ANALOGUE PHOTICAL COMPUTING SYSTEM AND METHOD

Abstract

A system includes a coding device configured to code a continuous variable, a coefficient device including a controllable modulation element configured to modulate the coded continuous variable, and a controllable detector configured to detect the coded and modulated continuous variable.

Description

[0001] This application claims the benefit of the preliminary US patent application 63 / 539,979, filed on September 22, 2023, the entire contents of which are incorporated into this document by reference. RIGHTS OF THE GOVERNMENT

[0002] This invention was developed with government support under contract number FA8750-23-C-1001, awarded by the Air Force Research Laboratory (AFRL). The government is granted certain rights to the invention. TECHNICAL AREA

[0003] This revelation generally concerns photonic computing. BACKGROUND

[0004] Computationally expensive problems, such as NP-hard problems, are those that cannot be solved quickly even with fast computers and whose scalability is also poor with an increasing number of problem variables. Examples include supply chain optimization, decryption, routing in communication networks, public transport routing, and the like. Conventional computers with central processing units (CPUs) evaluate solutions sequentially at a rate determined by the CPU's clock cycle and are therefore unsuitable for many NP-hard problems. Many NP-hard problems can be reformulated as Ising problems, which are inherently non-linear and strongly coupled by many-particle interactions.NP-hard problems, formulated as Ising problems, can be factored into a binary representation and solved using optimization algorithms such as quadratic unbounded binary optimization (QUBO). QUBO is isomorphic to, or similar in form to, an Ising model, which might contain an array of interacting binary quantum states. Coprocessors for solving Ising problems, such as quantum annealing (QA), overcome the limitations of CPUs in solving NP-hard problems through massive parallelism enabled by quantum entanglement and the use of simulated annealing. Quantum annealers solve NP-hard problems by mapping them to a QUBO model and then exploiting the symmetry of the QUBO model on the Ising model. Solutions are found by allowing the Ising spins to evolve naturally into a ground state.However, quantum anneals have problems with regard to complex hardware, short decoherence times of quantum states, and poor hardware scalability. SUMMARY

[0005] In general, systems and techniques for computing solutions to NP-hard problems using a QUBO model and an analog encoding of light, which is used as a continuous variable representative of QUBO spin values, are described. For example, an analog computing system for implementing such a QUBO model may include a photonic integrated circuit (PIC) and a spatial light modulator (SLM).The PIC includes a resonator configured to modulate at least one of the amplitude, phase, or polarization of light to encode the light with an analog encoding of the light based on a differentiable function, and the SLM is configured to perform an optical vector matrix multiplication (OVMM) on the encoded light by modulating the amplitude, phase, or polarization of the encoded light according to an NP-hard problem associated with an Ising problem.

[0006] In an example, this disclosure describes a system that includes: a coding device configured to code a continuous variable; a coefficient device comprising a controllable modulation element configured to modulate the coded continuous variable; and a controllable detector configured to detect the coded and modulated continuous variable.

[0007] In another example, this disclosure describes a method that involves encoding, by means of an encoding device, a continuous variable; modulating, by means of a controllable modulation element of a coefficient device, the encoded continuous variable; and detecting, by means of a controllable detector, the encoded and modulated continuous variable.

[0008] In another example, this disclosure describes a system for iteratively solving a quadratic unconstrained optimization (QUO) problem using gradient descent and optical vector matrix multiplication (OVMM), wherein the system includes: a photonic integrated circuit (PIC) configured to encode continuous variables represented as analog voltages onto an array of optical signals; lenses configured to perform the spatial driving of the optical signals exiting the PIC; matrices representing QUO coefficients programmed into a spatial light modulator (SLM); and a detector array configured to compute an output vector from the OVMM, the output vector representing gradients of the continuous variables.and an analog circuit configured to scale the gradients of the continuous variables and add noise.

[0009] The details of one or more examples of the disclosure are set forth in the accompanying drawings and in the following description. Further features, functions, and advantages of the disclosure will become apparent from the description and the drawings, as well as from the claims. BRIEF DESCRIPTION OF THE DRAWINGS Fig. Figure 1 is a block diagram illustrating an exemplary analog photonic computing system according to the techniques of the disclosure. Fig. Figure 2A is a block diagram illustrating an exemplary analog photonic computing system according to the techniques of the disclosure. Fig. Figure 2B is a block diagram illustrating an exemplary operational sequence of an analog photonic computing system according to the techniques of the revelation. Fig. Figure 3 is a schematic representation illustrating a perspective view of another exemplary analog photonic computing system according to the techniques disclosed. Fig. Figure 4 is a schematic representation showing part of the exemplary analog photonic computing system. Fig. 3 illustrated according to the techniques of revelation. Fig. Figure 5 is a flowchart of an exemplary procedure for an analog photonic computation according to the techniques disclosed.

[0010] The same reference symbols denote the same elements in the figures and in the description. DETAILED DESCRIPTION

[0011] In general, one or more aspects of this revelation describe systems and procedures for solving computationally difficult problems, such as NP-hard problems. For example, a computationally efficient QUBO-like solver uses a novel approach, such as quadratic unbounded smooth optimization (QUSO), based on optical vector-matrix multiplication and the analog encoding of variables, such as analog versions of binary QUBO spins. Implemented in an analog photonic computing system, the QUSO solver can be configured to encode analog spins (as opposed to binary spins) using analog optical variables and optimizes energy through a hardware implementation of gradient descent.

[0012] In some examples, the systems and methods disclosed in this work involve fast all-to-all spin coupling of a variety of spin variables, e.g., on the order of microseconds or less. In some examples, a system includes an encoding device, which may include a hybrid photonic integrated circuit (PIC) containing resonant structures, such as microdisc modulators, configured to encode analog spin amplitudes in light coupled to the PIC, and a coefficient device, which may include a spatial light modulator (SLM) configured to encode QUSO spins. In some examples, the analog photonic computing system includes a PIC configured to encode analog variables (spins), an SLM for encoding optical interaction weights (e.g.,QUBO weights, which are representative of coefficients that represent the computationally expensive problem that may be programmed into the SLM), and a variety of sensors operating in a high-speed loop to tune parameter values ​​and read out solutions.

