Optical ising calculation device

Abstract

[PROBLEM TO BE SOLVED] To provide a large-scale and highly accurate optical Ising calculation device capable of significantly increasing the number of spins, realizing optimum binary branching for a problem to be solved by an arbitrary nonlinear function, and stably and more quickly converging. [SOLUTION] This invention comprises: a pulse light source 1; an optical fiber loop 3 into which an optical pulse from the pulse light source 1 is introduced; an erbium-added optical fiber amplifier 4 provided in the optical fiber loop 3; a homodyne detection circuit 5 for detecting the optical pulse from the optical fiber loop 3; a matrix / nonlinear arithmetic circuit 6 for digitally calculating an interaction function and a nonlinear function for binary branching with respect to the optical pulse detected by the homodyne detection circuit 5; and an AM optical modulator 2 to which the optical pulse from the pulse light source 1 and information obtained in the digital calculation by the matrix / nonlinear arithmetic circuit 6 are inputted, and which modulates the inputted optical pulse and then makes the modulated optical pulse enter the optical fiber loop 3.

Description

Optical Ising computing device 【0001】 The present invention relates to an optical Ising computing device. This application claims priority under Japanese Patent Application No. 2024-216205, filed in Japan on December 11, 2024, the contents of which are incorporated herein by reference. 【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】 IMs include software machines based on computer analysis and computers that implement them in hardware. As a hardware implementation of an IM using light, a coherent Ising machine (CIM) has been proposed that uses a degenerated optical parametric oscillator (DOPO) and a digital feedback circuit (see, for example, Non-Patent Documents 1 and 2). A simpler CIM using an opto-electric oscillator (OEO) has also been proposed (see, for example, Non-Patent Document 3). In these machines, the phase (0,π) of the optical pulse is treated as (+1, -1) of the spin. CIMs have been demonstrated to have excellent computational capabilities, such as being able to rapidly compute optimization problems by taking advantage of the high speed of light. 【0004】 Furthermore, the inventors have proposed a method for synchronous modulation of solitons over ultra-long distances, which involves applying amplitude modulation synchronized with the pulse repetition frequency to the optical pulse within the optical fiber loop (see, for example, Non-Patent Document 4). Using this method, the accumulation of induced spontaneous emission (ASE) noise can be kept to a constant low level, and the waveform of the optical pulse can be kept clean by synchronous modulation even after interaction. 【0005】 T. Inagaki et al., “A coherent Ising machine for 2000-node optimization problems”, Science, 2016, 354, 603T. Honjo et al., “100,000-spin coherent Ising machine”, Sci. Adv., 2021, vol. 7, eabh0952F. Bohm et al., “A poor man's coherent Ising machine based on opto-electronic feedback systems for solving optimization problems”, Nat. Commun., 2019, vol. 10, 3538M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, “10 Gbit / s soliton data transmission over one million kilometres”, Electron. Lett., 1991, vol. 27, p.1270-1272 【0006】The CIMs described in Non-Patent Documents 1 to 3 use optical oscillators such as DOPO and OEO, and therefore the upper limit of the achievable spin number is determined by the resonator length. Currently, 100,000 spins can be achieved with a resonator length of 5 km, but further scaling up requires even longer resonators, which presents the challenge of difficulty in achieving stable oscillation. On the other hand, even with a limited resonator length, it is possible to increase the spin number by increasing the repetition rate of the optical pulse, but there is also the challenge that it is not always easy to increase the repetition frequency of DOPO and OEO. 【0007】 Furthermore, solving the binary minimum energy problem requires the existence of a stable binary bifurcation within the 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. As a result, in conventional CIMs, the nonlinearity used to generate binary bifurcations is limited to nonlinear functions that can be realized analogously with optical elements, which has resulted 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. 【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 in 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 that performs digital calculations on the optical pulses detected by the homodyne detection circuit, and an optical modulator that receives the optical pulses from the pulse light source and information obtained from the digital calculations of the arithmetic circuit, modulates the input optical pulses with the information, and then injects them into the optical fiber loop. The optical modulator is characterized in that the optical pulses after circulating in the optical fiber loop are detected by the homodyne detection circuit and input to the arithmetic circuit, the arithmetic circuit digitally calculates the interaction function of the optical pulses and a nonlinear function for binary branching, and then the optical modulator modulates the optical pulses from the pulse light source with the information obtained from the digital calculations and superimposes and interacts with the optical pulses in the optical fiber loop. 