Apparatus for tensorizing an integrated coherent ising machine
By using tensorized integrated coherent Ising machines and leveraging multi-wavelength Ising node sets and tensorized optical coupling matrices, the problem of limited scalability of Ising machines is solved, enabling more efficient and lower-cost solutions to NP-hard problems.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HEWLETT PACKARD ENTERPRISE DEV LP
- Filing Date
- 2024-04-19
- Publication Date
- 2026-07-14
AI Technical Summary
Existing Ising machines have limited scalability when dealing with complex NP-hard problems. Traditional quantum annealing-based Ising machines struggle to handle more complex problems without increasing space and cost. While integrated coherent Ising machines offer greater scalability, further improvements are still needed.
A tensor-quantized integrated coherent Ising machine is adopted. By utilizing a multi-wavelength Ising node set and a tensor-quantized optical coupling matrix, multi-wavelength photonic tensor strings are cascaded through passive optical cross-connection. The tensor string decomposition algorithm is implemented to reduce hardware and space occupation, forming an Ising machine feedback loop.
With less hardware and a smaller footprint, the scalability of the Ising machine is improved, manufacturing costs and power consumption are reduced, control complexity is decreased, and complex NP-hard problems can be solved more efficiently.
Smart Images
Figure CN119067227B_ABST
Abstract
Description
Technical Field
[0001] This disclosure generally relates to the Isin machine. Background Technology
[0002] The Ising model, as a model for ferromagnets, originated in solid-state physics. The Ising model maps a wide range of combinatorial optimization problems for which efficient and accurate classical algorithms do not yet exist. The Ising model can be derived from the Hamiltonian function (…). To describe it, where, It is spin and The elements of the coupling matrix between them.
[0003]
[0004] The Ising model can be used to formulate NP-hard combinatorial optimization problems with only polynomial costs (i.e., problems such as the Traveling Salesman Problem, where the number of possible solutions increases exponentially with the number of system components). Therefore, machines / devices that can efficiently and effectively solve the Ising model would be very valuable. Summary of the Invention
[0005] According to one aspect of this disclosure, an apparatus for a tensor-quantized integrated coherent Ising machine is provided, comprising: a multi-wavelength Ising node set including bistable Ising nodes associated with individual optical wavelengths; a tensor-quantized optical coupling matrix, wherein the tensor-quantized optical coupling matrix includes a plurality of multi-wavelength photonic tensor string (TT) core layers cascaded together via passive optical cross-connections; a multi-wavelength Ising node set to tensor-quantized optical coupling matrix waveguide that optically connects outputs from the multi-wavelength Ising node set to inputs of the tensor-quantized optical coupling matrix; and a tensor-quantized optical coupling matrix to multi-wavelength Ising node set waveguide that optically connects outputs from the tensor-quantized optical coupling matrix to inputs of the multi-wavelength Ising node set.
[0006] According to another aspect of this disclosure, an apparatus for a tensor-integrated coherent Ising machine is provided, comprising: a multi-wavelength Ising node set including bistable Ising nodes implemented on a Mach-Zehnder interferometer (MZI), wherein the bistable Ising nodes are associated with individual optical wavelengths; a tensor-integrated optical coupling matrix, wherein the tensor-integrated optical coupling matrix includes a plurality of multi-wavelength photonic tensor string (TT) core layers cascaded together via passive optical cross-connections; a multi-wavelength Ising node set to tensor-integrated optical coupling matrix waveguide that optically connects the output from the multi-wavelength Ising node set to the input of the tensor-integrated optical coupling matrix; and a tensor-integrated optical coupling matrix to multi-wavelength Ising node set waveguide that optically connects the output from the tensor-integrated optical coupling matrix to the input of the multi-wavelength Ising node set; wherein the multi-wavelength Ising node set to tensor-integrated optical coupling matrix waveguide and the tensor-integrated optical coupling matrix waveguide are optically connected to the multi-wavelength Ising node set and the tensor-integrated optical coupling matrix to form an Ising machine feedback loop.
[0007] According to another aspect of this disclosure, an apparatus for a tensor-integrated coherent Ising machine is provided, comprising: a bistable Ising node associated with a single optical wavelength; a tensor-integrated optical coupling matrix, wherein the tensor-integrated optical coupling matrix includes a plurality of multi-wavelength photonic tensor string (TT) core layers cascaded together via passive optical cross-connections; a multiplexer that multiplexes optical signals received from the bistable Ising node to the multiplexer waveguide onto the input waveguide of the tensor-integrated optical coupling matrix; a demultiplexer that demultiplexes signals received from the output waveguide of the tensor-integrated optical coupling matrix onto the demultiplexer-to-bistable Ising node waveguide; the bistable Ising node-to-multiplexer waveguide optically connects output optics from the bistable Ising node to the multiplexer; and the demultiplexer-to-bistable Ising node waveguide optically connects output optics from the demultiplexer to the bistable Ising node. Attached Figure Description
[0008] This disclosure is described in detail with reference to the following accompanying drawings, based on one or more different examples. The drawings are provided for illustrative purposes only and depict only examples.
[0009] Figure 1 Example integration of the Coherent Ising Machine (CIM) is described based on various examples of currently disclosed technologies.
[0010] Figure 2 Example bistable Ising nodes are depicted according to various examples of currently disclosed techniques.
[0011] Figures 3A to 3C Example tensor-integrated CIM is described based on various examples of currently disclosed technologies.
[0012] Figures 4A to 4D Another example of tensor-based integrated CIM is described, based on various examples of currently disclosed technologies.
[0013] Figure 5 An example set of multi-wavelength Ising nodes is depicted according to various examples of currently disclosed techniques.
[0014] Figures 6A to 6D Example tensor-quantized optical coupling matrices are depicted according to various examples of currently disclosed techniques.
[0015] Figure 7 Example Mach-Zehnder interferometer (MZI) grids are depicted according to various examples of currently disclosed techniques.
[0016] Figure 8 Example MZI mesh elements are depicted according to various examples of currently disclosed technologies.
[0017] Figure 9 Examples of weight matrix TT decomposition for parameter compression are depicted according to various examples of currently disclosed techniques.
[0018] The accompanying drawings are not exhaustive and do not limit this disclosure to the precise form disclosed. Detailed Implementation
[0019] An Ising machine is a device built / designed to find the absolute or approximate ground state of an Ising model. Since NP-hard combinatorial optimization problems (referred to as NP-hard problems in this paper) can be reformulated using the Ising model, these Ising machines can be used to solve NP-hard problems (i.e., find approximate solutions to NP-hard problems).