[0013] The sensors and techniques described in this paper can be used to solve NP-hard and / or APX-hard problems, such as satisfiability (SAT), MAX-SAT, and MAX-CUT, and can provide computations and / or solutions with reduced overall energy consumption and improved speed, e.g., 17 picojoules (pJ) or less per matrix element at a readout rate of 1 megahertz (MHz) or greater for each matrix multiplication. For example, the disclosed systems and methods can avoid the use of digital logic, such as field-programmable gate arrays (FPGAs), to calculate the interaction energy between all spin states and are instead based on analog elements that require significantly less energy, e.g.,Light propagating through a PIC incorporating resonant modulators and a SLM configured to adjust the amplitude, phase, or polarization of light from the photonic channels in free space, as well as a coherent optical readout via light sensors, is encoded and / or modulated. In some examples, the systems and methods provide scalable all-to-all coupling of all analog variables (e.g., spins). This all-to-all coupling can provide improved accuracy of solvers for computationally difficult problems modeled as QUBO-type problems. In some examples, the systems and methods provide improved computational efficiency, such as improved energy or power used to output a solution. This quantity can include the number of iterations of high-speed loops multiplied by the energy consumed per loop.

[0014] Fig. Figure 1 is a block diagram illustrating an exemplary analog photonic computing system 100 according to the techniques of disclosure. In the example shown, the system 100 includes a light source 102, an encoding device 104, a decomposition device 106, a coefficient device 108, controllable detectors 110, a processing module 112, an analog-to-digital converter (ADC), and a sensor readout 114. The system 100 can be configured to solve computationally difficult problems modeled as QUBO-type problems.

[0015] A QUBO model has a similar form to an Ising model. An Ising model is a mathematical model of ferromagnetism in statistical mechanics, consisting of discrete variables representing the magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or -1). The Ising model energy function is given by equation (1): EIsing=−∑i≠jJijsisj−∑i hisi where J ij an interaction is and h i an externally applied magnetic field. The first term is the energy contribution from the interaction between all spins in the system, and the second term is the self-energy of each spin due to the externally applied magnetic field h. i The QUBO energy function is expressed in a matrix Q, in which each element Q ij the coupling between binary variables q i and q j The canonical form of the QUBO energy equation is equation (2): EQUBO=∑ij Qijqiqj

[0016] The form of the QUBO energy equation (2) is mathematically similar to the Ising model, but it is neither analytical nor differentiable. If the QUBO spin variable q is instead represented by an analytical and differentiable coding function f(q*), where the * indicates that q can take any value between 0 and 1, e.g., f(q*) is an analogous function of the continuous variable q*, then the analytical form of the QUBO energy function can be a differentiable quadratic unbounded smooth optimization (QUSO) with the energy equation (3): EQUSO=∑ij Qijf(qi*)f(qj*)

[0017] For gradient descent, the variable optimization results from equation (4): qt+1=qt−α∇F(qt) where t is an iteration variable. Equation (4) can be obtained by differentiating the QUSO energy equation as dE QUSO / dq ican be simplified to equation (5). qi(tn+1)=qi(tn)−αf'(qj(tn))∑i Qijf(qi(tn))

[0018] In this simplified form of equation (5), the quadratic dependence on spin becomes linear, and the spin encoding f(q) and its derivative 2f'(q) are computed directly in each iteration t (e.g., each time step). Each continuous variable (e.g., the analogue of the QUBO spin value in equation 5) is updated by calculating the difference between the previous continuous variable and the α-scaled gradient of the QUSO energy, which is proportional to the vector-matrix multiplication of the previous continuous variable and the coupling matrix Q. In equations (4) and (5), it is implied that the variable q is a real-valued continuous variable in the interval [0,1] (e.g., the *-notation is omitted hereafter).

[0019] The final form of the energy gradient of equation (5) is proportional to the vector-matrix multiplication (VMM) of the encoded input spins and the coupling matrix. System 100 can be used to encode input spins and perform a VMM of the encoded spins and the coupling matrix, e.g., using optical components.

[0020] In the example shown, the light source 102 is configured to output light to the coding device 104. The light source 102 can be a laser, a light-emitting diode, or any suitable light source. The light source 102 can output ultraviolet light, visible light, infrared light, or light with any suitable wavelength and / or frequency. The light source 102 can be a broadband light source configured to output light encompassing a variety of wavelengths / frequencies, or monochromatic or essentially monochromatic light, such as laser light. In some examples, the light source 102 can output light with random polarization (e.g., unpolarized light), partially polarized light, or polarized light, such as linearly, circularly, or elliptically polarized light.

[0021] The coding device 104 is configured to receive light 120 from the light source 102. For example, the coding device 104 can include a PIC which includes a waveguide, and the light source 102 and the PIC can be arranged such that the light 120 from the light source 102 is coupled to the waveguide of the PIC.

[0022] The coding device 104 can be configured to encode a continuous variable. For example, a property of the light 120 coupled to the coding device 104 can represent a continuous variable. That is, a measurable property of the light 120, such as its amplitude, phase, and / or polarization, can represent a continuous variable. A continuous variable can take on any value or an infinite number of possible values ​​within a range (e.g., from 0 to 1), unlike, for example, a binary variable, which has only two values, or a digital or discrete variable, which has a finite number of possible values ​​within the range. The coding device 104 can be configured to encode the continuous variable, e.g., the property of light 120.For example, the coding device 104 can be configured to modulate the property of light 120, e.g., according to an analog and differentiable function. For example, in equations (3)-(5), the amplitude, phase, and / or polarization of light 120 can be represented by q, and the coding device 104 can be configured to modulate the amplitude, phase, and / or polarization of light 120 according to f(q), where f() is a differentiable function. In some examples, the coding device 104 is configured to encode the continuous variable, e.g., the amplitude, phase, and / or polarization of light 120, using analog encoding.For example, the coding device 104 can include an optoelectronic component, such as a resonator, which is continuously tunable via an analog voltage and / or analog current and can be configured to proportionally change a property of light 120. In some examples, the resonator can include a microdisc modulator. At least a portion of the light 120 coupled to the waveguide of the coding device 104 can be coupled to the resonator, and the resonator can be tuned and / or changed to modulate the amplitude, phase, and / or polarization of the portion of light 120 according to the analog and differentiable function, e.g., to change the property of the portion of light proportionally by a first amount based on the analog and differentiable function.For example, the modulation of the amplitude, phase, and / or polarization of light 120 (the encoding of the continuous variables) by the resonator can also be continuous and lead to one of an infinite number of values ​​within a range of the differentiable function corresponding to the range of the continuous variables. (In this context, the expression "A and / or B" means "at least one of A or B.")