【0010】The optical digital computing device according to the second aspect of the present invention includes a digitally represented pulsed light source, a digital memory for inputting the digital optical pulses from the pulsed light source and for software description of the propagation of the plurality of digital optical pulses in the long optical fiber, a homodyne detection circuit represented digitally so as to detect the digital optical pulses output from the digital memory, an arithmetic circuit for performing digital calculation on the digital optical pulses detected by the homodyne detection circuit, and a digitally represented optical modulator for inputting the digital optical pulses from the pulsed light source and the information obtained by the digital calculation of the arithmetic circuit, modulating the input digital optical pulses with the information, and then inputting the modulated pulses into the digital memory. By digitally calculating, the digital optical pulses from the digital memory are detected by the homodyne detection circuit and input into the arithmetic circuit. In the arithmetic circuit, after digitally calculating the interaction function of the digital optical pulses and the non-linear function for binary branching, in the optical modulator, the digital optical pulses from the pulsed light source are modulated with the information obtained by the digital calculation and superposed and interacted with the previous digital optical pulses in one round in the digital memory before the calculation. 【0011】 The optical digital computing device according to the second aspect of the present invention preferably uses a large-capacity digital memory instead of the optical fiber loop of the optical digital computing device according to the first aspect of the present invention, and is configured by constructing all of the optical digital computing devices according to the first aspect of the present invention with software to form a digital simulator. 【0012】The optical Ising computing device according to the third aspect of the present invention includes 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 the loss of the optical fiber loop, an optical filter provided in the optical fiber loop, an intra-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 an optical pulse generated from the CW light circulating in the optical fiber loop from the optical fiber loop, an arithmetic circuit for performing digital calculation on the optical pulse detected by the homodyne detection circuit, and an optical modulator into which the CW light from the CW light source and information obtained by the digital calculation of the arithmetic circuit are input, and after modulating the input CW light with the information, the optical modulator is incident on the optical fiber loop. The optical pulse circulating in the optical fiber loop is detected by the homodyne detection circuit and input to the arithmetic circuit. In the arithmetic circuit, after digitally calculating an interaction function and a non-linear function for binary branching, in the optical modulator, the CW light from the CW light source is modulated with the information obtained by the digital calculation, and is superposed and interacted with the optical pulse in the optical fiber loop, which is characterized in that. 【0013】 The optical Ising computing device according to the third aspect of the present invention is preferably configured by using a CW (Continuous Wave) light source instead of the optical pulse light source of the optical Ising computing device according to the first aspect of the present invention. 【0014】 The optical Ising computing devices according to the first and third aspects of the present invention may generate binary branching by combining a lossless circulating loop and the calculation of a non-linear function in the arithmetic circuit without oscillating a pulse in the optical fiber loop. 【0015】 The optical Ising computing device according to the second aspect of the present invention may generate binary branching by combining a lossless circulating loop and the calculation of a non-linear function in the arithmetic circuit without oscillating a pulse 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, it is preferable that the optical fiber loop consists 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 computation. 【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 within 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. 【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 pulses, 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 circulation 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. 【0026】This is a block diagram showing the configurations of conventional (a) DOPO-type CIM and (b) OEO-type CIM. This is a block diagram showing the configuration of an optical Ising computer apparatus according to the first embodiment of the present invention. These are the circuit transmission waveforms of a 10 GHz pulse train for (a) 10,000 km (200 laps), (b) 30,000 km (600 laps), and (c) 50,000 km (1,000 laps) of the optical Ising computer apparatus shown in Figure 2. These are the circuit transmission waveforms (when using synchronous amplitude modulation) of a 10 GHz pulse train 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) of the optical Ising computer apparatus shown in Figure 2. These are graphs showing the rise of spontaneous binary bifurcation in the optical Ising calculator of the first embodiment of the present invention for (a) α = 1.1, β = 0, (b) α = 1.5, β = 0, and (c) α = 2.0, β = 0. These are graphs showing the convergence of cut-off values ​​in (a) K2000 and (b) G22 in the calculation of a 2000 × 2000 Max-cut