[0020] Traditional Ising machines typically utilize quantum annealing to find the absolute or approximate ground state of the Ising model based on quantum fluctuations. Due to limitations in the interconnection properties of Ising nodes in quantum annealing-based systems, these traditional Ising machines may be difficult to scale. Due to scalability constraints, these traditional Ising machines may struggle to solve increasingly complex (i.e., more complex) NP-hard problems without incurring excessive increases in footprint and cost.
[0021] Recently, the Coherent Ising Machine (CIM) has been introduced, which finds the absolute or approximate ground state of the Ising model by processing coherent optical signals (e.g., optical signals with the same / similar frequencies and waveforms). CIM has greater scalability potential than quantum-annealed Ising machines because it does not have the Ising node interconnection constraint property of quantum-annealed systems.
[0022] Among various CIMs, integrated CIMs (i.e., integrated photonic circuits implementing CIMs) have attracted considerable attention due to their high energy efficiency, compact footprint, high speed, and low manufacturing cost. For example, PCT / US2015 / 048952 (which is incorporated herein by reference in its entirety) proposes a CIM architecture comprising: (1) a bistable Ising node implemented using a tunable optical resonator / amplifier with self-feedback; (2) a coupling matrix; and (3) a waveguide connecting the bistable Ising node and the coupling matrix to form an Ising machine feedback loop.
[0023] While integrated CIM is generally more scalable than traditional / quantum annealing-based Ising machines, there is still great expectation to further improve the scalability of integrated CIM.
[0024] In this context, an example of this technology provides a “tensified” integrated CIM that enhances scalability by utilizing a tensified optical coupling matrix. The tensified optical coupling matrix may include a multi-wavelength photonic tensor string (TT) core layer cascaded together via passive optical cross-connections. The multi-wavelength photonic TT core may include a Mach-Zehnder interferometer (MZI) grid (i.e., an interconnected lattice / array of MZIs) that modulates the phase and / or amplitude of optical signals of multiple wavelengths.
[0025] Tensor-quantized optical coupling matrices can be implemented using a tensor string (TT) decomposition algorithm, which efficiently compresses the overparameterized coupling matrix (especially the low-rank sparse coupling matrix) used to solve the Ising model. Furthermore, by cascading multi-wavelength photonic TT cores via passive optical cross-connections, further reductions in hardware (e.g., fewer MZIs) and footprint can be achieved. Therefore, the tensor-quantized integrated CIM of this technique can be extended to solve complex NP-hard problems with less hardware and a smaller footprint compared to existing integrated CIMs. Correspondingly, compared to existing integrated CIMs, the tensor-quantized integrated CIM can have lower manufacturing costs, consume less power, and require less control complexity.
[0026] As described in more detail below, tensor-quantized integrated CIM can achieve further scalability optimizations through intelligent / specialized design of bistable Ising nodes. For example, the bistable Ising nodes of the tensor-quantized integrated CIM can be implemented via one or more multi-wavelength Ising node sets. A multi-wavelength Ising node set can include multiple bistable Ising nodes, where each bistable Ising node in the multi-wavelength Ising node set is associated with a separate optical wavelength. A single multi-wavelength Ising node set to a tensor-quantized optical coupling matrix waveguide can optically connect the output from the multi-wavelength Ising node set to the input multi-wavelength photon TT core of the tensor-quantized optical coupling matrix. Correspondingly, a single tensor-quantized optical coupling matrix to a multi-wavelength Ising node set waveguide can optically connect the output multi-wavelength photon TT core of the tensor-quantized optical coupling matrix to the input of the multi-wavelength Ising node set. Therefore, the multi-wavelength Ising node set to a tensor-quantized optical coupling matrix waveguide and the tensor-quantized optical coupling matrix to a multi-wavelength Ising node set waveguide can optically connect the multi-wavelength Ising node set and the tensor-quantized optical coupling matrix to form an Ising machine feedback loop.
[0027] Multi-wavelength Ising node ensembles can reduce the hardware and footprint required to implement tensor-integrated CIMs using currently disclosed techniques. In other words, tensor-integrated CIMs utilizing a multi-wavelength Ising node ensemble architecture can achieve greater scalability compared to potential alternative tensor-integrated CIM designs.
[0028] For example, in existing integrated CIMs, bistable Ising nodes are not grouped into sets of multi-wavelength Ising nodes. Instead, each bistable Ising node is associated with its own bistable Ising node-to-coupled matrix waveguide and its own coupling matrix-to-bistable Ising node waveguide. Therefore, implementing a tensorized integrated CIM using this existing bistable Ising node arrangement typically requires multiplexers to multiplex the optical signals received from the bistable Ising nodes onto the waveguides associated with the input multi-wavelength photonic TT cores of the tensorized optical coupling matrix. Correspondingly, demultiplexers will be needed to demultiplex the signals received from the output multi-wavelength photonic TT cores of the tensorized optical coupling matrix onto the waveguides leading to the bistable Ising nodes. Depending on the size of the tensorized integrated CIM (e.g., the number of multi-wavelength photonic TT cores per layer), the number and / or size of these multiplexers and demultiplexers can also increase. Furthermore, for including N Tensorized integration of CIM with 1 bistable Ising node, this simple bistable Ising node arrangement will require N A bistable Ising node to the multiplexer waveguide and N A demultiplexer is connected to a bistable Ising node waveguide.
[0029] However, by utilizing a multi-wavelength Ising node array instead of a simple / conventional bistable Ising node arrangement, the currently disclosed tensor-integrated CIM can: (a) reduce / eliminate the aforementioned multiplexers and demultiplexers; (b) reduce the number of waveguides required to connect the bistable Ising nodes and the tensor coupling matrix; and (c) improve the on-chip layout / merging of the bistable Ising node hardware. Therefore, compared to potentially alternative (and simpler) tensor-integrated CIM designs, tensor-integrated CIM implementing a multi-wavelength Ising node array can achieve greater compactness (i.e., a smaller footprint) with less hardware. These reductions in footprint and hardware enable the implementation of larger (and more robust) systems on a smaller chip.
[0030] Examples of this technology will be described in more detail below with reference to the accompanying figures.
[0031] Figure 1 An example integrated CIM 100 is depicted. Integrated CIM 100 can represent a generic integrated CIM, which is an improvement upon the currently disclosed examples of the technology.
[0032] As depicted, the integrated CIM 100 includes: (1) a bistable Ising node 110; (2) a coupling matrix 130; (3) a bistable Ising node-to-coupling matrix waveguide 120; and a coupling matrix-to-bistable Ising node waveguide 125. The bistable Ising node-to-coupling matrix waveguide 120 and the coupling matrix-to-bistable Ising node waveguide 125 connect the bistable Ising node 110 to the coupling matrix 130 to form an Ising machine feedback loop.