[0023] In some examples, the coding device 104 can include a plurality of waveguides and / or a waveguide that divides into a plurality of waveguides, e.g., N waveguides. Each waveguide of the plurality of waveguides can correspond to an output channel of the coding device 104; e.g., the coding device 104 is configured to output a plurality of light channels to the coefficient device 108. The coding device 104 can include a plurality of modulators (e.g., resonators) corresponding to the plurality of channels; for example, the coding device 104 can include a different modulator that is optically coupled to the waveguide of each channel. The coding device 104 can be configured such that each modulator is independently addressable and / or controllable, e.g., to change the resonance and / or modulation of the light in that channel independently of all other channels.The coding device 104 can be configured such that each channel represents an independent continuous variable and is configured to independently code each of the plurality of independent variables of each channel, e.g. as described above.

[0024] The continuous variables, such as the amplitude, phase, and / or polarization of the light in each channel, can be representative of a parameter (e.g., a spin value) of a quadratic unbounded model (QUO), such as a QUSO model. Decomposition 106 is configured to map a computationally difficult problem to the QUO matrix Q (e.g., QUBO / QUSO). Decomposition 106 can represent any system or process for decomposing the computationally difficult problem into the matrix Q, such as filling Q with values ​​representative of the computationally difficult problem. The values ​​representative of the computationally difficult problem can be the coefficients of the matrix Q.

[0025] The coefficient device 108 can be configured to perform a vector-matrix multiplication on the coded continuous variable, e.g., the coded (or modulated) light 122 from the coding device 104. For example, the coefficient device 108 includes one or more controllable modulation elements configured to modulate one or more coded continuous variables, e.g., to modulate a property of one or more continuous variables in an analog domain. In some examples, the one or more modulation elements of the coefficient device 108 can be representative of a coefficient of the QUO model, e.g., the coefficients of Q.The coefficient device 108 can be configured to modulate the coded continuous variable by modulating the coded property of light by proportionally changing the property of light based on one or more coefficients of the QUO model by a second amount.

[0026] In some examples, the coefficient device 108 can include a spatial light modulator (SLM) configured to modulate the amplitude, phase, and / or polarization of the coded light 122 incident on and propagating through the SLM. For example, the coded light 122 exiting each channel of the coding device 104 can be converted into a vector, e.g., by spatially propagating the coded light 122 in one direction and focusing the coded light 122 over a plurality of modulation elements, e.g., M modulation elements, of the SLM in that direction. The SLM of the coefficient device 108 is then configured to perform an element-wise multiplication of the vector by modulating the amplitude, phase, and / or polarization of the coded light 122 by an amount equal to its matrix Q value.For example, each modulation element of the SLM can correspond to an element of the matrix Q and be configured to exhibit a transmission, e.g., from 0% to 100%, proportional to the value of the corresponding matrix element. The emitted light 124 from the multitude of modulation elements of the SLM can be focused onto controllable detectors 110, and the controllable detectors 110 can be configured to detect, capture, and / or measure the amplitude, phase, and / or polarization of the now encoded and vector matrix-multiplied emitted light 124, e.g., to detect, capture, and / or measure an encoded and modulated continuous variable.In some examples, by focusing the emitted light 124 from the multitude of SLM modulation elements and detecting, capturing and / or measuring the focused amplitude, phase and / or polarization of the emitted light 124, a summation of the vector matrix multiplication, e.g. according to the preceding equations (3) and (5), is provided.

[0027] In the example shown, the system 100 can include the processing module 112, which facilitates a feedback loop. For example, the controllable detectors 110 can measure the output light 124 from the N channels of the coding device 104 and the coefficient device 108, multiplied by the vector matrix, at a first time t. n or during iteration t n detect and the processing module 112 can encode the continuous variable, e.g., of light, at a second time point and / or during a second iteration t n+1, e.g., according to equation (5) above, based on the detected output light 124. In some examples, the processing module 112 may be configured to receive one or more signals 126 from controllable detectors 110, indicating values ​​representative of the summation part of equation (5). For example, controllable detectors 110 may be configured to output signals 126 as an analog electrical signal proportional to the mathematical product of the coded continuous variables and coefficients of the QUO model to the processing module 112 and / or the analog-to-digital converter (ADC) and readout 114. The processing module 112 may further be configured to output signals 128 representing the value of the next iteration of the continuous variable, q. i (t n+1), are representative of equation (5). The processing module 112 can output the signals 128, for example, as voltage and / or current signals, and the coding device 104 can be configured to receive the signals 128, for example, at the modulators of each of the N channels. The signals 128 can cause the resonances of the modulators of the coding device 104 to change so that they correspond to the new value (of the subsequent second time point / subsequent second iteration) of the continuous variable, for example, to encode the new value of the continuous variable. As described above, this encoding can include modulating the light 120 according to the new resonance.

[0028] System 100 outputs one or more signals indicating the values ​​of the continuous variable q and can indicate a partial solution, a solution per iteration, and / or a converged solution. In the example shown, the ADC and readout 114 can be configured to convert the detected / measured amplitude, phase, and / or polarization of the light 124 into digital values ​​130 that are representative of the values ​​of the continuous variable q of the computationally difficult problem. In some examples, the ADC and readout 114 can be configured to output digital values ​​130 of each of the N continuous variables (channels) q at each iteration and / or upon convergence of the gradient descent feedback loop of System 100 to a solution, e.g., a minimized QUSO energy of equation (3), where the q values ​​can stabilize according to the convergence criteria.In some examples, signals output by the sensors 112 can be output from the system 100. In some examples, the system 100 can output digital values ​​140 and / or signals 128 to an external processing module. In some examples, the processing module 112 can include the ADC and readout 114, or be configured to convert the detected / measured amplitude, phase, and / or polarization of the light 124 into digital values ​​130 that are representative of the values ​​of the continuous variable q of the computationally difficult problem.