problem using the optical Ising calculator of the first embodiment of the present invention. These are α-β maps of cut-off values ​​for (a) K2000 (left is the distribution of the maximum value, right is the distribution of the mean value) and (b) G22 (left is the distribution of the maximum value, right is the distribution of the mean value) when the tanh function is used as the nonlinear function in the optical Ising calculator of the first embodiment of the present invention. These are α-β maps of cut-off values ​​for (a) K2000 (left is the distribution of the maximum value, right is the distribution of the mean value) and (b) G22 (left is the distribution of the maximum value, right is the distribution of the mean value) when the step function is used as the nonlinear function in the optical Ising calculator of the second embodiment of the present invention. These are α-β maps of the cut-off values ​​for (a) K2000 (left is the distribution of the maximum value, right is the distribution of the mean value) and (b) G22 (left is the distribution of the maximum value, right is the distribution of the mean value) when a cubic polynomial (Van der Pol type) is used as the nonlinear function in the optical Ising calculator of the third embodiment of the present invention. These are α-β maps of the cut-off values ​​for (a) K2000 (left is the distribution of the maximum value, right is the distribution of the mean value) and (b) G22 (left is the distribution of the maximum value, right is the distribution of the mean value) when a cosine function is used as the nonlinear function in the optical Ising calculator of the fourth embodiment of the present invention.Figures 7-10 show the results, and a table comparing the results of DOPO and Simulated Annealing. (a) A time chart of the optical Ising computer of the fifth embodiment of the present invention, considering the processing delay in the FPGA, when detecting the amplitude of the optical pulse that has propagated through the nth cycle and feeding the feedback signal obtained by the FPGA back to the (n+1)th optical pulse. (b) A time chart of the optical Ising computer of the sixth embodiment of the present invention, considering the processing delay in the FPGA, when detecting the amplitude of the optical pulse that has propagated through the nth cycle and feeding the feedback signal obtained by the FPGA back to the (n+2)th optical pulse. (a) A graph showing the convergence of the cut-off value in the calculation results of the 2000x2000 problem (G22) for the following cases: (a) when there is no processing delay in the FPGA, (b) when there is a processing delay in the FPGA as shown in Figure 12(a) (0.25 ms), and (c) when there is a processing delay in the FPGA as shown in Figure 12(b) (0.5 ms). This is a block diagram showing the configuration of the optical Ising calculator according to the seventh embodiment of the present invention. The calculation results for the 10,000 × 10,000 problem (K10,000) of the optical Ising calculator according to the seventh embodiment of the present invention include (a-1) a graph showing the convergence of the cutoff value and (a-2) a histogram of the maximum cutoff value, as well as the calculation results for the 10,000 × 10,000 problem (K10,000) of the optical Ising calculator according to the first embodiment of the present invention include (b-1) a graph showing the convergence of the cutoff value and (b-2) a histogram of the maximum cutoff value. This is a block diagram showing the configuration of the optical Ising calculator according to the eighth embodiment of the present invention. The calculation results for the 2000 × 2000 (K2000) problem of the optical Ising calculator according to the eighth embodiment of the present invention include (a) a graph showing the cycle dependence of the cutoff value, (b) a graph showing the phase change of the pulse for each cycle, and (c) a graph showing the change in optical power within the loop for each cycle. 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. This is a block diagram showing the configuration of the optical Ising computing device of the ninth embodiment of the present invention.(a) A graph showing the frequency dependence of the cutoff value for the calculation result of the 2000 × 2000 (K2000) problem using the optical Ising calculation device of the ninth embodiment of the present invention, and (b) A graph showing an enlarged view of the rising edge of (a). This is a block diagram showing the configuration of the optical Ising calculation device of the tenth embodiment of the present invention. (a-1) The intensity I of the pulse waveform after propagation of 30,000 km when a 10 ps pulse of light is incident from the outside in a state without feedback (α=0, β=0) using the optical Ising calculation device of the first embodiment of the present invention. 2 +Q 2 , and (b-1) graphs showing amplitudes I and Q, and (a-2) intensity I of the pulse waveform after propagation of 30,000 km when CW light is incident on the optical Ising calculator of the tenth embodiment of the present invention in a feedback-free state (α=0, β=0). 