Analog computation system and method of performing analog computation

Abstract

The present disclosure provides systems and methods for performing analog computations. In one arrangement, an input data stream includes a plurality of input data units. An analog computation operation is performed on the input data stream to generate an output data stream including output data units. Each output data unit includes a sequence of calculated values corresponding to a sequence of symbols of an input data unit corresponding to the output data unit. An output value corresponding to each output data unit is generated by applying an encoding function to the calculated values to generate an attenuated respective encoded waveform. An output value is generated by sampling a combination of encoded waveforms at a sampling time. The position of the encoded waveform in the sequence represents the importance of the symbol of the corresponding input data unit.

Description

Technical Field

[0001] This disclosure relates to analog computing systems and methods, and more particularly, but not exclusively, to analog computing systems and methods configured to operate and perform computations optically, such as performing linear computation operations optically. Background Technology

[0002] State-of-the-art artificial intelligence (AI) architectures, such as large-scale machine learning (ML), deep learning (DL), and generative pre-trained transformer (GPT) models, contain billions of trainable parameters to enable their complex functions.

[0003] At the time of writing, AI, ML, and DL models are playing a vital role across various sectors of society, from medical diagnostics and drug discovery to financial forecasting, personalized e-commerce, and autonomous transportation. Undoubtedly, the importance and scale of their role will increase rapidly over the next decade. Many existing learning models rely on the processing and evaluation of large matrix operations for training (parameter optimization) and inference (applications in their respective fields). Standard central processing units (CPUs) on electronic computers are not well-suited for certain types of arithmetic operations, particularly those involving large matrix sizes. For example, matrix inversion is a multi-step process involving memory operations of multiplying and rotating the matrix with each element. This is expensive in terms of both time and hardware resources. The multiplication and accumulation processes used in many algorithms can iterate hundreds of times over the same data, further increasing the time complexity of the operation. O(n) This is expensive in terms of read-modify-write operations and the use of multiplication and accumulation logic. When the matrix size exceeds the CPU cache size, data is transferred to much slower, high-capacity memory components, which further limits computational speed. Graphical processing units (GPUs) and tensor processing units (TPUs) are currently the most advanced technologies supporting the AI ​​revolution, designed specifically for highly parallelized processing of large matrix operations. Massive parallel processing is ideal for reducing the training time of large-scale AI networks, such as state-of-the-art transformer models containing billions of parameters. However, as society's reliance on AI increases, computing hardware must continue to evolve to provide even greater computing speed, capacity, and parallelism while reducing pressure on cost and energy resources.

[0004] Analog optical processing offers an alternative approach to information computation and transmission, where data is encoded in optical signals rather than electronic signals. Optical signals inherently offer advantages such as low latency and low transmission loss, and can be naturally combined and segmented using simple optical elements like lenses, mirrors, and beam splitters. Optical computation can also leverage increased degrees of freedom, such as photon wavelength and polarization, and unlock higher bandwidth data transmission. The complexity and dimensionality of first-generation all-optical neural networks (currently emerging) cannot compete with the billions of parameters present in learning models within silica; however, optical processing has already been used to significantly accelerate existing AI models. Free-space optics and photonic component arrays have been developed to perform linear and nonlinear transformations on optical data at high speeds, and promise to further reduce energy consumption per computation.

[0005] The speed and efficiency metrics of an optical processor depend on the optimization of its components, which typically include light sources (diode lasers, LEDs), intensity and / or phase modulators (electro-optic / absorption, thermo-optic, liquid crystal), signal processors (transimpedance amplifiers, digital-to-analog converters (DACs) / analog-to-digital converters). (ADC) and photodetectors. Given that modern electronic platforms are predominantly digital, optical analog signals are typically derived from input digital data. Data relay can be handled by a digital-to-analog converter (DAC) coupled to a light source capable of (e.g., 8-bit) analog intensity modulation; however, this is a slow and expensive combination. A DAC combining GHz modulation with high bit resolution is a bottleneck to system cost. More importantly, the limitation on the selected light source is a significant drawback of this approach, as few light sources are designed for high-speed analog modulation. Even applying external modulation to continuous light sources is challenging and expensive with current off-the-shelf components. Electro-optic based GHz modulators remain expensive (£1-10k), while cheaper alternatives such as electroabsorption modulators and acousto-optic modulators cannot achieve such high bandwidths. Furthermore, the lowest-priced components among these remain difficult to deploy in large numbers, limiting system scalability. Photonic integrated modulators reduce space footprint and promise future scalability, but their mainstream availability remains limited.

[0006] To realize the potential of optical computing, analog processing requires an inexpensive, low-power, and scalable approach.

[0007] In their 2017 paper, "A 40-Gb / s PAM-4 Transmitter Based on a Ring-Resonator Optical DAC in 45-nm SOI CMOS," Moazeni et al. disclosed an optical digital-to-analog (ODAC) converter based on a segmented silicon photonic microring resonator, which directly encodes information from binary electronic signals into incident light signals. High / low voltage levels are applied to 16 pn junctions surrounding the microring segments, providing 4-bit intensity resolution. Essentially, this design requires spatial separation of the incoming binary data stream into adjacent segments. Furthermore, the physical dimensions of the microring and its design rules limit the achievable bit depth.

[0008] Sobu, Y., Tanaka, S., Tanaka, Y., Akiyama, Y., and Hoshida, T. disclosed an alternative ODAC using a binary-driven segmented modulator architecture in their presentation “High-Speed-Operation of Compact All-Silicon Segmented Mach-Zehnder Modulator Integrated with Passive RC Equalizer for Optical DAC Transmitter” at Optical Fiber Communications Conference and Exhibition (OFC) 1-3 (2020). This architecture was demonstrated on a silicon platform using a Mach-Zender modulator (MZM) architecture.

[0009] Despite the challenges and scalability limitations that remain with photonic platforms, silicon-based optical modulators represent a promising solution for integrating photonic processors. Alternative modulator platforms are also gaining relevance, including lithium niobate-on-insulator, barium titanate, and indium phosphide, although accessibility of manufacturing facilities remains relatively problematic.

[0010] Time-coded optical transmitters (ODACs) for converting binary serial data into analog signals have recently been demonstrated. Crucially, these ODACs require wavelength-multiplexed inputs that are intensity-weighted before signal encoding by a high-speed modulator. Amplitude-modulated optical signals are also a focus for researchers seeking to improve data transmission systems. It has been demonstrated that a 6-bit optical signal (64QAM) can be generated at a data transmission rate of 112.8 Gb / s using a single modulator driven by multiple 8-level electrical signals and acting on eight separate wavelength-multiplexed channels. In this scheme, the generation of the 8-level electrical signals effectively employs three separate laser diodes and photodiodes, which is incompatible with reducing system cost, size, and complexity. Similar DAC-less optical transmitters replace these binary optical transmitters with simpler, but parasitic, electronic resistive elements.

[0011] Digital signal transmission involves encoding analog information into discrete digital signals for efficient and reliable communication over various media. Digital optical signals can be directly driven by digital electronic circuits, eliminating the need for power-intensive digital-to-analog or analog-to-digital converters (DACs or ADCs). These digital signals can be modulated most simply using on-off keying (OOK) techniques, which involve switching the amplitude of a carrier signal between two predetermined levels to represent binary data. Alternative modulation techniques such as Pulse Amplitude Modulation (PAM), Pulse Width Modulation (PWM), or Phase Shift Keying (PSK) can be used to transmit optical signals while optimizing some aspects of the process. At the receiving end, demodulation and a DAC / ADC can be used to construct an analog signal from the received digital data.