[0033] As depicted, each of the bistable Ising nodes in the bistable Ising node 110 can implement the input from its input. To its output Nonlinear input-output relationship .function It can be a function similar to a threshold.
[0034] As depicted, coupling matrix 130 applies analog weights to the output of the bistable Ising node 110. For example, coupling matrix 130 can compute a weighted sum of the outputs of the bistable Ising node 110 in the following manner:
[0035]
[0036] Here, the output from the bistable Ising node 110 will be... Multiply by weight To generate a signal In the recurrent feedback loop, the coupling matrix to the bistable Ising node waveguide 125 will receive the first waveguide from the coupling matrix 130.i The output is connected to the first bistable Ising node 110. i The input of the bistable Ising node (e.g., ).
[0037] Through the aforementioned Ising machine feedback loop, the ensemble CIM 100 can find the absolute or approximate ground state of the Ising model. Since NP-hard problems can be reformulated using the Ising model, the ensemble CIM 100 can be used to solve such NP-hard problems.
[0038] In combination Figure 2 Before describing the hardware implementation of the bistable Ising node 110 in more detail, it may be helpful to understand some of the advantages offered by the integrated CIM100 compared to conventional quantum annealing-based Ising machines. For example, the integrated CIM100 includes full-pair full connectivity between the bistable Ising node 110 and the coupling matrix 130. That is, from the bistable Ising node 110... N The outputs are connected to the coupling matrix 130 via the bistable Ising node to the coupling matrix waveguide 120. N One input. Relatedly, from coupling matrix 130. N The output is connected via a coupling matrix to the bistable Ising node waveguide 125. N There are 110 input bistable Ising nodes. Due to this all-pair full connectivity, the integrated CIM 100 can outperform traditional quantum annealing-based Ising machines due to its associated higher connectivity and reconfigurability. For example, the computational power of the Ising machine can be determined by the number of Ising nodes, but it can also be determined by the independent non-zero weights in Equation 2. The number of connections is determined by the number of possible links between Ising nodes. As implied above, integrated CIM systems, such as the integrated CIM 100, process coherent optical signals. Therefore, These are complex values. Although traditional applications might only use real values. Weight, but integrated CIM 100 can be used to act on The real orthogonal phase-sensitive nonlinearity. This facilitates the handling of spin variables in the specific orthogonality of the supermode stored in the anticorrelated internal states of the two resonators 210(a) and 210(b).
[0039] Figure 2 An example bistable Ising node 200 is depicted. Bistable Ising node 200 can represent a bistable Ising node not implemented in the multi-wavelength bistable Ising node set. Bistable Ising node 200 can be from... Figure 1 An example of a bistable Ising node in bistable Ising node 110.
[0040] As depicted, the bistable Ising node 200 includes two optical resonators (i.e., optical resonators 210(a) and 210(b)) implemented on the arms of a Mach-Zehnder interferometer (MZI), i.e., the first arm waveguide 214 and the second arm waveguide 215. In some examples, optical resonators 210(a) and 210(b) may include the same optical ring resonator with dispersive optical nonlinearity.
[0041] The MZI on which optical resonators 210(a) and 210(b) are implemented includes: (a) a first arm waveguide 214; (b) a second arm waveguide 215; (c) an input-side optical coupler 218; and (d) an output-side optical coupler 219. As depicted, the input-side optical coupler 218 receives a first input from the coupling matrix to the bistable Ising node waveguide 220 and a second input from the feedback loop waveguide 216. The input-side optical coupler 218 then outputs a first output to the first arm waveguide 214 and a second output to the second arm waveguide 215. The output-side optical coupler 219 receives a first input from the first arm waveguide 214 and a second input from the second arm waveguide 215. The output-side optical coupler 219 then outputs a first output to the bistable Ising node to the coupling matrix waveguide 222 and a second output to the feedback loop waveguide 216. The input-side optical coupler 218 and the output-side optical coupler 219 can be various types of optical couplers, including 50-50 beam splitters, multimode interferometers (MMIs), directional couplers, etc.
[0042] As depicted, the bistable Ising node 200 also includes a feedback loop waveguide 216 and a bias pump 230. The output of the bias pump 230 can be optically coupled to the feedback loop waveguide 216. As will be described in more detail below, the bias pump 230 and optical resonators 210(a) and 210(b) can be configured to store two anticorrelated states associated with the bistable Ising node 200. That is, through the feedback loop and the MZI structure, the bistable Ising node 200 can selectively modify the cyclic power of the symmetric supermodes of optical resonators 210(a) and 210(b) such that optical resonators 210(a) and 210(b) exhibit two anticorrelated states.
[0043] In various examples, the bistable Ising node 200 may also include bias field couplers 250 and 252. Bias field couplers 250 and 252 can inject bias fields into spin variables (e.g., one of the four non-relativistic coordinates of an electron) and help monitor the current spin amplitude.
[0044] Since the examples of the currently disclosed technology are designed for understanding, the bistable asymmetry of a single optical resonator can be avoided by encoding the spin states in two optical resonators (e.g., optical resonators 210(a) and 210(b)) configured such that their internal states are anticorrelated. Therefore, the bistable Ising node 220 can exhibit a forked bifurcation when the drive from the bias pump 230 increases the power of the bias field above a threshold level (the phase of the bias field may be weakly correlated with the length of the feedback loop waveguide 216). This may be analogous to the bifurcation that occurs in a degenerate optical parametric oscillator (DOPO). In this sense, the bistable Ising node 200 can model certain conventional CIMs based on DOPO, but with the added advantage that the input field of the bias pump 230 has the same wavelength as the signal field of the bias pump 230. Furthermore, the bistable Ising node 200 is independent of any particular type of optical nonlinearity and can also adapt to devices with nonlinear losses.
[0045] As implied above, a strong bias field entering the first MZI input (e.g., the first input of the input-side optical coupler 218) can produce a tunable phase-sensitive gain for transmitting small signals from the second MZI input (e.g., the second input of the input-side optical coupler 218) to the MZI output (e.g., the output from the input-side optical coupler 218). The maximum gain can be determined by detuning the bias (and signal) drive from the common optical resonator resonant frequency. There may be a threshold detuning beyond which optical resonators 210(a) and 210(b) become bistable within a certain input power range. To implement the two states for spin encoding, coherent feedback can be used to couple the resonator modes of optical resonators 210(a) and 210(b). For example, by using an appropriately chosen bias feedback phase, the two metastable states can be made unstable, such that optical resonators 210(a) and 210(b) can only exhibit anticorrelated internal states.