2 +Q 2 (a) A graph showing amplitudes I and Q. A graph showing the rise of the binary branching of (a-1) I component and (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 calculation device of the first embodiment of the present invention, and (b) A graph showing the rise of the binary branching of (a-2) I component and (b-2) Q component when CW light is incident in a feedback state (α=1.5, β=0) of the optical Ising calculation device of the tenth embodiment of the present invention. (a) A graph showing the frequency dependence of the cut-off value of the calculation result of the 2000×2000 (K2000) problem when a 10 ps pulse light is incident from the outside of the optical Ising calculation device of the first embodiment of the present invention, and (b) a graph showing the frequency dependence of the cut-off value of the calculation result of the 2000×2000 (K2000) problem when CW light is incident on the optical Ising calculation device of the tenth embodiment of the present invention. 【0027】 The embodiments of the present invention will be described below based on the drawings and other references. 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 determined by the variable u. n This is equivalent to the problem of finding combinations. 【0028】 【0029】The variable u in Equation (1) m , u n represents the states (+1 or -1) of the m-th and n-th spins (the electric field amplitudes of the optical pulses), and in the present invention, they are the electric field amplitudes of the m-th and n-th optical pulses in the same cycle. J m,n is the interaction coefficient between the spins. IM is a calculation process for finding the combination of u that minimizes the energy function E in Equation (1) when the coupling coefficient J m,n representing its property is given according to the problem to be solved. 【0030】 [Conventional Ising Machine (IM)] 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 are shown in FIG. 1. The conventional DOPO type IM shown in FIG. 1(a) includes a pulse light source 51, an amplitude (AM: Amplitude Modulation) 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 pulsed light is incident via the optical modulator 52, a phase-sensitive optical amplifier (PSA: Phase Sensitive Amplifier, gain g > loss l) 54 excited by an optical pulse wavelength-converted by a wavelength converter 54a provided in the optical fiber loop 53, a homodyne detection circuit 55 for detecting the optical pulse from the optical fiber loop 53, and a matrix operation circuit 56 for performing digital calculation using the amplitude (real part component) of the pulsed light detected by the homodyne detection circuit 55. 【0031】In DOPO, N pulses circulate within an optical fiber ring resonator (optical fiber loop 53), each pulse having equal amplitude and a randomly assigned phase of either 0 or π. DOPO utilizes a phase-sensitive optical amplifier 54, which generates a nonlinear optical effect depending on the phase relationship between the pump light and the signal light, ensuring that the phase of each pulse is either 0 or π. Therefore, DOPO oscillates in a steady state when the interaction Hamiltonian in equation (1) is minimized. In DOPO, pulses are branched from the optical fiber loop 53, and the phases of the N pulses are detected by homodyne detection with the local light source. All pulse amplitudes are either +1 or -1, and their sign can be determined by coherent detection of the electric field. This signal is input to a matrix arithmetic circuit 56. The matrix arithmetic circuit 56 consists of an A / D converter, an FPGA (Field-Programmable Gate Array), and a D / A converter. The FPGA calculates the N amplitudes u of the kth cycle, as expressed in equation (2). m (k) (m = 1 ~ N) and J pre-stored in the FPGA m,n The sum of the products (associative sum) of these is calculated digitally. 【0032】 【0033】 The value of the electrical signal f obtained in this way n (k) calculates the spin interaction. This signal is superimposed on an optical pulse using an LN modulator, and the nth pulse u is circulating through the optical fiber loop 53 of DOPO. n By combining with (k), interaction between any pulses in the optical fiber loop 53 is realized. 【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 around 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 branch. 【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】 【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 to it, and its nonlinearity is not necessarily strong. In this invention, we considered that if we could artificially create a more steep nonlinearity than that of 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 EDFA 4 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 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 We calculate the product with [k] (corresponding to equation (2)) and the nonlinear operation related to equation (8), which includes the operation for binary branching (corresponding to equations (5) and (6)). 【0044】 【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 applies 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 optical pulse of the k+1th loop. As a result, u n [k] and u n+1 The 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 bifurcation machine due to the linear optical fiber loop 3 and the gain of the feedback circuit. 【0046】 【0047】 A key feature of the optical Ising computing apparatus 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, to 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 pulse loop transmission using EDFA, induced spontaneous emission (ASE) noise accumulates with each subsequent loop, gradually degrading the OSNR. 