light source is modulated with the information obtained from the digital calculations, and is superimposed and interacted with the digital optical pulse from the previous cycle stored in the digital memory before the calculations. A distinctive optical Ising computing device.

3. CW light source, A fiber optic loop into which CW light from the aforementioned CW light source is introduced, An erbium-doped optical fiber amplifier is provided within the optical fiber loop to compensate for the loss of the optical fiber loop, An optical filter provided within the optical fiber loop, An in-loop optical modulator operating at a modulation frequency that is an integer fraction of the optical delay time within the optical fiber loop, A homodyne detection circuit detects optical pulses generated from the CW light circulating in the optical fiber loop from the optical fiber loop, A calculation circuit that performs digital calculations on the optical pulse detected by the homodyne detection circuit, The system includes an optical modulator that receives the CW light from the CW light source and information obtained from the digital calculations of the calculation circuit, modulates the input CW light with the information, and then injects it into the optical fiber loop. The optical pulses circulating in the optical fiber loop are detected by the homodyne detection circuit and input to the calculation circuit. The calculation circuit then digitally calculates the interaction function and the nonlinear function for binary branching. The optical modulator then modulates the CW light from the CW light source using the information obtained from the digital calculation, and superimposes and interacts with the optical pulses in the optical fiber loop. A distinctive optical Ising computing device.

4. The optical Ising computing apparatus according to claim 1 or 3, characterized in that it generates a binary branch by combining a lossless loop and the calculation of a nonlinear function in the arithmetic circuit without oscillating pulses in the optical fiber loop.

5. The optical Ising calculator according to claim 2, characterized in that it generates a binary branch by combining a lossless loop and the calculation of a nonlinear function in the arithmetic circuit without oscillating pulses in the digital memory.

6. The optical Ising computing apparatus according to any one of claims 1 to 3, characterized in that the homodyne detection circuit detects the phase of the real component of the optical pulse.

7. The optical Ising computing apparatus according to any one of claims 1 to 3, characterized in that the homodyne detection circuit detects the phase of the imaginary component of the optical pulse.

8. The optical Ising calculator according to any one of claims 1 to 3, characterized in that the homodyne detection circuit simultaneously detects both the real and imaginary components of the optical pulse.

9. The optical Ising computing apparatus according to any one of claims 1 to 3, wherein the optical modulator comprises an AM optical modulator that modulates the amplitude of the optical pulse, and modulates the real part component of the optical pulse.

10. The optical Ising computing apparatus according to any one of claims 1 to 3, wherein the optical modulator comprises an AM optical modulator for modulating the amplitude of the optical pulse and a π / 2 optical phase shifter, and modulates the imaginary component of the optical pulse.

11. The optical Ising computing apparatus according to any one of claims 1 to 3, wherein the optical modulator comprises an IQ optical modulator that modulates the amplitude and phase of the optical pulse, and modulates the real and imaginary components of the optical pulse simultaneously.

12. The optical Ising calculator according to any one of claims 1 to 3, characterized in that the calculation circuit calculates an arbitrary nonlinear function.

13. The optical Ising computing apparatus according to claim 1 or 3, characterized in that the optical fiber loop consists of long fibers ranging from several kilometers to several hundred kilometers in length.

14. The optical Ising computing apparatus according to claim 1 or 3, characterized in that the optical fiber loop consists of a hollow core fiber.

15. The optical fiber loop has an in-loop optical modulator inserted into it, By driving the in-loop optical modulator with a sinusoidal signal synchronized with the repetition of the optical pulses circulating around the optical fiber loop, amplitude modulation synchronized with the optical pulses is applied. The optical Ising computing apparatus according to claim 1, characterized in that it is a feature of the present invention.

16. The optical Ising computing apparatus according to claim 1 or 3, characterized in that the erbium-doped optical fiber amplifier has a gain equal to the loss compensation amount of the optical fiber loop.

17. The optical Ising calculator according to any one of claims 1 to 3, characterized in that the feedback signal obtained by the calculation circuit from the nth optical pulse is fed back to the (n+1)th and subsequent optical pulses.

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