[0046] As implied above, the bistable Ising node 200 can be viewed as a tunable amplifier with feedback (TAFB), characterized by a forked branching at a specific threshold bias field power. Above this threshold bias field power, the aforementioned anti-correlation state may exist. The amplitude of the bias pump 230 can be used as a parameter for driving the bias field power to and / or up to the threshold bias field power. The spin variable can be encoded in a specific orthogonal array as a function of the pump amplitude.
[0047] Figures 3A to 3C An example tensor quantization integration CIM 300 according to various examples of this technology is described.
[0048] As depicted, the tensor-quantized integrated CIM 300 includes: (a) a multi-wavelength Ising node set (e.g., multi-wavelength Ising node sets 312, 314, and 316); (b) a tensor-quantized optical coupling matrix 330; (c) a multi-wavelength Ising node set to tensor-quantized optical coupling matrix waveguide 320, which optically connects the output from the multi-wavelength Ising node set to the input of the tensor-quantized optical coupling matrix 330; and (d) a tensor-quantized optical coupling matrix to multi-wavelength Ising node set waveguide 325, which optically connects the output from the tensor-quantized optical coupling matrix 330 to the input of the multi-wavelength Ising node set. Therefore, the multi-wavelength Ising node set to tensor-quantized optical coupling matrix waveguide 320 and the tensor-quantized optical coupling matrix 325 optically connect the multi-wavelength Ising node set and the tensor-quantized optical coupling matrix 330 to form an Ising machine feedback loop. As depicted, the tensor-quantized integrated CIM 300 may also include up to... g Each optical wavelength is introduced into the laser 360 (e.g., a comb laser) in the tensor-quantized integrated CIM 300.
[0049] Combining Figure 5 A more detailed description of an example multi-wavelength Ising node set is provided. Similarly, [the following will be combined with...] Figures 6A to 6D A more detailed description of the example tensor quantization optical coupling matrix is provided. Nevertheless, it may be useful to describe the composition and operation of the tensor quantization integrated CIM 300 at a higher level before proceeding to these figures.
[0050] As implied above, examples of this technology provide “tensified” integrated CIMs (e.g., tensified integrated CIM 300) that improve scalability by utilizing tensified optical coupling matrices (e.g., tensified optical coupling matrix 330) that include multi-wavelength photonic tensor string (TT) core layers cascaded together via passive optical cross-connects (e.g., passive optical cross-connects 335) (e.g., a first layer including multi-wavelength photonic TT cores 332(a) and 332(b), a second layer including multi-wavelength photonic TT cores 334(a) and 334(b), a third layer including multi-wavelength photonic TT cores 336(a) and 336(b), a fourth layer including multi-wavelength photonic TT cores 338(a) and 338(b), etc.). Multiwavelength photonic TT cores (e.g., multiwavelength photonic TT core 332(a)) may include a Mach-Zehnder interferometer (MZI) grid (i.e., a lattice / array of interconnected MZIs—see example) that modulates the phase and / or amplitude of an optical signal. Figure 7 (For more details)
[0051] Tensor-quantized optical coupling matrices / cascaded multi-wavelength photonic TT cores can implement tensor string (TT) decomposition algorithms, which efficiently compress the overparameterized coupling matrices (especially low-rank sparse coupling matrices) used to solve the Ising model. Furthermore, by cascading multi-wavelength photonic TT cores via passive cross-connections, further hardware reduction (e.g., fewer MZIs) and a further reduction in footprint can be achieved. Therefore, the tensor-quantized integrated CIM of this technology (e.g., tensor-quantized integrated CIM 300) can be extended to solve complex NP-hard problems with less hardware and a smaller footprint compared to existing integrated CIMs. Correspondingly, compared to existing integrated CIMs, tensor-quantized integrated CIMs can have lower manufacturing costs, consume less power, and require less control complexity.
[0052] As implied above, tensor-based integrated CIM can achieve further scalability optimizations through intelligent / specialized design of bistable Ising nodes. For example, the bistable Ising nodes of tensor-based integrated CIM can be implemented via one or more sets of multi-wavelength Ising nodes (e.g., multi-wavelength Ising node sets 312, 314, 316, etc.). A set of multi-wavelength Ising nodes (e.g., multi-wavelength Ising node set 312) can include multiple bistable Ising nodes, wherein each bistable Ising node in the multi-wavelength Ising node set is associated with a separate optical wavelength (see example...). Figure 5 (For further details). A single multi-wavelength Ising node set to a tensorized optical coupling matrix waveguide (see, for example, a separate multi-wavelength Ising node set to a tensorized optical coupling matrix waveguide 320) can optically connect the output from the multi-wavelength Ising node set to the input multi-wavelength photonic TT core of the tensorized optical coupling matrix (e.g., multi-wavelength photonic TT core 332(a)). Correspondingly, a single tensorized optical coupling matrix to a multi-wavelength Ising node set waveguide (see, for example, a separate tensorized optical coupling matrix to a multi-wavelength Ising node set waveguide 325) can optically connect the output multi-wavelength photonic TT core of the tensorized optical coupling matrix (e.g., multi-wavelength photonic TT core 338(a)) to the input of the multi-wavelength Ising node set. Therefore, the multi-wavelength Ising node set to the tensor optical coupling matrix waveguide and the tensor optical coupling matrix to the multi-wavelength Ising node set waveguide can be optically connected to the multi-wavelength Ising node set and the tensor optical coupling matrix to form an Ising machine feedback loop.
[0053] As implied above, multi-wavelength Ising node ensembles can reduce the hardware and footprint required to implement tensor-integrated CIMs using currently disclosed techniques. In other words, tensor-integrated CIMs utilizing a multi-wavelength Ising node ensemble architecture can achieve greater scalability compared to potential alternative tensor-integrated CIM designs.
[0054] To illustrate, Figures 4A to 4D An example alternative tensor ensemble CIM 400 that does not utilize a multi-wavelength Ising node set is described.