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 within 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 IM 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 EDFA 4 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 EDFA 4 increases, suppressing the decrease in power within the optical fiber loop 3. In this way, the gain saturation of the EDFA 4 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 EDFA 4 is not present in the conventional DOPO and OEO IM 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】 【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 EDFA4 is set to 4 dB, and a 1 nm bandwidth optical filter is inserted at the output of 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】 【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, by using this nonlinear function, it is possible to easily 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 with a maximum of ±1, for example, in the AM optical modulator 52 in Figure 1, the optical field u0 of the maximum magnitude will be 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) take random 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 (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】 【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 Figure 9(a) K2000, the maximum value of 32725 (marked with a circle in the figure) is obtained when (α,β) = (0.7, 0.01), and in Figure 9(b) G22, 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. From these results, the tanh function yields high cutoff values ​​for both the K2000 and G22 problems, and the average values ​​for K2000 and G22 show superior results compared to the DOPO-type IM. The tanh function is difficult to realize in the prior art, and this result demonstrates 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 the nth time can be detected and used to directly feed back the feedback signal obtained by the FPGA circuit to the nth optical pulse. However, if the processing takes a long time, it becomes difficult to feed it back to the nth optical pulse. In the optical Ising computing device of the fifth embodiment of the present invention, taking into account 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 is 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 is fed back to the (n+2)th optical pulse. This time chart is shown in Figure 12(b). 【0070】 The 2000x2000 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 optical Ising computing apparatus of the seventh embodiment 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 fibers, which are shortened ordinary optical fibers. In hollow core fibers and short 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 the hollow core fiber is ideally a vacuum and there are no losses, dispersions, 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 branching 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, as shown in Figure 14, to digitally represent the optical pulse and to describe the propagation of multiple optical pulses in a long optical fiber in software. 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 calculation 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 and causes it to interact. 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 a propagation delay equivalent to the orbit time of the optical fiber loop 3 (in the optical Ising computing apparatus of the first to sixth embodiments of the present invention, the propagation distance is L = 50 km) is calculated by taking the speed of light in the fiber as 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 the 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. In addition, 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 calculation 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 optical pulse supplied from the outside 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 only the Q channel. 【0077】 In this case, the nonlinear function F of the Q channelQ , n [k] is given by equation (13) below. Furthermore, the feedback to the loop is given a phase rotation of π / 2, as shown in equation (14) below. 【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] for feedback, so the instability due to the nonlinear effect appears at phases of 0 and π. 【0079】 In the optical Ising calculator 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. In addition, 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 independently generate a binary branch. 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】 These two are fed back simultaneously, but as shown below, the Q channel must undergo a phase rotation of π / 2 relative to the I channel, as shown in equation (16) below and equation (14) above. In coherent pulse propagation, the nonlinear phase rotation due to the Kerr effect introduces interaction between the I channel and the Q channel. 【0083】 In the optical Ising calculation device 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: 2: Amplitude u of the Q channel Q (Spin x) Q ) defined by: 【0085】 The overall picture of the loop traversal 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 Ｑ A 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 eighth embodiment of the present invention. The dip in the cutoff value that occurred when only the I channel (first embodiment, Figure 6) and only the Q channel (eighth embodiment, Figure 17(a)) were fed back has disappeared in the optical Ising calculation device of the ninth 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 ninth embodiment of the present invention, energy is transferred between the two channels, and the overall power (I 2 +Q2 Since the value 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 of 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 of 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 digital coherent communication system that has already been commercialized. Note that in the optical Ising computer of the seventh to ninth embodiments of the present invention, the pulse light source 1 may also be replaced with the CW (Continuous Wave) light source 11. Repetition frequency f of AM synchronous modulation