[0029] The Processing Module 112 can be implemented as software, but in some examples, it can also include any combination of hardware, firmware, and software. The Processing Module 112 can include a processing circuit that executes instructions and a memory in which instructions and / or data are stored. The combination of processing circuit and memory can retrieve, store, and / or execute the instructions and / or data of one or more applications, modules, or software. The processing circuit and memory can also be operatively coupled to one or more other software and / or hardware components, including, but not limited to, one or more of those described in Fig. The components illustrated in Figure 1. The processing module 112 can be implemented in one or more processors, including one or more microprocessors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or any other equivalent integrated or discrete logic circuits, as well as any combination of such components. The term "processor" or "processing circuit" can generally refer to any of the logic circuits mentioned above, alone or in combination with other logic circuits, or to any other equivalent circuit.

[0030] Fig. 2A is a block diagram illustrating an example of an analog photonic computing system, and Fig. 2B is a block diagram that shows an exemplary functional sequence of the computer system. Fig. 2A illustrates this. Fig. 2A and Fig. System 2B is described together below. System 200 can be an example of System 100 described above.

[0031] In the Fig. In the example shown in Figure 2A, spin encoding (e.g., the encoding of a continuous variable) can be represented by the amplitude of light. The laser 202 is configured to output light to the splitter 204. The splitter 204 is configured to divide the input power of the light into N channels. For example, the encoding device 104 may include a splitter 204 configured to divide the light from the light source 202 into N waveguides of the encoding device 104, each channel containing a different variable optical attenuator (VOA) of VOAs 206. The VOAs 206 may be examples of modulators of the encoding device 104, and the VOAs 206 may be configured to initialize the amplitude of the light that is representative of a continuous spin value for each channel.In some examples, the VOAs include 206 fiber-based microelectromechanical (MEMS) devices or a resonator, such as a microdiscresonator, or any suitable means for electrically modulating the transmission of light in each of the N channels. With reference to... Fig. 2B the VOAs 206 can be configured to encode the continuous spin values ​​as optical fields at (252), where the encoding is the modulation of the amplitude of the light by the VOAs 206.

[0032] In the examples shown, each channel can scalarly initialize a spin vector V by converting the light output from each channel of the VOAs 206 (e.g., output from the coding device 104) into M equal sub-elements V. Msubdivided. For example, the N channels of the VOAs 206 can be arranged along a first direction, and a cylindrical lens can focus the light exiting from each of the N channels of the VOAs 206 along a plurality of modulation elements of the SLM 208 in a second direction, which is essentially perpendicular to the first direction.

[0033] In some examples, the light emerging from the VOAs 206 may be linearly polarized, e.g., in the transverse electrical (TE) plane, and an NP-hard problem may be mapped to a QUSO shape (or QUBO shape) and normalized to values ​​between 0 and 1, e.g., by encoding coupling coefficients at (254) as QUSO matrix Q as grayscale transmission values ​​of the SLM 208 and analyzer 210 between a pass (e.g., "1" or essentially 100% transmission) and a block (e.g., "0" or essentially 0% transmission).

[0034] In some examples, the coupling matrix Q can be encoded by shifting the relative phase of the TE mode and the transverse magnetic (TM) mode of the light. The resulting phase shift transforms the initially linear polarization into an elliptical polarization. In some examples, the SLM 208 can perform the encoding with a relative phase delay of up to 10 bits of accuracy across 1200 x 1920 arrays of individual modulation elements. In some examples, the vector V MThe light exiting the VOAs 206 has a linear polarization rotated halfway between the x- and y-axes (e.g., relative to the arrangement of the modulation elements of the SLM 208) to achieve improved sensitivity to phase shifts prior to its impact on the coupling surface of the SLM 208. The SLM 208 can be configured to impart an electrically tunable phase delay to the light propagating through each modulation element of the SLM 208, thereby rotating the polarization of the light as it then propagates through the analyzer 210, which can be a linear polarizer.

[0035] For example, the SLM 208 can be a liquid crystal module (LCM) comprising a two-dimensional array of individually electrically controllable liquid crystal modulation elements between two crossed linear polarizers. In other examples, the SLM 208 can be a microelectromechanical system (MEMS) or device comprising a two-dimensional array of individually electrically controllable modulation elements configured to modulate, change, and / or modify the amplitude, phase, and / or polarization of light. In other examples, the SLM 208 can be any device configured to modulate, change, and / or modify the amplitude, phase, and / or polarization of light over a spatial area. The NK channels corresponding to the VOAs 206 can be arranged as a series along a first direction, and an optic (e.g.,(including a cylindrical lens) can propagate the light along a second direction, which is essentially perpendicular to the first direction, and focus the light along M modulation elements of a slit of the SLM 208. The SLM 208 and the analyzer 210 can determine the encoded spins and coefficients at (256) by performing a vector(V. M Multiply the )-matrix(Q) multiplication for each of the channels by modulating the amplitude of the light via the modulation elements of the SLM 208 and the analyzer 210, e.g. according to Q ij f(q i (t n)) of the preceding equation 5. The vector-matrix multiplication for each channel is summed at (258) by focusing the light exiting the SLM 208 and the analyzer 210 onto the sensors 212, which collect and detect the light propagating through all M modulation elements of the SLM 208 to one of the sensors 212, which add or summe the vector multiplied by the matrix by detecting / measuring the light focused onto the sensor. For example, N sensors 212 may be present, with each sensor detecting and / or measuring the light from each of the N channels after propagation through the SLM 208 and the analyzer 210 and focusing it onto each of the N sensors. The N measurements can then be summed, e.g., by a processing circuit configured to receive measurements from the sensors 212.In some examples, the final readout is performed by projecting the element-wise result of the polarization through a polarization analyzer 210 and summing a total of M times over the N channels to convert the input vector set N x 1 into a set of output gradients 1 × M.

[0036] In some cases, calibration may be necessary because the signal readout is not linear with respect to polarization. For example, the values ​​of the coupling coefficients of the SLM 208's Q-matrix can be pre-compensated to generate the desired output amplitude modulation from the SLM 208 and the analyzer 210. In some examples, other encodings (e.g., more complex encodings) can be achieved by projecting copies of the input pins (e.g., V). M-vectors) on various SLMs 208. For example, the coupling can be carried out by decomposing the QUSO / QUBO matrix Q into a multitude of sparse, positive definite matrices and summing the resulting outputs of each one.