[0055] As depicted, the tensor quantization integrated CIM 400 includes: (a) bistable Ising nodes (e.g., bistable Ising nodes 411-416), wherein each of the bistable Ising nodes is associated with a separate optical wavelength; (b) a tensor quantization optical coupling matrix 430, which includes multi-wavelength photonic tensor string (TT) core layers cascaded together via passive optical cross-connections (e.g., passive optical cross-connection 435) (e.g., a first layer including multi-wavelength photonic TT cores 432(a) and 432(b), a second layer including multi-wavelength photonic TT cores 434(a) and 434(b), a third layer including multi-wavelength photonic TT cores 436(a) and 436(b), a fourth layer including multi-wavelength photonic TT cores 438(a) and 438(b), etc.); (c) (d) Multiplexer 470, which multiplexes the optical signal received from the bistable Ising node to multiplexer waveguide 440 onto the input waveguide of tensor coupling matrix 430; (e) Demultiplexer 480, which demultiplexes the signal received from the output waveguide of tensor coupling matrix 430 onto demultiplexer-to-bistable Ising node waveguide 445; (f) Bistable Ising node-to-multiplexer waveguide 440, which optically connects the output from the bistable Ising node (e.g., the output from bistable Ising nodes 411-416) to multiplexer 470; and (f) Demultiplexer-to-bistable Ising node waveguide 445, which optically connects the output from demultiplexer 480 to the bistable Ising node. As depicted, each bistable Ising node of the tensor-quantized integrated CIM 400 can be implemented on its own MZI and has its own separate bistable Ising node-to-multiplexer waveguide and demultiplexer-to-bistable Ising node waveguide. Therefore, each bistable Ising node of the tensor-quantized integrated CIM 400 can be implemented with... Figure 2 It is implemented in a similar manner to the bistable Ising node 200.
[0056] As depicted, the tensor quantization integrated CIM 400 includes some features that are the same as or similar to those of the tensor quantization integrated CIM 300 (e.g., the tensor quantization optical coupling matrix 430 includes a structure that is the same as or similar to that of the tensor quantization optical coupling matrix 330, and can hold up to...). g The system incorporates lasers of various wavelengths (e.g., 460, etc.), but there are some key differences. For example, due to the lack of a multi-wavelength Ising node ensemble architecture in the tensor-integrated CIM 300, the tensor-integrated CIM 400 includes a greater number of waveguides between its Ising nodes and their tensor-integrated coupling matrix. For example, if both the tensor-integrated CIM 300 and the tensor-integrated CIM 400 include... N Each multi-wavelength Ising node set of the tensor-integrated CIM 300 includes Ising nodes. g If there are 2 Ising nodes, then the tensor quantization ensemble CIM 400 can include 2 nodes between its Ising nodes and the tensor quantization optical coupling matrix. g More than twice the waveguide. Due to the lack of the multi-wavelength Ising node set architecture of the tensor-quantized integrated CIM 300, the tensor-quantized integrated CIM 400 also includes a multiplexer 470 (which may include one or more individual multiplexers) and a demultiplexer 480 (which may include one or more individual demultiplexers).
[0057] As implied above, the bistable Ising nodes in existing integrated CIMs are not grouped into multi-wavelength Ising node sets. Instead, each bistable Ising node is associated with its own MZI, its own bistable Ising node-to-coupled matrix waveguide, and its own coupled matrix-to-bistable Ising node waveguide (see, for example...). Figure 2 (e.g., the bistable Ising node 200). Therefore, implementing a tensor-integrated CIM using this existing bistable Ising node arrangement—tensor-integrated CIM 400 being an example—typically requires a multiplexer to multiplex the optical signal received from the bistable Ising node onto the waveguide associated with the input multiwavelength photonic TT core of the tensor-integrated optical coupling matrix. Correspondingly, a demultiplexer will be needed to demultiplex the signal received from the output multiwavelength photonic TT core of the tensor-integrated optical coupling matrix onto the waveguide leading to the bistable Ising node. Depending on the size of the tensor-integrated CIM (e.g., the number of multiwavelength photonic TT cores per layer), the number and / or size of these multiplexers and demultiplexers can also be increased. Furthermore (and as implied above), implementing such a simple / existing bistable Ising node arrangement in a tensor quantization integrated CIM (e.g., tensor quantization integrated CIM 400) may require more waveguides between the bistable Ising nodes and the tensor quantization optical coupling matrix than a tensor quantization integrated CIM utilizing a multi-wavelength Ising node set (e.g., tensor quantization integrated CIM 300).
[0058] Therefore, by utilizing a multi-wavelength Ising node array instead of a simple / conventional bistable Ising node arrangement, the currently disclosed tensor-integrated CIM (e.g., tensor-integrated CIM 300) can: (a) reduce / eliminate the aforementioned multiplexers and demultiplexers; (b) reduce the number of waveguides required to connect the bistable Ising nodes and the tensor coupling matrix; and (c) improve the on-chip arrangement / combining of the bistable Ising node hardware. Thus, compared to potentially alternative (and simpler) tensor-integrated CIM designs, the tensor-integrated CIM implementing a multi-wavelength Ising node array can achieve greater compactness (i.e., a smaller footprint) with less hardware. These reductions in footprint and hardware enable the implementation of larger (and more robust) systems on a smaller chip.
[0059] Figure 5 An example multi-wavelength Ising node set 500 is depicted according to various examples of currently disclosed techniques. The multi-wavelength Ising node set 500 can be an example of the multi-wavelength Ising node set of the tensor quantization integrated CIM 300 of Figure 3.
[0060] As depicted, the multi-wavelength Ising node set 500 includes those implemented on a Mach-Zehnder interferometer (MZI). g A bistable Ising node, wherein each bistable Ising node in the multi-wavelength Ising node set is associated with a separate optical wavelength. A given bistable Ising node may include two identical optical resonators configured to modulate light of the associated wavelength of the given bistable Ising node. For example, the first bistable Ising node in the multi-wavelength Ising node set 500 may include optical resonators 510(1)(a) and 510(1)(b). Optical resonators 510(1)(a) and 510(1)(b) may be configured to modulate light of a first wavelength. With bias pump 530 (which may be with...) g Together with the multi-wavelength bias pump associated with each wavelength, optical resonators 510(1)(a) and 510(1)(b) can also be configured to store two bistable / anti-correlated states. Relatedly, the first of the multi-wavelength Ising node sets 500... g The bistable Ising node may include an optical resonator 510 ( g (a) and 510 ( g (b). Optical resonator 510 ( g (a) and 510 ( g (b) can be configured to modulate the first g Wavelength of light. Together with the bias pump 530, the optical resonator 510 ( g (a) and 510 ( g(b) It can also be configured to store two bistable / anticorrelated states.
[0061] As implied above (and as depicted), the multi-wavelength Ising node set 500 g A bistable Ising node is implemented on a public MZI.