[0012] Compared to traditional binary OOK, PAM is typically used to achieve higher data rates within the same bandwidth. PAM-4 involves switching the amplitude of the carrier signal between four predefined levels, such that each PAM-4 symbol represents a 2-bit code. Typically, the PAM-N scheme can increase the data rate by up to M times, where M = Log2(N) and N is an integer. PAM is a commonly used technique in high-speed communications where the goal is to maximize data throughput.

[0013] PWM is a special case of pulse density modulation (PDM) used to encode analog information into digital signals by varying the pulse width, while maintaining a constant data rate or pulse frequency. In PWM, the amplitude of the digital signal remains constant. The bit depth of PWM depends on the number of discrete pulse widths that can be formed, and is therefore limited by clock speed at high frequencies. Summary of the Invention

[0014] One object of the present invention is to provide a high-performance simulation computing system that can be implemented at low cost.

[0015] According to one aspect of the present invention, an analog computing system is provided, comprising: an analog computing core configured to receive an input data stream, the input data stream including a plurality of input data units, each input data unit including a sequence of m symbols, where m is an integer, and the analog computing core configured to process the input data stream by performing analog computing operations on the symbols of the input data stream to generate an output data stream, the output data stream including a plurality of output data units corresponding to a plurality of input data units, each output data unit including a sequence of calculated values ​​corresponding to a sequence of m symbols of the input data unit corresponding to the output data unit, each calculated value being processed by performing analog computing operations on the symbols of the input data unit corresponding to the output data unit. The system generates the output data stream by performing analog computation operations on the symbols; and a receiver system configured to receive the output data stream; generate an output value corresponding to each output data unit by the following steps: applying an encoding function to a sequence of calculated values ​​of the output data units to generate a sequence of corresponding encoded waveforms, each encoded waveform decaying over time; and generating the output value by sampling the combination of encoded waveforms at a sampling time, wherein: the analog computation kernel is configured to generate the output data stream such that the encoded waveforms begin at a corresponding time before the sampling time, wherein the position of each encoded waveform in the sequence of encoded waveforms indicates the importance of the corresponding symbol of the corresponding input data unit, and the encoded waveform corresponding to a lower importance symbol is earlier in the sequence than the encoded waveform corresponding to a higher importance symbol.

[0016] There are various advantages associated with performing analog computation rather than digital computation, especially when performing analog computation optically. However, it is still necessary to move digital data in and out of the analog computation core. The generation of time-decayed coded waveforms allows this functionality to be achieved without a DAC (even when using PAM modulation, as it has been shown that PAM modulation can be driven without a DAC), which, as mentioned above, increases system complexity and / or cost. This is especially true when parallel computation is required, where otherwise a separate DAC might be needed for each channel. Therefore, the analog computation system according to this disclosure can provide fast, inexpensive, and / or scalable analog computation. The method of this disclosure is also simpler than alternative techniques for avoiding or reducing the need for a DAC, which may, for example, require splitting the optical signal into different wavelengths and modulating the different wavelengths to encode information. The analog computation system of this disclosure can be implemented without high-resolution light sources, external modulators, wavelength multiplexing, and / or photonic integration.

[0017] In one embodiment, the receiver system includes a low-pass filter configured to apply a coding function. The low-pass filter can be implemented particularly efficiently using inexpensive and / or readily available components.

[0018] In one embodiment, the receiver system includes an RC circuit configured to apply an encoding function, optionally connected to an operational amplifier to provide an active low-pass filter. The RC circuit can be implemented using inexpensive components and can be easily tuned to provide suitable filter characteristics (e.g., time constant τ). The use of an operational amplifier can improve the signal-to-noise ratio and performance, and can also be present in electronics provided throughout the system for other purposes (e.g., for analog-to-digital conversion, ADC), such as built into the ADC pre-amplification stage, thus requiring almost no additional components.

[0019] In one embodiment, the receiver system includes an optical resonator configured to apply a coding function. The optical resonator is optionally configured to have a time-impact response that generates an exponentially decaying coded waveform that encodes a bit depth over time. The optical resonator operates in the optical domain, which can provide inherent advantages over alternative digital methods, such as lower noise. Furthermore, the optical output from the optical resonator has a lower bandwidth than the optical input, thus placing lower requirements on the receiving photodiode compared to when the coding function and sampling are applied to the output from the photodiode.

[0020] In an embodiment, the receiver system includes an optically excitable system configured to generate an coded waveform, optionally an exponentially decaying coded waveform, based on the decay rate of photoexcited electrons from higher to lower energy levels within the optically excitable system. This type of implementation also operates in the optical domain and can achieve similar advantages to optical resonators in this respect, while generally being easier to fabricate. The characteristics of the optically excitable system will be determined by the selection of material and / or doping properties rather than the precise fabrication of the structure. Furthermore, exponential decay can be formally more precise than the exponential decay easily achievable using an optical resonator.

[0021] According to one aspect of the present invention, a method for performing analog computation is provided, comprising: receiving an input data stream including a plurality of input data units, each input data unit including a sequence of m symbols, wherein m is an integer; and processing the input data stream by performing analog computation operations on the symbols of the input data stream to generate an output data stream, the output data stream including a plurality of output data units corresponding to a plurality of input data units, each output data unit including a sequence of calculated values ​​corresponding to a sequence of m symbols of the input data unit corresponding to the output data unit, wherein each calculated value is obtained by performing analog computation operations on the symbols of the input data unit corresponding to the output data unit. The input data unit is generated by performing analog calculations on the corresponding symbols of the input data unit; and the output value corresponding to each output data unit is generated by the following steps: applying an encoding function to a sequence of calculated values ​​of the output data unit to generate a sequence of corresponding encoded waveforms, each encoded waveform decaying over time; and generating the output value by sampling the combination of encoded waveforms at the sampling time, wherein the output data stream causes the encoded waveforms to begin at a corresponding time before the sampling time, wherein the position of each encoded waveform in the sequence of encoded waveforms indicates the importance of the corresponding symbol of the input data unit, and the encoded waveform corresponding to the lower importance symbol is earlier in the sequence than the encoded waveform corresponding to the higher importance symbol. Attached Figure Description

[0022] Embodiments of this disclosure will be further described by way of example only with reference to the accompanying drawings.

[0023] Figure 1 (a) depicts an example architecture for a single-channel analog computing system.

[0024] Figure 1 (b) depicts an example architecture for a multichannel analog computing system.

[0025] Figure 2 A portion of an example digital signal that will be processed by an analog computing system is depicted.

[0026] Figure 3 Depicting Figure 2 An example n-bit representation of the values ​​of a sample of a digital signal.

[0027] Figure 4 Depicting the serialized bit stream Figure 3 The value of .

[0028] Figure 5 An example input processing of a multi-channel implementation of an analog computing core in an analog computing system is described.

[0029] Figure 6 Describing for Figure 5Example output processing of the simulation computing kernel.

[0030] Figure 7 An example is depicted showing the result of applying the exponential bit encoding function to a value calculated for a sample of the bit depth over time.

[0031] Figure 8 It depicts how the contribution to the combined signal derived from the overlapping bit-coded waveform evolves over time.

[0032] Figure 9 The sequence of bit-coded waveforms in two example output data units is depicted, and the corresponding output values ​​are generated by sampling at the corresponding sampling times.

[0033] Figure 10 An example RC circuit (top) and its corresponding impulse response (bottom) are depicted.

[0034] Figure 11 An example RC circuit connected to an operational amplifier is depicted (top figure) and its corresponding impulse response (bottom figure).

[0035] Figure 12 An example of an optical resonator in the form of a Fabry-Perot cavity is depicted.

[0036] Figure 13 An example of an optical resonator in the form of a microring resonator is depicted.

[0037] Figure 14 (a) depicts the optical excitation of a system in which two energy levels can be optically excited.