[0037] In some examples, the processing circuit can be configured to add the self-energy term to equation (1) and add noise to the resulting measured values ​​at (260). In some examples, adding noise to the resulting measurements from sensors 212 can provide improved convergence to a global minimum of the QUSO energy function, e.g., the exit criteria for the feedback loop and the specification of a solution to the computationally difficult problem. For example, noise may be required to exit a local minimum of the QUSO energy function in order to arrive at a global minimum of the QUSO energy function.

[0038] In some examples, the processing circuit can receive signals indicating the measurements of sensors 212, add the self-energy term based on the current spin values ​​at (260), add noise at (260), and update the real-valued spin parameters at (264). For example, the processing circuit can update the encoding of the continuous spin values ​​(e.g., light) from the VOAs 206 at a time point after the last measurements by sensors 212 in an iterative feedback loop. In some examples, the processing circuit can apply any required nonlinearity or changes to the nonlinearity at (262), e.g., compensation of the SLM 208 due to its nonlinear polarization response and / or nonlinear readout of sensors 212.

[0039] Fig. Figure 3 is a schematic representation illustrating a perspective view of an exemplary analog photonic computing system 300, and Fig. Figure 4 is a schematic representation showing part of the exemplary analog photonic computing system 300. Fig. 3 illustrated. Fig. 3 and Fig. The four systems are described together below. System 300 can be an example of the systems 100 and / or 200 described above.

[0040] In the examples shown, the system 300 includes the PIC 304, the SLM 308, and the sensors 310A and / or 310B. The PIC 304 can be used for the coding device 104. Fig. 1. be representative and configured to encode a continuous variable, e.g., a quantity representing an analog QUSO spin value, e.g., any value between 0 and 1. In some examples, a property of light, e.g., the amplitude, phase, and / or polarization of the light, can be representative of the continuous variable, and the PIC 304 can be configured to encode the continuous variable by modulating the amplitude, phase, and / or polarization of the light. In the example shown, the light 302 is laser light with a wavelength of 1550 nanometers (nm), and the PIC 304 includes a variety of modulators 324 configured to modulate the amplitude of light 302, e.g., according to a differentiable function f, e.g., equation (5).

[0041] In the example shown, the PIC 304 incorporates the splitter 322. The splitter 322 can comprise a first part 322a, configured to receive light 302, and a second part 322b, configured to couple the received light to a plurality of waveguides, for example, to split the light into a plurality of channels (e.g., N channels), each channel containing a waveguide. Each of the N channels can correspond to one of N continuous variables; for example, the N channels transmit light representing N analog QUSO spin values. The plurality of modulators 324 can each be optically coupled to a respective waveguide of the N channels and configured to modulate the amplitude of the light before the light exits the channel.The modulators 324 can be any optical or optoelectronic component configured to modulate any of the amplitude, phase, and / or polarization of the light. In the example shown, the modulators 324 each comprise a microdisc modulator or a microdiscresonator. Each modulator 324 is configured to be independently electrically controllable; for example, the resonance of each modulator 324 can be controlled by applying a voltage or current signal via electrical contacts 326, thereby controlling the amplitude of light exiting the channel. The PIC 304 can be configured using modulators 324 to encode a continuous variable, such as light, using an analog encoding of a differentiable function. In the example shown, the light from each channel i (where i = 1 to N) can be used for a continuous variable q. ibe representative, and each of the 324 modulators can be configured to represent the continuous variable q i to encode using an analog coding, e.g. by adjusting the resonance of each modulator so that it produces an amplitude of the light coupled to each modulator 324 according to f(q i ) outputs, where f is a continuously differentiable function. In the example shown, the PIC 304 is configured to output the modulated light to the SLM 308, e.g., as coded light.

[0042] The lens 332 can be configured to focus light from each channel of the PIC 304 onto a variety of modulation elements of the SLM 308. For example, the outputs of the N channels of the PIC 304 can be arranged in a row in the x-direction, as shown in Fig. Figure 3 shows that the lens 332 can include a collimating lens and a cylindrical lens, and the lens 332 can be configured to spread the light from the PIC 304 in the y-direction and to focus the light from the PIC 304 onto a variety of modulation elements of the SLM 308. The spread, focused coded light from the PIC 304 can form a vector, V M , represent, where the value of each element j of the vector f(q) i ) is.

[0043] The SLM 308 can be used for the coefficient device 108 from Fig. 1. The SLM 308 can comprise N x M individually addressable modulation elements arranged in an array, with each modulation element configured to have a transmission between 0% and 100%. For example, each modulation element of the SLM 308 is configured to modulate the amplitude, phase, and / or polarization of incident light according to an analog modulation, such as by any grayscale transmission, phase delay, or retardation value. In the example shown, each modulation element of the SLM 308 is configured to modulate the amplitude of the coded light exiting the PIC 304 by controlling the transmission of the modulation element.In some examples, each controllable modulation element of the SLM 308 corresponds to a different coefficient of a QUO model and is configured to modulate a coded continuous variable of the QUO model by an amount equal to the corresponding coefficient.

[0044] In some examples, each modulation element of the SLM 308 is configured to modulate the coded variable using optical vector matrix multiplication (OVMM) by modulating, independently of any of the other modulation elements of the SLM's plurality of modulation elements, at least one of the amplitude, phase, or polarization of the coded light exiting the PIC 304. For example, the transmission values ​​of each modulation element of the SLM 308 may be representative of a coefficient representing a computationally difficult problem, such as after the decomposition of the computationally difficult problem. The M × N modulation elements of the SLM 308 may then be representative of the QUSO matrix Q, and each modulation element of the SLM 308 may modulate the amplitude of the coded light by attenuating a portion of the coded light as it propagates through the modulation element, for example, by...from no attenuation (passage or 100% transmission) to complete attenuation (blocking or 0% transmission). For example, the lens 322 can split the coded light of the nth channel into M values, and each value is multiplied by each of the M modulation elements of the nth column of the SLM 308 due to propagation through each of the M modulation elements.

[0045] The lens 334 can be configured to focus the coded light modulated by each modulation element of the multitude of modulation elements of the SLM 308 onto the sensors 310A or 310B. For example, the lens 334 can be configured to focus the light emerging from each modulation element of each of the N columns of the SLM 308 onto each corresponding N sensor of the N sensors of the sensors 310A or 310B.