[0062] Implemented on it g The MZI of a bistable Ising node includes: (a) a first arm waveguide 514; (b) a second arm waveguide 515; (c) an input-side optical coupler 518; and (d) an output-side optical coupler 519. As depicted, the input-side optical coupler 518 receives a first input from the tensor-quantized optical coupling matrix to the multi-wavelength Ising node assembly waveguide 520 and a second input from the feedback loop waveguide 516. The input-side optical coupler 518 then outputs a first output to the first arm waveguide 514 and a second output to the second arm waveguide 515. The output-side optical coupler 519 receives the first input from the first arm waveguide 514 and the second input from the second arm waveguide 515. The output-side optical coupler 519 then outputs the first output to the multi-wavelength Ising node assembly to the tensor-quantized optical coupling matrix waveguide 522 and the second output to the feedback loop waveguide 516. The input-side optical coupler 518 and the output-side optical coupler 519 can be various types of optical couplers, including 50-50 beam splitters, multimode interferometers (MMIs), directional couplers, etc.
[0063] Through the feedback loop / MZI structure, the multi-wavelength Ising node set 500 can selectively modify the cyclic power of the symmetric supermode of the optical resonator implemented on the arm of the MZI, causing the optical resonator to exhibit two anti-correlation states. The coupler inside the feedback loop waveguide 516 can be used to add a bias signal from the bias pump 530 (as implied above, these bias signals can be coupled with…) g Each wavelength is associated with it.
[0064] In various examples, the multi-wavelength Ising node set 500 may also include bias field couplers (not depicted) implemented on each of the tensor-quantized optical coupling matrix to multi-wavelength Ising node set waveguide 520 and multi-wavelength Ising node set to tensor-quantized optical coupling matrix waveguide 522, respectively. Such bias field couplers can inject bias fields into the spin variable and help monitor the current spin amplitude.
[0065] Since the examples of the currently disclosed technology are designed for understanding, the bistable asymmetry of a single optical resonator can be avoided by encoding the spin states in two optical resonators (e.g., optical resonators 510(1)(a) and 510(1)(b)) such that their internal states are anticorrelated. Therefore, a given bistable Ising node in the multi-wavelength Ising node set 500 can exhibit a forked bifurcation because the drive from the multi-wavelength bias pump 530 increases the power of the bias field above a threshold level. This may be analogous to the bifurcation that occurs in a degenerate optical parametric oscillator. In this sense, a given bistable Ising node can model some conventional CIM based on a degenerate optical parametric oscillator (DOPO), but with the added advantage that the input field of the bias pump 530 has the same wavelength as the signal field of the bias pump 530. Furthermore, a given bistable Ising node is independent of any particular type of optical nonlinearity and can also adapt to devices with nonlinear losses.
[0066] As implied above, a strong bias field entering the first MZI input (e.g., the first input of input-side optical coupler 518) can generate a tunable phase-sensitive gain for transmitting small signals from the second MZI input (e.g., the second input of input-side optical coupler 518) to the second MZI output (e.g., the output from input-side optical coupler 418). The maximum gain can be determined by detuning the bias (and signal) drive from the common optical resonator resonant frequency. For example, there may be a threshold detuning beyond which optical resonators 510(1)(a) and 510(1)(b) become bistable within a certain input power range. To implement the two states for spin encoding, coherent feedback can be used to couple the resonator modes of optical resonators 510(1)(a) and 510(1)(b). For example, by using a first appropriately selected bias feedback phase (driven by bias pump 530), the two metastable states can be made unstable, such that optical resonators 510(1)(a) and 510(1)(b) can only exhibit anti-correlated internal states. Optical resonators 510(2)(a) and 510(2)(b) can be configured such that a second bias feedback phase (driven by bias pump 530) causes optical resonators 510(2)(a) and 510(2)(b) to exhibit anti-correlated states. Accordingly, optical resonator 510( g (a) and 510 ( g (b) can be configured such that the third bias feedback phase (driven by bias pump 530) causes the optical resonator 510 ( g (a) and 510 ( g (b) It exhibits an inverse correlation, and so on.
[0067] It should be understood here that the multi-wavelength Ising node set 500 is merely one example implementation of a multi-wavelength Ising node set. For example, another implementation of a multi-wavelength Ising node set may include a bus waveguide and multiple microring resonators with internal reflections. Another implementation of a multi-wavelength Ising node set may include multiple directly coupled dual microring resonators.
[0068] Figures 6A to 6D An example tensor quantization optical coupling matrix 600 according to various examples of the currently disclosed technology is depicted. It should be understood that the tensor quantization optical coupling matrix 600 is merely an example, and other embodiments may include tensor quantization optical coupling matrices with different configurations embodying the same / similar principles.
[0069] Specifically, examples of this technology provide a “tensified” integrated CIM that improves scalability by utilizing a tensified optical coupling matrix (e.g., tensified optical coupling matrix 600) comprising multi-wavelength photonic tensor string (TT) core layers (e.g., photonic TT core layer 4, photonic TT core layer 3, photonic TT core layer 2, and photonic TT core layer 1) cascaded together via passive optical cross-connections. The multi-wavelength photonic TT cores may include a Mach-Zehnder interferometer (MZI) grid (i.e., an interconnected lattice / array of MZIs—see example) that modulates the phase and / or amplitude of optical signals. Figure 7 (For more details)
[0070] Tensor-quantized optical coupling matrices / cascaded multi-wavelength photonic TT cores can implement a tensor string (TT) decomposition algorithm that efficiently compresses the overparameterized coupling matrix (especially the low-rank sparse coupling matrix) used to solve the Ising model. Furthermore, by cascading multi-wavelength photonic TT cores via passive cross-connections, further hardware reduction (e.g., fewer MZIs) and a further reduction in footprint can be achieved. Therefore, the tensor-quantized integrated CIM of this technique can be extended to solve complex NP-hard problems with less hardware and a smaller footprint compared to existing integrated CIMs. Correspondingly, compared to existing integrated CIMs, the tensor-quantized integrated CIM can have lower manufacturing costs, consume less power, and require less control complexity.
[0071] Now, referring to the TT decomposition algorithm, since the examples in this technique are designed for understanding, the weight matrix... It can be represented in TT format. Matrix dimension. M and N We can assume that it is factored into and ,in, d Defined as M andN The number of factors. μ and v It can be from W index ( i,j ) to second order -2 d Weight Tensor W index The natural double radiation. Therefore, W The TT decomposition can be interpreted as the singular value decomposition (SVD) of a multidimensional matrix. For example, in... Figure 9 As can be seen, the TT decomposition can be performed on the weight tensor as described in Equation 3 below. W Represented as a series of tensor products:
[0072]
[0073] Here, the four-way tensor It is a TT core, and the total number of tensor cores is d .vector It is TT rank, and In this way, the total number of parameters can be derived from... M × N Reduced to the sum of parameters in the TT core, that is, .