[0038] Figure 14 (b) depicts the exponential decay of the electron density of photoexcited electrons from the conduction band to the valence band in optically exciteable systems.

[0039] Figure 15 An example optical matrix-vector-multiplication (MVM) system configured to use the analog computing system of this disclosure is described.

[0040] Figure 16 It shows Figure 15 Top and side views of selected components of the MVM system.

[0041] Figure 17 It is a flowchart depicting the framework of the method for performing simulation calculations.

[0042] Figure 18 It is a graph depicting the intensity (vertical axis) of the PAM-2, PAM-4, and PAM-8 representations of the Example 12-bit data stream relative to the time step (horizontal axis).

[0043] Figure 19 and Figure 20 This demonstrates how to process 8-bit integers using encoding functions. Figure 19 Example PAM-4 represents the method for recovering analog data signals ( Figure 20 The curve graph of ).

[0044] Figure 21 Examples of 8-bit integer values ​​represented by PWM-2 and PWM-4 are shown, where PWM-2 has two possible pulse widths, one of which is zero, and PWM-4 has four possible pulse widths. The embodiments of this disclosure described below provide low-cost analog computing capabilities without the use of a DAC. Detailed Implementation

[0045] Figure 1 (a) and Figure 1 (b) depicts example single-channel and multi-channel architectures for an analog computing system 2 according to this disclosure. The examples represent values ​​in binary form, such that each symbol represents only a single bit of data, but this is not required; the method can also be used where multiple values ​​are represented by multiple symbols (each symbol encoding more than one bit of data). System 2 includes a transmitter system 4, an analog computing core 6, and a receiver system 8. For the single-channel example, system 2 is configured to receive a digital input signal consisting of one channel of n-bit data, process the data, and generate a digital output signal consisting of one channel of n-bit data. For the multi-channel example, system 2 is configured to receive a digital input signal consisting of n-bit data from P channels, process the data, and generate a digital output signal consisting of n-bit data from Q channels.

[0046] Figure 2 A portion of an example digital input signal 5, which will be processed by system 2, is depicted. Digital input signal 5 can be m symbolic digital input signals, where m is an integer, optionally greater than 1. For example... Figure 3 As shown, the digital input signal 5 can be represented by a set of samples s1, s2, etc., which represent the value of the digital input signal 5 at the corresponding time point (horizontal axis) (vertical axis). The transmitter system 4 can be configured to receive such a digital input signal 5 and generate an input data stream (which, in the case of each symbol representing a single bit, can be referred to as input bit stream 10) to be input to the analog computing core 6. The transmitter system 4 can, for example, represent the value in binary form and serialize the data to provide... Figure 4An input bitstream 10 in the form shown. Thus, an input data stream (e.g., input bitstream 10) can include multiple input data units 12. Each input data unit 12 includes a sequence of m symbols. If the input data unit 12 is an n-bit data unit 12, then m = n when the input data stream is an input bitstream, otherwise m < n. Each input data unit 12 corresponds to a respective one of the values of samples s1, s2, etc. In the case of a bitstream, each symbol (i.e., bit) can have one of two possible values (e.g., 0 or 1 in the example shown). For example, the value x of each sample can be represented as , where represents the n-bit sequence of the input data unit. In other examples, each symbol can represent multiple bits. Thus, the transmitter can be configured to generate the input data stream by multi-bit symbol coding, optionally by pulse amplitude modulation, pulse width modulation, or pulse density modulation.

[0047] The transmitter system 4 can include a transmitter (e.g., a binary transmitter) configured to generate an input data stream (e.g., an input bitstream) from a received digital input signal 5 and send the input data stream to the analog computing core 6. Depending on the nature of the analog computing core 6, the transmitter can be optical or electronic. Suitable optical transmitters can include LEDs and laser diodes, which can be directly modulated by a binary digital signal or externally modulated by an electro-optic modulator, an acousto-optic modulator, an optical MEMS modulator, etc. Electronic transmitters can operate in different standards in current mode or voltage mode. Further details of example transmitters (e.g., binary transmitters) are given in the sections titled "Optical Transmitters" and "Electronic Transmitters" below.

[0048] Figure 5 and Figure 6 depict an example analog computing system and data streams.

[0049] As Figure 5 shown, a digital input signal 5 is provided, which includes n-bit data for four channels . Three example samples are depicted for each channel. The transmitter system 4 uses symbols in, for example, binary form to represent values and serializes the data to provide an input data stream (e.g., input bitstream 10) that includes a sequence of input data units 12.

[0050] The analog computing core 6 is configured to: process the input data stream (e.g., input bitstream 10) by performing analog computing operations on the symbols (e.g., bits) of the input data stream (e.g., input bitstream 10) to generate an output data stream 20 as depicted in Figure 6 7. For example, the analog computing core 6 can perform a linear calculation Linear computation can include linear mappings of linear subspaces. Linear computation can be performed over n time steps. The bandwidth of the analog computation core 6 should typically be greater than the input data rate to avoid any mixing and crosstalk between adjacent data pulses. Examples of linear computations that can be performed using this architecture include Fourier transform, matrix inversion, matrix convolution, differentiation (including Grad and Laplace operators), and integration. Fourier optics forms a fundamental component of diffractive neural networks, and the Fourier transform has recently been used to improve transformers for natural language processing. The Fourier transform function can be implemented by introducing diffractive elements within the analog computation core 6. Matrix inversion and convolution can be implemented by adding digital optical processing devices.

[0051] The output data stream 20 includes a plurality of output data units 22. Each output data unit 22 corresponds to a plurality of input data units 12 (e.g., there is a one-to-one correspondence between output data units 22 and input data units 12). Each output data unit 22 includes a sequence of calculated values, which corresponds to a sequence of m symbols (e.g., m = n bits in the case of an input bit stream) of the input data unit 12 corresponding to that output data unit 22. Each calculated value is generated by performing an analog computation operation on the corresponding symbol (e.g., bit) of the input data unit 12 corresponding to the output data unit 22.

[0052] Receiver system 8 is configured to receive output data stream 20. Receiver system 8 processes output data stream 20 to generate an output value corresponding to each output data unit 22. Figure 6 In the example shown, receiver system 8 includes a photodetector 28. The photodetector 28 converts light representing the output data stream 20 into an electronic signal. The electronic signal is processed to generate an output value. Figure 6 In the example, the generated output value sequence provides n-bit data from four channels. .like Figures 7 to 9 As depicted, each output value is generated by applying an encoding function (which can be referred to as a bit encoding function if the input data stream is an input bit stream) to the calculated value of the output data unit 22 to generate a corresponding encoded waveform (which can be referred to as a bit encoded waveform 24 if the input data stream is an input bit stream) and sampling the combination of the encoding functions (e.g., bit encoding functions) at sampling time 26. Each encoded waveform (e.g., bit encoded waveform) decays over time, for example, decreasing in amplitude from the earliest temporal portion of the encoded waveform. For example, the values ​​of the encoding functions at sampling time 26 can be summed to provide the corresponding output value.

[0053] Figure 7An example is depicted showing the result of applying an encoding function (e.g., a bit encoding function) to the calculated value U1 in the example. The encoding function (e.g., a bit encoding function) can be configured to generate exponentially decaying encoded waveforms (e.g., bit encoded waveform 24). Each encoded waveform can decay to half its original value over a time period. M The time interval is equal to the position difference of the encoded waveform corresponding to the time-adjacent calculated values ​​of the output data unit, where M is the number of bits of data encoded in each symbol of the input data unit. When the encoded waveform is a bit-coded waveform (M=1), for example, for each time step in the output data stream (e.g., each time step is the time difference between time-adjacent calculated values ​​in the output data stream), each bit-coded waveform can be attenuated to half its original size. This is in... Figure 7 The diagram shows eight time steps 41-48. At time step 41, which is the earliest part of the bit-coded waveform, the bit-coded waveform has an amplitude equal to the calculated value U1, and decreases to half its original value for each subsequent time step 42-48, reaching a minimum value U1 / 2 at time step 48. 7 .