[0046] The sensors 310A and / or 310B (collectively “sensors 310”) can be configured to detect and / or measure the amplitude, phase, and / or polarization of the coded light after modulation by the SLM 308. For example, sensor 310A can comprise a two-dimensional CCD pixel array, and sensor 310B can comprise a one-dimensional photodiode array whose pixels are elongated in the opposite direction relative to the array. In some examples, the SLM 308, lens 334, and sensors 310A or 310B are configured to perform the OVMM between Q and f(q) and the summation of equation (5).

[0047] In some examples, the SLM 308, the lens 334, and the sensors 310A or 310B are configured to perform a coherent OVMM. For example, the input vector V MLocal oscillators can be added, and pure phase modulation can be applied to the SLM 308. Phase coherence can then be achieved by controlling the optical path, for example, by optical elements such as lenses, mirrors, prisms, baffles, apertures, and the like, by limiting the output to the main beam of the forward-propagating light. In some examples, the System 300 can be configured to perform OVMM by using a coherent light source (e.g., a laser) instead of an incoherent light source, such as a vertical-cavity-side-emitting laser (VCSEL), to integrate the spin encoder (modulators 324) into the PIC 304.

[0048] The 310 sensors can be used for the 110 detectors. Fig. 1 and / or the sensors 212 from Fig. 2. be representative. In some examples, the sensors 310 can be configured to output one or more signals that are representative of the measured amplitude, phase, or polarization of the modulated and coded light. For example, the sensors 310 can be configured to output signals 342 that are representative of the measured amplitudes. The signals 342 can be electrical voltage and / or amplitude signals, and the modulators 324 can be configured to receive the signals 342 and change the coding based on the received signals. For example, modulators 324 can be configured to change the resonance of the modulators 324 based on signals 342 in order to encode light with a second and subsequent coding, e.g., in a feedback loop.In some examples, the PIC 304 can be configured to encode a first encoding of a continuous variable at a first time point (e.g., to encode a property of light), and the modulators 324 (e.g., optoelectronic component) of each channel are configured to encode the property of the light with a second encoding at a second time point after the first time point by proportionally changing the property of the light based on the electrical signal 342 output by a corresponding controllable detector element of the detector array 310.

[0049] In some examples, the system 300 can be configured to impart analog electronic nonlinearity and / or noise to the signals 342. For example, exponentially decaying noise according to equation (6) can be injected into the signals 342 to improve, for example, convergence accuracy. η(t)=ηoexp(−t2 / τ2)

[0050] In some examples, the sensors 310 comprise a detector array comprising a plurality of controllable detector elements configured to output a plurality of analog electrical signals (e.g., signals 126 and / or 342), each controllable detector element being configured to output a corresponding analog electrical signal of the plurality of analog electrical signals proportional to a sum of one or more coded and modulated continuous variables.

[0051] Fig. Figure 5 is a flowchart of an exemplary procedure for an analog photonic calculation according to the techniques disclosed. Although the procedure refers to systems 100, 200 and 300, Fig.As described in sections 1-3, the procedures discussed in this document may involve and / or utilize other systems and procedures in other examples.

[0052] The coding device 104 can encode a continuous variable (502). The continuous variable can be representative of a parameter of a quadratic unconstrained optimization (QUO) model. In some examples, the coding device 104 can encode the continuous variable based on a continuously differentiable function. The coding device 104 can encode the continuous variable by encoding a property of light, e.g., at least one of the amplitude of the light, a phase of the light, or a polarization of the light.

[0053] The coefficient device 108 can modulate the coded continuous variable (504). For example, the SLM 308 can be a coefficient device 108 and can include one or more controllable modulation elements that are representative of one or more coefficients of the QUO model. The SLM 308 can modulate the coded continuous variable by modulating the coded property of light, e.g., by modulating at least one of the coded amplitude of the light, the coded phase of the light, or the coded polarization of the light.

[0054] One or more detectors 110 can detect the coded and modulated continuous variable (506). For example, sensors 310 can be representative of detectors 110, and sensors 310 can detect, capture, and / or measure the coded and modulated property of light emitted from the SLM 308. The sensors 310 can output one or more analog electrical signals 342 that are proportional to the product of the coded continuous variable (e.g., the coded property of light) and one or more coefficients of the QUO model (e.g., one or more of the controllable modulation elements of the SLM 308) and the output signals 342.

[0055] In some examples, the PIC 304 can output coded light from a multitude of channels, e.g., N channels, where the coded light is representative of an analog coded continuous variable, and the SLM 308 can modulate at least one of the amplitude, phase, or polarization of the coded light output by the PIC 304. In some examples, the procedure involves decomposing a computationally difficult problem into a set of coefficients, and the coefficients are represented by a transmission value of each element of the multitude of modulation elements of the SLM 308, e.g., for modulating the amplitude of the coded light.In some examples, the SLM 308 can modulate the coded light using OVMM, independently of any of the other modulation elements of the SLM's plurality of modulation elements, which modulate at least one of the amplitude, phase, or polarization of the coded light exiting the PIC 304.

[0056] In some examples, the System 300 can operate in an iterative feedback loop configured to converge towards a convergence criterion, such as a local or global minimum of the QUSO energy function of equation (3), a stability criterion of the amplitudes measured by the sensors 310, or any suitable convergence criterion. For example, the System 300 can include a system for iteratively solving a quadratic unconstrained optimization (QUO) problem using gradient descent and optical vector matrix multiplication (OVMM). The System 300 can include a PIC 304 configured to encode continuous variables represented as analog voltages onto an array of optical signals, and lenses 332 configured to perform the spatial driving of the optical signals exiting the PIC 304 (e.g.,The system 300 includes spatial control of the optical signals from the multitude of channels of the PIC 304), and matrices (e.g., Q) representing QUO coefficients programmed into the SL 308 (e.g., programmed into the modulation elements of the SLM 308). The system 300 can include a detector array (e.g., sensors 310) configured to compute an output vector (e.g., signals 342) from the OVMM (e.g., a vector of detected, acquired, and / or measured coded and modulated properties of light from each of the detectors of the detector array as one or more signals 342). The output vector can represent gradients of the continuous variable, e.g., of the QUO model. The system 300 may include an analog circuit configured to scale the gradients of the continuous variables and add noise, and in some examples apply and / or add nonlinearities to signals 342.

[0057] The following examples can illustrate one or more aspects of the revelation:

[0058] Example 1: System comprising: a coding device configured to code a continuous variable; a coefficient device comprising a controllable modulation element configured to modulate the coded continuous variable; and a controllable detector configured to detect the coded and modulated continuous variable.