[0074] Referring now to the example tensor optical coupling matrix 600 in Figure 6, the tensor optical coupling matrix 600 can be configured to receive input from 1024 bistable Ising nodes associated with 32 individual optical wavelengths. Here, 1024 × 1024 is factored into 8 × 4 × 4 × 8 × 8 × 4 × 4 × 8. As depicted, the total number of photonic TT core layers is four (i.e., d = 4), and the total number of wavelengths is 32 (i.e., g = 32). Therefore, in each example, the set of multi-wavelength Ising nodes coupled to the tensor optical coupling matrix 600 can each include 32 bistable Ising nodes associated with 32 individual wavelengths.
[0075] Here, the rank of TT can be set to and .
[0076] Therefore, the tensor-quantized optical coupling matrix 600 includes four photonic TT core layers—photonic TT core layer 4, photonic TT core layer 3, photonic TT core layer 2, and photonic TT core layer 1—with dimensions of respectively... , , and The passive optical cross-connection between photonic TT core layer 4 and photonic TT core layer 3 can implement index switching between the spatial domains of the intermediate signal. A passive optical cross-connection between photonic TT core layer 2 and photonic TT core layer 1 can implement similar index switching. As depicted, the passive optical cross-connection between photonic TT core layer 3 and photonic TT core layer 2 can implement different functions. In particular, they can include wavelength-spatial cross-connections that effectively switch the index between the spatial and wavelength domains of the intermediate signal. The wavelength-spatial cross-connection between photonic TT core layer 3 and photonic TT core layer 2 can be implemented using a wavelength division multiplexing (WDM) transponder. In some examples, wavelength-spatial cross-connections can be implemented using O / E / O conversion and passive electrical cross-connections.
[0077] As depicted, each multiwavelength photonic TT core of the tensor optical coupling matrix 600 may comprise an 8 × 8 MZI grid. Therefore (and as depicted), the tensor optical coupling matrix 600 comprises sixteen 8 × 8 MZI grids, and passive optical cross-connections between the multiwavelength photonic TT cores (i.e., 8 × 8 MZI grids) of different photonic TT core layers, resulting in a total of sixteen 8 × 8 MZI grids, 448 MZIs, and 32 cascaded MZI stages. The input optical signal received by the tensor optical coupling matrix 600 from the bistable Ising node can first be modulated using an array of thirty-two 32-wavelength wavelength division multiplexing (WDM) microring modulators. Then, before the tensor optical coupling matrix 600 outputs the optical signal back to the bistable Ising node, the signal can be multiplied by the multiwavelength photonic TT cores of each photonic TT core layer.
[0078] As depicted, a 32-wavelength comb laser can provide a light source for the system's 32-wavelength optical signals.
[0079] Figure 7 An example Mach-Zehnder interferometer (MZI) grid 700 is depicted according to various examples of currently disclosed techniques.
[0080] As implied above, the currently disclosed multi-wavelength photonic TT core may include an MZI grid (i.e., an interconnected lattice / array of MZIs). Therefore, MZI grid 700 can represent the currently disclosed multi-wavelength photonic TT core.
[0081] As depicted, the MZI mesh 700 can be implemented using a "rectangular" MZI mesh represented by 2 × 2 MZI as building blocks. N × N The identity matrix. That is, each component element of the MZI mesh 700 (e.g., U 1,1It can include 2 × 2 MZI.
[0082] Figure 8 An example MZI mesh element 800 is depicted according to various examples of the currently disclosed technology. The MZI mesh element 800 may include constituent MZI mesh elements of the MZI mesh 700. U i,j one.
[0083] As depicted, the MZI grid element 800 may include 2 × 2 MZIs. The 2 × 2 MZIs may include: (a) a first optical coupler 810 and a second optical coupler 812; and (2) a first phase shifter 820 and a second phase shifter 822. The optical couplers 810 and 812 may be various types of optical couplers, including 50-50 beam splitters, multimode interferometers (MMIs), directional couplers, etc.
[0084] As implied above, Figure 9 Examples of weight matrix TT decomposition for parameter compression are depicted according to various examples of currently disclosed techniques.
[0085] As used herein, the term “optical connection” (and its variants, “operationally connected”, etc.) can refer to a direct or indirect connection between two components that allows optical signals to be transmitted from one component to the other.
[0086] As used herein, the term “or” can be interpreted in an inclusive or exclusive sense. Furthermore, descriptions of resources, operations, or structures in the singular form should not be construed as excluding the plural. Unless expressly stated otherwise, or understood otherwise in the context in which they are used, conditional language (among others, such as “can,” “could,” “might,” or “may”) is generally intended to convey that certain embodiments include certain features, elements, and / or steps that are not included in other embodiments.
[0087] Unless otherwise expressly stated, the terms and phrases used in this document, and their variations thereof, should be interpreted as open-ended rather than restrictive. Adjectives and similar terms such as “conventional,” “traditional,” “normal,” “standard,” and “known” should not be interpreted as limiting the described items to items available for a given period of time or prior to a given time, but should be understood to encompass traditional, conventional, normal, or standard techniques that may be available or known at any time now or in the future. In some cases, the presence of broad words and phrases (such as “one or more,” “at least,” “but not limited to,” or other similar phrases) should not be interpreted as indicating an intention or requirement for a narrower scope where such broad phrases may not exist.
Claims
1. An apparatus for a tensor-based integrated coherent Ising machine, comprising: A multi-wavelength Ising node set, which includes bistable Ising nodes associated with individual optical wavelengths; Tensor-quantized optical coupling matrix, wherein the tensor-quantized optical coupling matrix includes multiple multi-wavelength photon tensor strings TT core layers cascaded together via passive optical cross-connections; A multi-wavelength Ising node set is connected to a tensor quantized optical coupling matrix waveguide, which optically connects the output from the multi-wavelength Ising node set to the input of the tensor quantized optical coupling matrix; as well as Tensed quantized optical coupling matrix to multi-wavelength Ising node set waveguide, which optically connects the output from the tensed quantized optical coupling matrix to the input of the multi-wavelength Ising node set.
2. The apparatus of claim 1, wherein, The multi-wavelength Ising node set is optically connected to the tensor quantization optical coupling matrix waveguide and the tensor quantization optical coupling matrix is optically connected to the multi-wavelength Ising node set waveguide to form the Ising machine feedback loop.