[0054] The analog computing core 6 is configured to generate the output data stream in such a way that the encoded waveforms (e.g., bit-coded waveform 24) begin sequentially at corresponding times before the final sampling time 26 (e.g., for Figure 7 The example shown is at time step 41. The sequence of calculated values ​​can be, for example, a sequence with regular intervals (by...). Figure 9 The sequences 51-57 shown (illustrated) are provided to the receiver system 8. The position of each coded waveform (e.g., a bit-coded waveform) in the sequence indicates the significance of the corresponding symbol (e.g., a bit) of the input data unit 12. Therefore, the difference in the (temporal) position of the coded waveforms indicates the difference in the significance of the corresponding symbol (e.g., a bit) of the input data unit 12. The coded waveform corresponding to the lower significance bit starts earlier and is therefore positioned earlier in the sequence than the coded waveform corresponding to the higher significance bit. Figure 9 This sequence of coded waveforms for two example pulses (labeled "Input Pulse 1" and "Input Pulse 2") is depicted. Each pulse contains a coded waveform corresponding to eight calculated values ​​U1 through U8 of an output data unit. The eight calculated values ​​U1 through U8 are derived by performing analog calculations on eight corresponding symbols (e.g., bits) of the input data unit. The calculated value U1 is derived from the least important symbol (e.g., bit), and the calculated value U8 is derived from the most important symbol. Figure 9As shown, the offset 51 of the encoded waveform corresponding to the calculated value U1 (representing the time interval between the start of the encoded waveform and sampling time 26) is the largest. Therefore, at sampling time 26, the encoded waveform corresponding to the calculated value U1 decays more than any other encoded waveform. The offset 52 of the encoded waveform corresponding to the calculated value U2 is smaller than the offset 51 to take into account the fact that the corresponding symbol (e.g., bit) in the input data unit 12 has higher importance. Therefore, at sampling time 26, the encoded waveform corresponding to the calculated value U2 will decay less than the encoded waveform corresponding to the calculated value U1. The same principle applies to the encoded waveforms corresponding to each of the calculated values ​​U3 to U8, where the corresponding encoded waveforms will gradually decay smaller and smaller at sampling time 26, with the encoded waveform of U8 decaying at all.

[0055] Figure 8 This diagram schematically illustrates how the contribution of the combined signal derived from the overlapping bit-coded waveforms evolves over time for one pulse. The lightest bars in the graph represent the contribution of the bit-coded waveform corresponding to the calculated value U1 (the top row of values ​​at the bottom of the graph). Gradually darkening bars represent the bit-coded waveforms corresponding to the calculated values ​​U2, U3, U4, etc., derived from bits of progressively higher importance (the lower rows of values ​​at the bottom of the graph). In each column of values ​​at the bottom of the graph, it can be seen that the calculated values ​​U1 through U4 contribute proportionally to the importance of the bits from which the calculated values ​​are derived. Each bit-coded waveform decays to half its original value over a period of time, equal to the difference in offset between the bit-coded waveforms corresponding to the temporally adjacent calculated values ​​of the output data units.

[0056] Each output value generated by receiver system 8 by sampling a combination of bit-coded waveforms at a sampling time of 26 can be represented as a vector sum. , where y k These are the calculated values ​​U1, U2, etc. discussed above. As long as the simulation calculation function f( If the linear transformation is linear, then due to the additivity and homogeneity of the linear transformation, it is possible to rewrite each output value as... Thus, System 2 can perform analog calculations using n-bit digital input data without using any digital-to-analog converters (DACs) in System 2. The same principle applies to the case of using symbols representing more than one bit, so that analog calculations using m-symbol digital input data (where each symbol represents more than one bit) can also be performed in System 2 without using any digital-to-analog converters (DACs).

[0057] In the case of multiple input and output channels, the output value generated by the receiver system 8 on multiple channels can be written as Y=F(X), where It uses N-dimensional n-bit input with N transmitter channels. It uses an M-dimensional n-bit output with M receiver channels, and F(·) is an N-dimensional to M-dimensional linear transformation. N and M do not need to be the same. This method is effective in this case because:

[0058] In the final step, only binary inputs are within F(·), and the n outputs are summed and exponentially weighted to produce the final result.

[0059] like Figure 6 As shown, the output value Y generated by sampling at sampling time 26 can be provided as input to the analog-to-digital converter (ADC) 62. The ADC converts the output value Y into a binary bit stream 64, which can then be converted into n-bit digital output data 66 for output.

[0060] like Figure 6 As schematically depicted, in some arrangements, receiver system 8 includes a low-pass filter 60, which is configured to apply an appropriate form of coding function (e.g., a bit coding function).

[0061] In some arrangements, the low-pass filter 60 is implemented using a resistor-capacitor (RC) circuit, which can be implemented using simple circuit components and easily configured to have the desired characteristics (e.g., an appropriate time constant). Figure 10 The image above shows an example configuration. Figure 10 (The figure below) illustrates an example impulse response. The time constant τ of the quantization encoding function is given by τ = RC, where R is the resistance value and C is the capacitance value. In the time domain, the impulse response is exp(-t / RC). Therefore, consecutive input pulses with equal time intervals (Δt) will be attenuated such that the pulse train is multiplied by an exponential encoding function (which may be called the attenuation envelope). In the arrangement of this disclosure, where weighting between adjacent bits requires a 2x difference, Δt can be arranged to satisfy Δt = RC Ln2, which results in the pulse being precisely multiplied by the desired bit weight. For example, for an 8-bit ADC sampling rate of 1 gigasamples / s (i.e., 8 Gb / s), a filter with 50 Ω and 3.6 pF would be suitable. When the receiver system 8 is used in an optical computing system, the photodetector, consisting of a photodiode and a transimpedance amplifier (TIA), will have intrinsic junctions and parasitic capacitances; embodiments of this disclosure can take advantage of this, and only require the addition of resistors to obtain the desired RC constant.

[0062] In some arrangements, an RC circuit can be connected to an operational amplifier. For example, the operational amplifier can be configured as a voltage follower, where the input signal is connected to an inverting input and the output is connected to a non-inverting input. Figure 11 The example configuration is shown in the image above. Figure 11 An example impulse response is shown in the figure below. This operational amplifier-based filter can provide similar advantages to the basic RC circuits discussed above, improving signal-to-noise ratio and / or performance with very low additional cost and components. This functionality can even be built into the ADC pre-amplification stage, thus requiring almost no additional parts.

[0063] In some arrangements, receiver system 8 includes an optical resonator, such as an optical cavity, configured to generate a time impulse response that produces an exponentially decaying coded waveform (e.g., a bit-coded waveform). The optical resonator can provide low-pass filter characteristics similar to an RC circuit. The characteristic frequency response of the transmission intensity of the optical cavity can be represented by an Airy function. Constrained by a small bandwidth relative to the free spectral range (requiring a small cavity length) (requiring high specular reflectivity), this frequency response approximates a Lorentz peak near the center frequency. The corresponding time response curve (Fourier transform) of the transmission intensity I(t) is an exponentially coded function:

[0064] Where c is the speed of light, T is the round-trip loss, and L is the cavity length. By adjusting the parameters T and L, an appropriate time constant can be selected for the desired pulse rate r. Again, taking r = 8 GHz as an example, an optical cavity with T = 0.01 and L = 0.3 mm would be suitable.

[0065] Other suitable optical resonators include microring resonators and microdisk resonators. These microresonators are typically fabricated on photonic integrated circuits and have high Q factors and small mode volumes.