[0059] Example 2: System according to Example 1, wherein the continuous variable is representative of a parameter of a quadratic unconstrained optimization (QUO) model; and wherein the controllable modulation element is representative of a coefficient of the QUO model.

[0060] Example 3: System according to Example 2, wherein the coding device is configured to encode the continuous variable using an analog encoding, wherein the coefficient device is configured to modulate a property of the encoded continuous variable in an analog domain, and wherein the controllable detector is configured to output an analog electrical signal proportional to a mathematical product of the encoded continuous variable and the coefficient of the QUO model.

[0061] Example 4: System according to Example 3, wherein a property of light is representative of the continuous variable, wherein the property of light includes at least one of an amplitude of the light, a phase of the light, or a polarization of the light, and wherein the coding device is configured to encode the continuous variable by proportionally changing the property of the light by a first amount, and wherein the coefficient device is configured to modulate the encoded continuous variable by modulating the encoded property of light by proportionally changing the property of the light based on the coefficient of the QUO model by a second amount.

[0062] Example 5: System according to Example 4, wherein the coding device includes a photonic integrated circuit (PIC) which includes an optoelectronic component configured to change the property of the light proportionally.

[0063] Example 6: System according to Example 5, wherein the optoelectronic component includes a resonator which includes a microdisc modulator.

[0064] Example 7: System according to any of Examples 4 to 6, wherein the encoding device is configured to encode a plurality of continuous variables, wherein the coefficient device comprises a plurality of controllable modulation elements, each controllable modulation element of the plurality of controllable modulation elements corresponding to a different coefficient of the QUO model and configured to modulate one encoded continuous variable of the plurality of encoded continuous variables by an amount corresponding to the corresponding coefficient, and wherein the detector comprises a detector array comprising a plurality of controllable detector elements configured to output a plurality of analog electrical signals, each controllable detector element configured to output a corresponding analog electrical signal of the plurality of analog electrical signals.that is proportional to a sum of one or more coded and modulated continuous variables.

[0065] Example 8: System according to Example 7, wherein a property of light is representative of each continuous variable of the plurality of continuous variables, wherein the property of light includes at least one of an amplitude of the light, a phase of the light, or a polarization of the light, wherein the coding device includes a splitter configured to couple the light into a plurality of channels of the coding device, wherein each channel corresponds to a continuous variable of the plurality of continuous variables, wherein each channel of the plurality of channels includes an optoelectronic component including a resonator configured to encode the continuous variable by proportionally changing the property of the light within the channel.

[0066] Example 9: System according to Example 8, further comprising a first cylindrical lens configured to focus the light exiting the coding device onto the plurality of controllable modulation elements of the coefficient device, wherein each controllable modulation element of the plurality of controllable modulation elements of the coefficient device is configured to modulate the coded continuous variable by modulating, independently of each of the other controllable modulation elements of the plurality of controllable modulation elements of the coefficient device, the coded properties of light exiting the coding device.

[0067] Example 10: System according to Example 9, wherein each controllable detector element of the detector array is configured to detect the modulated and encoded property of light of a corresponding channel of the encoding device, the system further comprising a second lens configured to focus the encoded and modulated property of light exiting the coefficient device onto the detector array.

[0068] Example 11: System according to Example 10, wherein each controllable detector element of the detector array is configured to output an electrical signal that is representative of the mathematical product of a corresponding coded continuous variable of the plurality of coded continuous variables and at least a part of the plurality of coefficients of the QUO model.

[0069] Example 12: System according to Example 11, wherein the encoding is a first encoding at a first time point, wherein the optoelectronic component of each channel is configured to encode the property of the light with a second encoding at a second time point after the first time point by proportionally changing the property of the light based on the electrical signal output by a corresponding controllable detector element of the detector array.

[0070] Example 13: System according to one of Examples 1 to 12, wherein the coefficient device includes a spatial light modulator (SLM).

[0071] Example 14: System according to one of Examples 1 to 13, wherein the analog coding device is configured to encode the continuous variable based on a continuously differentiable function.

[0072] Example 15: Method comprising encoding, by means of an encoding device, of a continuous variable; modulating, by means of a controllable modulation element of a coefficient device, of the encoded continuous variable; and detecting, by means of a controllable detector, of the encoded and modulated continuous variable.

[0073] Example 16: Procedure according to Example 15, wherein the continuous variable is representative of a parameter of a quadratic unconstrained optimization (QUO) model and wherein the controllable modulation element is representative of a coefficient of the QUO model.

[0074] Example 17: Method according to Example 16, further comprising outputting, through the controllable detector, an analog electrical signal that is proportional to the product of the coded continuous variable and the coefficient of the QUO model.

[0075] Example 18: Procedure according to Example 17, wherein coding the continuous variable involves coding the continuous variable based on a continuously differentiable function.

[0076] Example 19: Method according to Example 18, wherein encoding the continuous variable involves encoding a property of a light, wherein the property of light includes at least one of an amplitude of the light, a phase of the light or a polarization of the light, and wherein modulating the encoded continuous variable involves modulating the encoded property of the light.

[0077] Example 20: System for iteratively solving a quadratic unconstrained optimization (QUO) problem using gradient descent and optical vector matrix multiplication (OVMM), wherein the system includes: a photonic integrated circuit (PIC) configured to encode continuous variables represented as analog voltages onto an array of optical signals; lenses configured to perform the spatial driving of the optical signals exiting the PIC; matrices representing QUO coefficients programmed into a spatial light modulator (SLM); a detector array configured to compute an output vector from the OVMM, the output vector representing gradients of the continuous variables; and an analog circuit configured to scale the gradients of the continuous variables and add noise.

[0078] The techniques described in this disclosure may be implemented, at least in part, in hardware, software, firmware, or any combination thereof. For example, various aspects of the techniques may be implemented in one or more microprocessors, DSPs, ASICs, FPGAs, or any other equivalent integrated or discrete QRS logic circuits, as well as in any combination of such components implemented in external devices. The terms "processor" and "processing circuit" may generally refer to any of the logic circuits mentioned above, alone or in combination with other logic circuits, or to any other equivalent circuit, alone or in combination with other digital or analog circuits.