3. The apparatus of claim 1, wherein, The bistable Ising node is implemented on a Mach-Zehnder interferometer (MZI).
4. The apparatus of claim 3, wherein, The MZI of the multi-wavelength Ising node set includes: First arm waveguide; Second arm waveguide; The input-side optical coupler performs the following operations: The first input is received from the tensor-quantized optical coupling matrix to the multi-wavelength Ising node array waveguide, and the second input is received from the feedback waveguide. A first output is output to the first arm waveguide and a second output is output to the second arm waveguide; and The output-side optical coupler performs the following operations: Receives a first input from the first arm waveguide and a second input from the second arm waveguide, and The first output is output to the waveguide of the tensor quantized optical coupling matrix, and the second output is output to the waveguide of the feedback loop. The bistable Ising node in the multi-wavelength Ising node set is implemented between the input-side optical coupler and the output-side optical coupler on the MZI.
5. The apparatus of claim 4, wherein: The first bistable Ising node in the multi-wavelength Ising node set includes: A first optical resonator, optically coupled to the first arm waveguide between the input-side optical coupler and the output-side optical coupler, and A second optical resonator is optically coupled to the second arm waveguide between the input-side optical coupler and the output-side optical coupler; and The second bistable Ising node in the multi-wavelength Ising node set includes: A third optical resonator, which couples to the first arm waveguide between the input-side optical coupler and the output-side optical coupler, and A fourth optical resonator is coupled to the second arm waveguide between the input-side optical coupler and the output-side optical coupler.
6. The apparatus of claim 5, wherein: The first optical resonator and the second optical resonator are configured to modulate light of the associated wavelength of the first bistable Ising node; and The third and fourth optical resonators are configured to modulate light of the associated wavelength of the second bistable Ising node.
7. The apparatus of claim 5, further comprising a pump, wherein: The pump's output is optically connected to the feedback loop waveguide; The pump, the first optical resonator, and the second optical resonator are configured to store two inversely correlated states associated with the first bistable Ising node; and The pump, the third optical resonator, and the fourth optical resonator are configured to store two anticorrelated states associated with the second bistable Ising node.
8. The apparatus of claim 1, wherein, One of the multi-wavelength photonic TT core layers includes one or more multi-wavelength photonic TT cores.
9. The apparatus of claim 1, wherein, One of the one or more multi-wavelength photonic TT cores includes a Mach-Zehnder interferometer (MZI) grid.
10. An apparatus for a tensor-integrated coherent Ising machine, comprising: A multi-wavelength Ising node set, comprising bistable Ising nodes implemented on a Mach-Zehnder interferometer (MZI), wherein the bistable Ising nodes are associated with individual optical wavelengths; Tensor-quantized optical coupling matrix, wherein the tensor-quantized optical coupling matrix includes multiple multi-wavelength photon tensor strings TT core layers cascaded together via passive optical cross-connections; A multi-wavelength Ising node set is connected to a tensorized optical coupling matrix waveguide, which optically links the output from the multi-wavelength Ising node set to the input of the tensorized optical coupling matrix; and Tensed quantized optical coupling matrix to multi-wavelength Ising node set waveguide, which optically connects the output from the tensed quantized optical coupling matrix to the input of the multi-wavelength Ising node set; The multi-wavelength Ising node set to the tensor quantization optical coupling matrix waveguide and the tensor quantization optical coupling matrix to the multi-wavelength Ising node set waveguide optically connect the multi-wavelength Ising node set and the tensor quantization optical coupling matrix to form an Ising machine feedback loop.
11. The apparatus of claim 10, wherein, The MZI of the multi-wavelength Ising node set includes: First arm waveguide; Second arm waveguide; The input-side optical coupler performs the following operations: The first input is received from the tensor-quantized optical coupling matrix to the multi-wavelength Ising node array waveguide, and the second input is received from the feedback waveguide. A first output is output to the first arm waveguide and a second output is output to the second arm waveguide; and The output-side optical coupler performs the following operations: Receives a first input from the first arm waveguide and a second input from the second arm waveguide, and The first output is output to the waveguide of the tensor quantized optical coupling matrix, and the second output is output to the waveguide of the feedback loop. The bistable Ising node in the multi-wavelength Ising node set is implemented between the input-side optical coupler and the output-side optical coupler on the MZI.
12. The apparatus of claim 11, wherein: The first bistable Ising node in the multi-wavelength Ising node set includes: A first optical resonator, optically coupled to the first arm waveguide between the input-side optical coupler and the output-side optical coupler, and A second optical resonator is optically coupled to the second arm waveguide between the input-side optical coupler and the output-side optical coupler; and The second bistable Ising node in the multi-wavelength Ising node set includes: A third optical resonator, which couples to the first arm waveguide between the input-side optical coupler and the output-side optical coupler, and A fourth optical resonator is coupled to the second arm waveguide between the input-side optical coupler and the output-side optical coupler.
13. The apparatus of claim 12, wherein: The first optical resonator and the second optical resonator are configured to modulate light of the associated wavelength of the first bistable Ising node; and The third and fourth optical resonators are configured to modulate light of the associated wavelength of the second bistable Ising node.
14. The apparatus of claim 12, further comprising a pump, wherein: The pump's output is optically connected to the feedback loop waveguide; The pump, the first optical resonator, and the second optical resonator are configured to store two inversely correlated states associated with the first bistable Ising node; and The pump, the third optical resonator, and the fourth optical resonator are configured to store two anticorrelated states associated with the second bistable Ising node.
15. The apparatus of claim 10, wherein, One of the multi-wavelength photonic TT core layers includes one or more multi-wavelength photonic TT cores.
16. The apparatus of claim 10, wherein, One of the one or more multi-wavelength photonic TT cores includes an MZI grid.
17. An apparatus for a tensor-based integrated coherent Ising machine, comprising: Bistable Ising nodes, which are associated with individual wavelengths of light; Tensor-quantized optical coupling matrix, wherein the tensor-quantized optical coupling matrix includes multiple multi-wavelength photon tensor strings TT core layers cascaded together via passive optical cross-connections; A multiplexer that multiplexes the optical signal received from the bistable Ising node to the multiplexer waveguide onto the input waveguide of the tensor quantized optical coupling matrix; A demultiplexer that demultiplexes the signal received from the output waveguide of the tensor quantized optical coupling matrix onto the bistable Ising node waveguide; The bistable Ising node-to-multiplexer waveguide connects the output optics from the bistable Ising node to the multiplexer; and The demultiplexer-to-bistable Ising node waveguide connects the output optics from the demultiplexer to the bistable Ising node.
18. The apparatus of claim 17, wherein, The bistable Ising node-to-multiplexer waveguide and the demultiplexer-to-bistable Ising node waveguide connect the bistable Ising node and the tensor quantization optical coupling matrix to form an Ising machine feedback loop.