[0066] Figure 12 An example of an optical resonator in the form of a Fabry-Perot (FP) cavity is depicted, which has two parallel mirrors spaced apart by a distance *d*. The two mirrors have high reflectivity, typically greater than 99%, and are aligned such that reflected light from each mirror undergoes constructive interference with light from the other mirror. The output exhibits exponential decay, as shown in the figure above. To obtain a single exponentially decaying ray, the FP cavity must be operated via a “coaxial propagation” method as shown in the figure. Figure 13 Another example of an optical resonator in the form of a ring resonator is depicted. The ring resonator creates a circular path for light to circulate, thereby enhancing optical interactions and enabling applications in photonics and sensing.

[0067] In some arrangements, the receiver system 8 includes an optically excitable system configured to generate an exponentially decaying encoded waveform (e.g., a bit-coded waveform) based on the rate at which photoexcited electrons decay from higher energy levels in the optically excitable system to lower energy levels in the optically excitable system. Electrons within the material can be in an excited state upon absorbing photons. The average time an electron remains in this excited state is called the lifetime (τ), and is a property of the material—the system lifetime is the time required for the total number of excited-state particles to decrease to 1 / e of its original value. The incident light pulse generates a large number of excited-state particles, which decays exponentially with the time constant τ, thus providing a mechanism for realizing the desired form of the encoded function. Absorbent atoms / molecules can be selected to have a suitable natural linewidth. Figure 14 (a) schematically depicts the photoexcitation of a two-level system via a pulse, which results in an electron in the ground state E0 being raised to the excited state E1, provided the pulse energy matches the energy difference between the excited and ground states. The system initially contains excess energy, which needs to be released to return to the ground state. This excess energy can be released by emitting a photon or by transferring it to another system, such as a phonon or another electron. Figure 14 (b) depicts an example case involving molecules where electrons can transition from the valence band to the conduction band upon photoexcitation. In many cases, the energy decay rate follows an exponential decay curve, as shown in curve 80, which depicts the time-varying electron density of photoexcited electrons in the conduction band, where the energy initially decreases rapidly and then plateaus over time.

[0068] Performing optical integration in this way offers a variety of advantages, including the option of coherent operation, the passive nature of the optical components (reduced power consumption and electronic losses), and reduced requirements on the response time of photodiodes.

[0069] The arrangements disclosed herein can be provided as methods. These methods include any of the methods described above that can be provided as functions of a simulation computing system. Therefore, as Figure 17 As shown, a method for performing simulation calculations can be provided.

[0070] The method includes: receiving an input data stream (e.g., input bit stream 10) (step S1). The input data stream (e.g., input bit stream 10) includes a plurality of input data units 12. Each input data unit 12 includes a sequence of m symbols, where m is an integer. The input data units 12 may employ the methods described above, for example, as referenced above. Figure 4 Any form of description.

[0071] The method includes processing the input data stream (e.g., input bit stream 10) by performing analog computation operations on the symbols (e.g., bits) of the input data stream to generate an output data stream 20 (step S2). The output data stream 20 includes a plurality of output data units 22, which correspond to a plurality of input data units 12. The output data units 22 may employ the methods described above, for example, as referenced above. Figure 6 Any form of description. Each output data unit 22 includes a sequence of calculated values, the sequence of calculated values ​​corresponding to a sequence of m symbols of the input data unit 12 corresponding to the output data unit 22. Each calculated value is generated by performing an analog computation operation on the corresponding symbol (e.g., bit) of the input data unit 12 corresponding to the output data unit 22.

[0072] The method includes generating an output value corresponding to each output data unit. The method includes (step S3) applying an encoding function (e.g., a bit encoding function) to the calculated value of the output data unit 22 to generate a corresponding encoded waveform (e.g., bit encoded waveform 24). Each encoded waveform (e.g., bit encoded waveform 24) decays over time.

[0073] Output values ​​are generated by sampling a combination of coded waveforms (e.g., bit-coded waveform 24) at sampling time 26 (step S4). The output data stream causes the coded waveforms (e.g., bit-coded waveform 24) to begin at corresponding times (before sampling time 26) with different offsets relative to sampling time 26. The position of each coded waveform in the sequence of coded waveforms indicates the importance of the corresponding symbol (e.g., bit) of the corresponding input data unit. Therefore, different offsets represent differences in the importance of the symbols (e.g., bits) of the corresponding input data unit 12. The coded waveform corresponding to a lower importance bit begins earlier in the sequence than the coded waveform corresponding to a higher importance bit (i.e., at a time with a larger offset).

[0074] Application Example - Matrix Vector Multiplication (MVM) Figure 15 and Figure 16 An example of an analog computing core 6, which can be used as part of an analog computing system according to this disclosure, is depicted. In the example shown, computing core 6 includes an optical matrix-vector multiplication (MVM) system. Figure 15 It is a perspective view; Figure 16 (The image above) is a top view (showing the selected elements whose functions can be best represented in this view); Figure 16(Bottom view) is a side view (showing the selected components whose functionality is best illustrated in this view). The MVM system can use 1-inch optics and is configured to perform matrix-vector multiplication using a digital micromirror device (DMD) in the optical domain. The optical system can be a free-space optical system. This architecture can be adapted to perform a wider range of analog computational operations than the MVM. Depending on the user's needs, one or more of the optical components can be swapped or removed, and / or additional components can be added. The optical system can also be made more compact or extended by using lenses with shorter or longer focal lengths, respectively. The system's compactness can be increased by using 1 / 2-inch optics and adjusting the image size (e.g., using a beam expander or imaging optics).

[0075] Optical MVM systems can perform optical MVM to control the reflectivity of the incident wavefront by employing a series of optical components, such as cylindrical lenses and dielectric mirrors coupled to a laser, and digital light processing (DLP) devices. Two example types of DLP include: (1) liquid crystal on silicon (LCoS) spatial light modulators (SLMs), and (2) digital micromirror devices (DMDs) based on micro-electromechanical systems (MEMS). Although LCoS-SLMs are widely used in holography and projectors, their low refresh rate and phase flicker limit their application in high-speed optical computing. For applications requiring ultrafast light field manipulation, binary DMDs may be more suitable due to their extremely high refresh rate (tens of kilohertz), accuracy, polarization insensitivity, and high spatial bandwidth product expansion capability. Given the binary nature of DMDs, controlled intensity levels can be achieved using pulse width modulation methods or on / off pixel percentage methods. Furthermore, DMDs are much cheaper.

[0076] The first step in the computation process performed by the illustrated optical MVM system can be termed "bit-time encoding," in which a series of 8-bit pulse trains are encoded in time and subsequently transmitted via a programming interface to a series of transmitters (VCSELs or transceivers, etc.). These pulse trains are then fed into a single-mode fiber assembled in a laser fiber array 71, as shown. Figure 15As shown on the far left. Sequentially, from left to right, the beam waist at the exit of fiber array 71 diverges along the horizontal and vertical directions. The first pair of horizontal cylindrical lenses 72 and 74 act as a 4f imaging system, while a vertical cylindrical lens 73 with an effective focal length of 2f, placed in the Fourier plane, collimates the laser channel, thereby generating an extended Gaussian beam along the vertical axis. Each slender fiber output at the weight matrix plane 75 corresponds to the light input vector. Therefore, n fiber arrays will produce n input vectors.