[0079] In aspects implemented in software, at least some of the functions attributed to the systems and devices described in this disclosure may be executed as instructions on a computer-readable storage medium, such as RAM, DRAM, SRAM, magnetic disks, optical media, flash memory, or EPROM / EEPROM forms. The instructions may be executed to support one or more aspects of the functions described in this disclosure.

[0080] Furthermore, the functions described in this document can, in some respects, be provided in dedicated hardware and / or software modules. The representation of various features as modules or units is intended to highlight different functional aspects and does not necessarily mean that such modules or units must be implemented by separate hardware or software components. Rather, the functions assigned to one or more modules or units can be executed by separate hardware or software components or integrated into common or separate hardware or software components. Moreover, the techniques can be fully implemented in one or more circuits or logic elements. QUOTES INCLUDED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited patent literature

[0000] US 63 / 539,979

[0001]

Claims

[1] System, encompassing: a coding device configured to encode a continuous variable; a coefficient device comprising a controllable modulation element configured to modulate the coded continuous variable; and a controllable detector configured to detect the coded and modulated continuous variable. [2] System according to claim 1, wherein the continuous variable is representative of a parameter of a quadratic unconstrained optimization (QUO) model; and wherein the controllable modulation element is representative of a coefficient of the QUO model. [3] System according to claim 2, wherein the coding device is configured to encode the continuous variable using an analog encoding, wherein the coefficient device is configured to modulate a property of the coded continuous variable in an analog domain, and wherein the controllable detector is configured to output an analog electrical signal that is proportional to a mathematical product of the coded continuous variable and the coefficient of the QUO model. [4] System according to claim 3, wherein a property of light is representative of the continuous variable, wherein the property of light includes at least one of an amplitude of the light, a phase of the light or a polarization of the light, and wherein the coding device is configured to encode the continuous variable by proportionally changing the property of the light by a first amount, and wherein the coefficient device is configured to modulate the coded continuous variable by modulating the coded property of light by proportionally changing the property of light based on the coefficient of the QUO model by a second amount. [5] System according to claim 4, wherein the coding device comprises a photonic integrated circuit (PIC) comprising an optoelectronic component configured to change the property of the light proportionally. [6] System according to claim 5, wherein the optoelectronic component comprises a resonator comprising a microdisc modulator. [7] System according to claim 4, the coding device is configured to encode a variety of continuous variables, wherein the coefficient device comprises a plurality of controllable modulation elements, each controllable modulation element of the plurality of controllable modulation elements corresponding to a different coefficient of the QUO model and configured to modulate a coded continuous variable of the plurality of coded continuous variables by an amount corresponding to the respective coefficient, and wherein the detector comprises a detector array comprising a plurality of controllable detector elements configured to output a plurality of analog electrical signals, wherein each controllable detector element is configured to output a corresponding analog electrical signal of the plurality of analog electrical signals proportional to a sum of one or more encoded and modulated continuous variables. [8] System according to claim 7, wherein a property of light is representative for each continuous variable of the plurality of continuous variables, wherein the property of light comprises at least one of an amplitude of the light, a phase of the light or a polarization of the light, wherein the coding device comprises a splitter configured to couple the light into a plurality of channels of the coding device, each channel corresponding to one continuous variable of the plurality of continuous variables, wherein each channel of the plurality of channels includes an optoelectronic component which includes a resonator configured to encode the continuous variable by proportionally changing the property of the light within the channel. [9] System according to claim 8, further comprising: a first cylindrical lens configured to focus the light exiting the coding device onto the plurality of controllable modulation elements of the coefficient device, wherein each controllable modulation element of the plurality of controllable modulation elements of the coefficient device is configured to modulate the coded continuous variable by modulating, independently of any of the other controllable modulation elements of the plurality of controllable modulation elements of the coefficient device, the coded properties of light exiting the coding device. [10] System according to claim 9, wherein each controllable detector element of the detector array is configured to detect the modulated and encoded property of light of a corresponding channel of the encoding device, wherein the system further comprises: a second lens configured to focus the coded and modulated property of light exiting the coefficient device onto the detector array. [11] System according to claim 10, wherein each controllable detector element of the detector array is configured to output an electrical signal that is representative of the mathematical product of a corresponding coded continuous variable of the plurality of coded continuous variables and at least a part of the plurality of coefficients of the QUO model. [12] System according to claim 11, wherein the encoding is a first encoding at a first time point in time, wherein the optoelectronic component of each channel is configured to encode the property of the light with a second encoding at a second time point after the first time point by proportionally changing the property of the light based on the electrical signal output by a corresponding controllable detector element of the detector array. [13] System according to claim 1, wherein the coefficient device comprises a spatial light modulator (SLM). [14] System according to claim 1, wherein the analog coding device is configured to encode the continuous variable based on a continuously differentiable function. [15] Procedure, comprehensive: Coding, by means of a coding device, of a continuous variable; Modulation, by means of a controllable modulation element of a coefficient device, of the coded continuous variable; and Detect, by means of a controllable detector, the coded and modulated continuous variable. [16] Method according to claim 15, wherein the continuous variable is representative of a parameter of a quadratic unconstrained optimization (QUO) model and wherein the controllable modulation element is representative of a coefficient of the QUO model. [17] The method of claim 16, further comprising: Output, through the controllable detector, an analog electrical signal that is proportional to the product of the coded continuous variable and the coefficient of the QUO model. [18] Method according to claim 17, wherein the coding of the continuous variable comprises coding the continuous variable based on a continuously differentiable function. [19] Method according to claim 18, wherein the encoding of the continuous variable comprises encoding a property of a light, wherein the property of light comprises at least one of an amplitude of the light, a phase of the light or a polarization of the light, and wherein the modulating of the encoded continuous variable comprises modulating the encoded property of the light. [20] System for iteratively solving a quadratic unconstrained optimization (QUO) problem using gradient descent and optical vector matrix multiplication (OVMM), wherein the system comprises: a photonic integrated circuit (PIC) configured to encode continuous variables represented as analog voltages onto an array of optical signals; Lenses configured to perform spatial control of the optical signals exiting the PIC; Matrices representing QUO coefficients programmed into a spatial light modulator (SLM); a detector array configured to compute an output vector from the OVMM, where the output vector represents gradients of the continuous variables; and an analog circuit configured to scale the gradients of the continuous variables and add noise.

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