in the optical fiber loop 3 m If 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 in the case of a CW input, steady 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, the results of comparing the waveform change in the optical fiber loop 3 when a 10 ps pulse light is incident from the outside using the optical Ising computing device of the first embodiment of the present invention, and when CW light is incident using the optical Ising computing device of the tenth embodiment of the present invention, under conditions without feedback (α=0, β=0), 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 14 ps pulses as they circulate and propagate steadily within the optical fiber loop 3, and 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 in 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 functions even 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. 【0090】 As described in detail above, the present invention eliminates the need for an optical oscillator and enables the realization of an optical Ising computation 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 around 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. 【0091】1. Pulsed light source 2. AM optical modulator 2'. Loop-type AM optical modulator 3. Optical fiber loop 4. Erbium-doped optical fiber amplifier (EDFA) 5. Homodyne detection circuit 6. Matrix / nonlinear arithmetic circuit (arithmetic circuit) 6'. Digital memory 7. Synthesizer 8. Optical delay circuit 9. Optical phase shifter 10. IQ optical modulator 11. CW light source 12. Optical filter 51. Pulsed light source 52. (AM) optical modulator 53. Optical fiber loop 54. Phase-sensitive optical amplifier 55. Homodyne detection circuit 56. Matrix arithmetic circuit 57. Photodetector

Claims

1. An optical Ising computing apparatus comprising: 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 that receives the optical pulses from the pulse light source and information obtained from the digital calculations of the arithmetic circuit, modulates the input optical pulses with the information, and then injects them into the optical fiber loop; wherein the optical pulses after circulating in the optical fiber loop are detected by the homodyne detection circuit and input to the arithmetic circuit, the arithmetic circuit digitally calculates the interaction function of the optical pulses and a nonlinear function for binary branching, and then the optical modulator modulates the optical pulses from the pulse light source with the information obtained from the digital calculations and superimposes and interacts with the optical pulses in the optical fiber loop.

2. The system 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 multiple digital optical pulses in a long optical fiber; a digitally represented homodyne detection circuit that detects 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 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 arithmetic circuit, modulates the input digital optical pulses with the information, and then inputs them to the digital memory. An optical Ising computing device characterized by detecting the digital optical pulse from the digital memory with the homodyne detection circuit and inputting it to the arithmetic circuit by digital calculation, after which the arithmetic circuit digitally calculates the interaction function and the nonlinear function for binary branching of the digital optical pulse, and then modulating the digital optical pulse from the pulse light source with the information obtained from the digital calculation in the optical modulator, and superimposing and interacting it with the digital optical pulse from one cycle prior that is in the digital memory before the calculation.

3. The optical system 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 within the optical fiber loop to compensate for losses in the optical fiber loop; an optical filter provided within the optical fiber loop; an in-loop optical modulator operating at a modulation frequency of one integer fraction of the optical delay time within the optical fiber loop; a homodyne detection circuit that detects optical pulses generated from the CW light circulating in the optical fiber loop from the optical fiber loop; an arithmetic circuit that performs digital calculations on the optical pulses detected by the homodyne detection circuit; and an optical modulator into 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. An optical Ising computing apparatus characterized by detecting the optical pulses circulating in the optical file loop with the homodyne detection circuit and inputting them to the calculation circuit, digitally calculating an interaction function and a nonlinear function for binary branching in the calculation circuit, and then modulating the CW light from the CW light source with the information obtained from the digital calculation in the optical modulator, and superimposing and interacting it with the optical pulses in the optical file loop.

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 computing apparatus 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 for modulating 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 computing apparatus 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 Ising computing apparatus according to claim 1, comprising an in-loop optical modulator inserted in the optical fiber loop, wherein amplitude modulation synchronized with the optical pulse is 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.

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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