[0077] A DMD screen, located at 75 on the weight matrix plane, is optionally operated in two states (i.e., on and off) to project the weight matrix. Given the binary nature of the device, the gradation in the weights (0-1) is implemented as follows: the gradation will be proportional to the number of pixels turned on in the occupied region of the input vector. For example, let's assume a single input vector of light (from a single-mode fiber) occupies (m × n) pixels. Full-intensity reflection corresponding to a weight of 1 is achieved by turning on all (m × n) pixels, while zero-intensity reflection corresponding to a weight of 0 is achieved by turning off all (m × n) pixels. Then, any value between 0 and 1 will be achieved by turning on a portion of (m × n) pixels. By dividing (m × n) pixels into ((m / zp) × n) pixels, the single input vector can be further decomposed into multiple entries (z) corresponding to column vectors of size (z × 1), where p is the size of the off-state pixel interval between inputs, to achieve clear separation between each entry of the input light vector. To maximize the input vector array, p is ideally 0.

[0078] Once the weighting matrix is ​​applied, the first step of the multiplication and accumulation operations is performed simultaneously for all columns. The beam is then fed through a second series of cylindrical lenses 76-78, configured in reverse order of the first series of lenses 72-74. A vertical pair of cylindrical lenses 76, 78 performs 4f imaging, while a horizontal cylindrical lens 77 at the Fourier plane performs the second step of the multiplication and accumulation operations—the row summation of all input vectors. This provides a single column vector (zx1) at the output. This vector is then fed to a detection system, such as a photodiode array capable of GHz modulation speeds.

[0079] Therefore, the change of the input vector defined by the fiber array 71 over time is... Figure 15 and 16 The analog computing core 6 illustrated in the example provides the input bitstream. The output vector 79 is from... Figure 15 and Figure 16An example of the corresponding output data stream of the analog computing core 6 is illustrated. This output data stream can be processed by the receiver system 8 according to any arrangement of the present disclosure, thereby enabling the analog computing system without the need for any DAC.

[0080] The detailed example above primarily addresses DAC-less analog data transmission using only a binary modulation scheme with on-off keying (OOK). However, the method disclosed herein can be combined with other signal modulation schemes to perform analog computations. For example, the analog computation core can be configured to receive an input data stream comprising multiple input data units, each of which is not limited to a sequence of single bits in a bit stream, but may include a sequence of symbols, each symbol representing multiple bits. The receiver system should be accordingly adapted to process the output data stream and generate values ​​based on the output data units by applying the appropriate encoding function.

[0081] As an example, the following describes the use of pulse amplitude modulation (PAM) within an analog computing scheme. In the PAM-N digital modulation scheme, M bits of data are encoded across N discrete amplitude levels of the input signal, where M = Log2(N). Figure 18 The diagram shows PAM-2 (binary), PAM-4, and PAM-8 representations of some 12-bit data streams corresponding to the integer value "4019". Higher bit depth PAM representations allow the input data rate to the computing system to be increased up to M times. As with binary input data, the PAM signal can be processed by an encoding function at the receiver to recover the analog output data (see [link to documentation]). Figure 19 Advantageously, multiple signals transmitted over parallel channels with a common PAM format can undergo linear computation, enabling the use of any PAM format for the optical computation kernel concept discussed in this paper.

[0082] In the discussion above, it was pointed out that in the PAM-2 format, an n-bit value can be decomposed into binary components and represented as:

[0083] Where x k It can take the value 0 or 1. This can be generalized to the PAM-N format, where an n-bit value can be represented as:

[0084] Where x k These are integer values ​​from 0 to N-1. Assuming the optical computing kernel performs only linear transformations on the input data, the output data for some general PAM-N input data can be described by the following formula:

[0085] It still enables analog calculations to be performed using digital input data, without the need to include a DAC within the system.

[0086] Implementing the PAM-N digital modulation scheme at the transmitter of the system disclosed herein requires adjusting the waveform coding function at the receiver to correctly scale and sum the received data. This can generally still be achieved by applying an exponential attenuation function to the low-pass filter (LPF) of the received data. For PAM-N modulation, the time constant of the corresponding first-order LPF is described as follows:

[0087] in It is the pulse period of the input data. Figure 19 and Figure 20 The implementation of the LPF function on PAM-4 data is shown, which is used to sample at a certain time after the arrival of the final pulse in the data stream.

[0088] Another implementation of analog computing systems uses pulse width modulation (PWM) format for the input data stream. Figure 21 An example of an 8-bit integer value represented using PWM-2 is shown, with two possible pulse widths, one of which is zero. This is the same as PAM-2 or OOK described previously. A PWM-4 data stream represents an 8-bit value in half the pulse period because each symbol has a bit depth of 2, just like PAM-4. The difference here is that 2-bit encoding occurs within each pulse width of the possible values, which have arbitrary time units from 0 to 3. Finally, the LPF time constant required to encode a PWM-N data stream follows the same dependency on N as PAM-N described above.

[0089] The PWM implemented within the optical computing scheme of this disclosure can have more limitations than PAM. The achievable bit resolution may be limited by the relative size of the maximum pulse width compared to the pulse period. Additionally, compared to the OOK case (such as...) Figure 21 In contrast, a significantly higher clock frequency may be required to generate a small pulse width.

[0090] PWM is a special case example of a more general digital modulation scheme called Pulse Density Modulation (PDM), which is used to encode analog information into digital signals by changing the density or frequency of pulses. Therefore, in some embodiments, our analog computing scheme can also be implemented using a PDM input data stream.

[0091] Further example implementation details Light emitter Transmitters suitable for use in the arrangements of this disclosure (which may be binary transmitters or others) may include a range of transmitters suitable for rapidly converting (serial) electrical signals into optical output signals (e.g., binary optical output signals) via DC modulation or external modulation. It is desirable to optimize the design of these transmitters to minimize power consumption while maximizing system bandwidth without reducing their extinction ratio. Suitable categories of transmitters may include: Light Emitting Diode (LED): an inexpensive and widely available switchable light source; easily driven by any electrical system using MOSFETs (small scale) or dedicated LED driver integrated circuits (large scale).

[0092] Laser diodes: A preferred design coupled into optical fibers, but typically more expensive. They are also compatible with integrated circuit designs, in the form of vertical-cavity surface-emitting lasers. Common types of laser diodes include: ● Edge-emitting laser diodes: These laser diodes emit light perpendicular to the pn junction, producing a narrower output beam. These laser diodes are commonly used in optical communication systems and laser printers.

[0093] ●Vertical-cavity surface-emitting laser diodes (VCSELs): These laser diodes emit light parallel to the pn junction, producing a circular output beam. They are commonly used in computer mice, laser pointers, and fiber optic communication systems.

[0094] ● Distributed feedback (DFB) laser diodes: These laser diodes have a periodic grating structure that provides feedback to the laser cavity, thereby producing a narrow linewidth and a stable output wavelength. They are commonly used in optical communication systems, such as dense wavelength division multiplexing (DWDM) systems.

[0095] ● Quantum cascaded laser diodes: These laser diodes use quantum mechanics to generate laser light, which can be emitted in the mid-infrared range. They are commonly used in gas sensing, spectroscopy, and medical applications.

[0096] ●External cavity laser diodes: These laser diodes are coupled to an external cavity, such as a diffraction grating or a Fabry-Perot cavity, to improve spectral purity and output power. They are typically used in scientific and industrial applications that require high-quality lasers.

[0097] ● Tapered laser diodes: These laser diodes have a tapered shape, allowing laser light to be efficiently coupled into single-mode optical fibers. They are commonly used in fiber optic communication systems and high-power laser applications.

[0098] Solid-state lasers: still more expensive, but capable of higher power applications. With appropriately low optical loss and sensitive detection circuitry, the arrangement of this disclosure should not require such high optical power. Common types of solid-state lasers: ●Nd:YAG Lasers: Neodymium-doped yttrium aluminum garnet (Nd:YAG) lasers are among the most common solid-state lasers. They emit at a wavelength of 1064 nm and are used in a wide range of applications, such as materials processing, laser cutting, and medical surgery.

[0099] ●Er:YAG Lasers: Erbium-doped yttrium aluminum garnet (Er:YAG) lasers emit at a wavelength of 2940 nm and are strongly absorbed by water. They are commonly used in dermatology and dentistry for skin resurfacing and caries preparation.

[0100] ●Titanium sapphire lasers: Titanium sapphire (TiD-doped sapphire) lasers emit light in the visible and near-infrared ranges and have a wide tuning range. They are commonly used in scientific research, such as spectroscopy and microscopy.

[0101] ● Ruby lasers: Ruby lasers were the first practical solid-state lasers, emitting at a wavelength of 694 nm. They are commonly used in scientific research, such as fluorescence spectroscopy.

[0102] ● Aldebaran Lasers: Aldebaran lasers emit at a wavelength of 755 nm and have a wide tuning range. They are commonly used in medical applications such as tattoo removal and hair removal.

[0103] ●Cr:LiSAF Lasers: Chromium-doped lithium strontium aluminum fluoride (Cr:LiSAF) lasers emit at a wavelength of 850 nm and have a wide tuning range. They are commonly used in scientific research, such as nonlinear optics and time-resolved spectroscopy.

[0104] In addition to being directly modulated, these optical emitters can also be externally modulated by modulators such as the following.

[0105] Electro-optic modulators (EOMs) are devices that can modulate the intensity, phase, or polarization of light waves by applying an electric field to a material with electro-optic properties. The most common type of EOM is the Pockels cell, which consists of crystals, typically made of lithium niobate, and exhibits an electro-optic effect. The electro-optic effect refers to the change in the refractive index of a material when an electric field is applied. This change in refractive index can be used to modulate the phase of light waves passing through the material. By applying an alternating electric field to a Pockels cell, the phase of the light can be modulated at the same frequency as the electric field.

[0106] Acousto-optic modulator (AOM): An acousto-optic modulator (AOM) is a device that can modulate the intensity, frequency, or phase of a laser beam using sound waves. The most common type of AOM is a crystal designed to interact with both sound and light waves. The basic working principle of an AOM is as follows: A high-frequency sound wave is introduced into the crystal, causing it to deform and create a grating structure. When a laser beam passes through the crystal, it interacts with the grating structure and is diffracted, resulting in modulation of the beam. The degree of modulation depends on the frequency and amplitude of the sound wave applied to the crystal. By changing the frequency and amplitude of the sound wave, an AOM can be used to modulate the intensity or frequency of a laser beam. Acousto-optic modulators are widely used in optics and photonics due to their ability to quickly and precisely modulate laser beams.

[0107] MEMS-based optical modulators: MEMS (Micro-electromechanical Systems) optical modulators are devices that modulate light using microfabrication techniques. These devices are typically made on silicon substrates and consist of movable parts that can be moved by electrostatic or electromagnetic forces. The most common type of MEMS optical modulator is the MEMS-based Fabry-Perot interferometer (FPI). This device consists of two parallel mirrors separated by a small gap. By changing the distance between the mirrors, the interference pattern of the light reflected from the mirrors changes, resulting in modulation of the light. The movement of the movable mirrors is controlled by electrostatic or electromagnetic forces. An electrostatic force is generated by applying a voltage to electrodes located near the movable mirror, causing the mirror to move. Alternatively, an electromagnetic force can be used to move the mirror by applying a current to a coil located near the mirror. They offer advantages over other types of modulators, such as high speed, low power consumption, and compact size.

[0108] Some of these transmitters are already included in optical transceivers widely used in fiber optic communications. Therefore, these optical transceivers can be directly used for optical computing according to the arrangement of this disclosure.

[0109] When these transmitters are used for simulation calculations, the following practical issues should be considered.

[0110] Extinction Ratio – Optical emitters have an ultimate extinction ratio, meaning that under operating conditions, they cannot be completely turned off with a “0” input. This adds background to the simulation results. To mitigate this, an n-bit zero-bit stream can be sent to the system after the n-bit signal bit stream, and the background acquired during the zero-bit stream time window can be subtracted in post-processing.

[0111] Power stability – During the calculation process, the signal power needs to be stable and maintained at a level of at least n bits of accuracy.

[0112] Electron transmitter There are many different types of electronic transmitters. Almost all electronic transmitters are compatible with the proposed method, provided the signal can pass through a suitable low-pass filter. Any current-mode signaling scheme, such as Current-Mode Logic (CML) or Low Voltage Differential Signaling (LVDS), needs to be converted to voltage-mode signals for filtering, but this is a common conversion in electronics. The outputs of most modern devices, including Transistor Logic (TTL) and Complementary Metal Oxide Semiconductor (CMOS) type outputs, can be directly coupled to RC filter circuits. This includes TTL, Low Voltage Complementary Metal Oxide Semiconductor (LVCMOS), Positive Emitter Coupled Logic (PECL), and many other digital I / O standards.

[0113] A high-drive-strength line driver is also acceptable for this application, and a higher-power input signal will be provided if more attenuated bits need to be resolved after the filter.

[0114] The following numbered sub-items define embodiments of this disclosure.

[0115] 1. A simulation computing system, comprising: The simulation computing core is configured as follows: Receive an input bit stream, the input bit stream comprising multiple input data units, each input data unit comprising a sequence of n bits, where n is an integer, and The input bitstream is processed by performing analog computation operations on its bits to generate an output data stream, which includes a plurality of output data units corresponding to a plurality of input data units. Each output data unit includes a sequence of calculated values, which corresponds to an n-bit sequence of the input data unit corresponding to the output data unit. Each calculated value is generated by performing an analog computation operation on the corresponding bit of the input data unit corresponding to the output data unit. Receiver system, the receiver system being configured to: Receive the output data stream; The output value corresponding to each output data unit is generated through the following steps: The bit encoding function is applied to the sequence of calculated values ​​of the output data unit to generate a sequence of corresponding bit-encoded waveforms, each bit-encoded waveform decaying over time; and The output value is generated by sampling the combination of the bit-coded waveforms at the sampling time, wherein: The simulation core is configured to generate an output data stream such that the bit-coded waveforms begin at a corresponding time before the sampling time, wherein the position of each bit-coded waveform in the sequence of bit-coded waveforms indicates the importance of the corresponding bit of the corresponding input data unit, and the bit-coded waveform corresponding to the lower importance bit is earlier in the sequence than the bit-coded waveform corresponding to the higher importance bit.

[0116] 2. The system according to sub-item 1, wherein the bit encoding function is configured to generate an exponentially decaying bit-encoded waveform.

[0117] 3. The system according to sub-item 1 or 2, wherein each bit-coded waveform decays to half its original value over a time period, said time period being equal to the position difference of the bit-coded waveform corresponding to the calculated value that is temporally adjacent to the output data unit.

[0118] 4. The system according to any of the preceding sub-items, wherein sampling the combination of the bit-coded waveforms at the sampling time comprises: summing the values ​​of the bit-coded waveforms at the sampling time.

[0119] 5. The system according to any of the preceding sub-items, wherein the receiver system includes a low-pass filter configured to apply the bit encoding function.

[0120] 6. The system according to any of the preceding sub-items, wherein the receiver system includes an RC circuit configured to apply the bit encoding function, the RC circuit being optionally connected to an operational amplifier to provide an active low-pass filter.

[0121] 7. The system according to any of the preceding sub-items, wherein the receiver system includes an optical resonator configured to apply the bit encoding function, the optical resonator optionally being configured to have a time impulse response that generates an exponentially decaying bit-coded waveform.

[0122] 8. The system according to any of the preceding sub-items, wherein the receiver system includes an optically excitable system configured to generate a bit-coded waveform based on the decay rate of photoexcited electrons from a higher energy level in the optically excitable system to a lower energy level in the optically excitable system, optionally generating an exponentially decaying bit-coded waveform.

[0123] 9. The system according to any of the preceding sub-items, wherein the simulation calculation operation is a linear calculation.

[0124] 10. The system according to any of the preceding sub-items, wherein the system is configured to perform the analog calculation operation optically.

[0125] 11. The system according to sub-item 10, wherein the receiver system includes a photodetector configured to convert light representing the output data stream or the generated output value into an electronic signal, optionally the photodetector being a photodiode.

[0126] 12. The system according to any of the preceding sub-items further includes a transmitter system comprising a binary transmitter configured to generate the input bit stream from the received digital input signal and send the input bit stream to the analog computing core, the binary transmitter optionally being an optical binary transmitter configured to generate binary optical output or an electronic binary transmitter configured to generate electronic output.

[0127] 13. The system according to any of the preceding sub-items further includes an analog-to-digital converter (ADC) configured to convert the output value generated by the receiver system into a digital output signal.

[0128] 14. The system according to any of the preceding sub-items, wherein the system is configured to operate in a multi-channel mode, The analog computing core is configured to receive and process multiple input bit streams corresponding to multiple corresponding channels in parallel, and generate multiple corresponding output data streams; and The receiver system is configured to generate the output value for each channel.

[0129] 15. A method for performing simulation calculations, comprising: Receive an input bit stream, the input bit stream comprising multiple input data units, each input data unit comprising a sequence of n bits, where n is an integer, and The input bitstream is processed to generate an output data stream by performing analog computation operations on its bits. The output data stream includes a plurality of output data units corresponding to a plurality of input data units. Each output data unit includes a sequence of calculated values ​​corresponding to a sequence of n bits of the input data unit corresponding to the output data unit. Each calculated value is generated by performing an analog computation operation on the corresponding bit of the input data unit corresponding to the output data unit. The output value corresponding to each output data unit is generated through the following steps: The bit encoding function is applied to the sequence of calculated values ​​of the output data unit to generate a sequence of corresponding bit-encoded waveforms, each bit-encoded waveform decaying over time; and The output value is generated by sampling the combination of the bit-coded waveforms at the sampling time, wherein... The output data stream causes the bit-coded waveforms to begin at a corresponding time before the sampling time, wherein the position of each bit-coded waveform in the sequence of bit-coded waveforms indicates the importance of the corresponding bit of the corresponding input data unit, and the bit-coded waveform corresponding to the lower importance bit is earlier in the sequence than the bit-coded waveform corresponding to the higher importance bit.

Claims

1. A simulation computing system, comprising: The simulation computing core is configured as follows: Receive an input data stream, the input data stream comprising multiple input data units, each input data unit comprising a sequence of m symbols, where m is an integer, and The input data stream is processed by performing analog computation operations on the symbols of the input data stream to generate an output data stream. The output data stream includes a plurality of output data units corresponding to a plurality of input data units. Each output data unit includes a sequence of calculated values, which corresponds to a sequence of m symbols of the input data unit corresponding to that output data unit. Each calculated value is generated by performing an analog computation operation on the corresponding symbol of the input data unit corresponding to the output data unit. Receiver system, the receiver system being configured to: Receive the output data stream; The output value corresponding to each output data unit is generated through the following steps: The encoding function is applied to the sequence of calculated values ​​of the output data unit to generate a sequence of corresponding encoded waveforms, each of which decays over time; and The output value is generated by sampling the combination of the coded waveforms at the sampling time, wherein: The simulation core is configured to generate the output data stream such that the encoded waveforms begin at a corresponding time prior to the sampling time, wherein the position of each encoded waveform in the sequence of encoded waveforms indicates the importance of the corresponding symbol of the corresponding input data unit, and the encoded waveforms corresponding to lower importance symbols are earlier in the sequence than the encoded waveforms corresponding to higher importance symbols.

2. The system according to claim 1, wherein, The encoding function is configured to generate an exponentially decaying encoded waveform.

3. The system according to claim 1 or 2, wherein, Each coded waveform decays to half its original value over a period of time. M The time interval is equal to the position difference of the encoded waveform corresponding to the time adjacent calculated value of the output data unit, where M is the number of bits of data encoded in each symbol of the input data unit.

4. The system according to claim 3, wherein, M=1, causing each coded waveform to decay to half its original value within a time period, where the time period is equal to the position difference of the coded waveform corresponding to the calculated value that is temporally adjacent to the output data unit.

5. The system according to any one of the preceding claims, wherein, Sampling the combination of the encoded waveforms at the sampling time includes summing the values ​​of the encoded waveforms at the sampling time.

6. The system according to any one of the preceding claims, wherein, The receiver system includes a low-pass filter configured to apply the coding function.

7. The system according to any one of the preceding claims, wherein, The receiver system includes an RC circuit configured to apply the encoding function, and the RC circuit is optionally connected to an operational amplifier to provide an active low-pass filter.

8. The system according to any one of the preceding claims, wherein, The receiver system includes an optical resonator configured to apply the coding function, and optionally configured to have a time impulse response that generates an exponentially decaying coded waveform.

9. The system according to any one of the preceding claims, wherein, The receiver system includes an optically excitable system configured to generate an coded waveform based on the decay rate of photoexcited electrons from a higher energy level to a lower energy level in the optically excitable system, optionally generating an exponentially decaying coded waveform.

10. The system according to any one of the preceding claims, wherein, The simulation calculation operation is a linear calculation.

11. The system according to any one of the preceding claims, wherein, The system is configured to perform the simulation calculations optically.

12. The system according to claim 11, wherein, The receiver system includes a photodetector configured to convert light representing the output data stream or the generated output value into an electronic signal; optionally, the photodetector is a photodiode.

13. The system according to any one of the preceding claims further includes a transmitter system, the transmitter system including a transmitter configured to generate the input data stream from the received digital input signal and send the input data stream to the analog computing core, the transmitter optionally being an optical transmitter configured to generate optical output or an electronic transmitter configured to generate electronic output.

14. The system according to claim 13, wherein, The transmitter is configured to generate the input data stream by means of multi-bit symbol encoding, or optionally by means of pulse amplitude modulation, pulse width modulation, or pulse density modulation.

15. The system according to any one of the preceding claims further includes an analog-to-digital converter (ADC) configured to convert the output value generated by the receiver system into a digital output signal.

16. The system according to any one of the preceding claims, wherein the system is configured to operate in a multi-channel mode. The simulation core is configured to: receive and process multiple input data streams corresponding to multiple corresponding channels in parallel, and generate multiple corresponding output data streams; and The receiver system is configured to generate the output value for each channel.

17. A method for performing simulation calculations, comprising: Receive an input data stream, the input data stream comprising multiple input data units, each input data unit comprising a sequence of m symbols, where m is an integer, and The input data stream is processed by performing analog computation operations on the symbols of the input data stream to generate an output data stream. The output data stream includes a plurality of output data units corresponding to a plurality of input data units. Each output data unit includes a sequence of calculated values, which corresponds to a sequence of m symbols of the input data unit corresponding to that output data unit. Each calculated value is generated by performing an analog computation operation on the corresponding symbol of the input data unit corresponding to the output data unit. The output value corresponding to each output data unit is generated through the following steps: The encoding function is applied to the sequence of calculated values ​​of the output data unit to generate a sequence of corresponding encoded waveforms, each of which decays over time; and The output value is generated by sampling the combination of the coded waveforms at the sampling time, wherein, The output data stream causes the coded waveforms to begin at a corresponding time before the sampling time, wherein the position of each coded waveform in the sequence of coded waveforms indicates the importance of the corresponding symbol of the corresponding input data unit, and the coded waveforms corresponding to lower importance symbols are earlier in the sequence than the coded waveforms corresponding to higher importance symbols.

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