A system comprises a processor, and a resistive processing resistive processing unit coupled to the processor. The resistive processing unit comprises an array of cells, wherein the cells respectively comprise resistive memory devices, wherein at least a portion of the resistive memory devices are programmable to store weight values of a given matrix in the array of cells. The processor is configured to store the given matrix in the array of cells of the resistive processing unit, and perform a calibration process to generate a first set of calibration parameters for calibrating forward pass matrix-vector multiplication operations performed on the stored matrix in the array of cells of the resistive processing unit, and a second set of calibration parameters for calibrating backward pass matrix-vector multiplication operations performed on a transpose of the stored matrix in the array of cells of the resistive processing unit.

In one aspect, a computational machine includes an optical device configured to receive energy from an optical energy source and generate a number N1 of optical signals, and a number N2 of coupling devices, each of which controllably couples a plurality of the number N1 optical signals. The coupling devices are individually controlled to simulate a computational problem. In another aspect, a computational machine includes a number N1 of parametric oscillators and a number N2 of coupling devices, each of which controllably couples a plurality of the number N1 of parametric oscillators together. The coupling devices are individually controlled to simulate a computational problem.

Systems and methods for performing matrix operations using a path-number balanced optical network are provided. The optical network is formed as an array including active optical components and passive optical components arranged at a substantially central location of the array. The optical network includes at least NM active optical components which are used to implement a first matrix of any size N×M by embedding the first matrix in a second matrix of a larger size. The optical network performs matrix-vector and matrix-matrix operations by propagating one or more pluralities of optical signals corresponding to an input vector through the optical network.

Systems and methods for performing matrix operations using a path-number balanced optical network are provided. The optical network is formed as an array including active optical components and passive optical components arranged at a substantially central location of the array. The optical network includes at least NM active optical components which are used to implement a first matrix of any size N×M by embedding the first matrix in a second matrix of a larger size. The optical network performs matrix-vector and matrix-matrix operations by propagating one or more pluralities of optical signals corresponding to an input vector through the optical network.

Aspects relate to methods and systems for optical matrix calculation. An exemplary system includes at least a first light source configured to output at least a first optical output having a first wavelength, at least a second light source configured to output at least a second optical output having a second wavelength substantially different from the first wavelength, at least an optical modulator configured to modulate the at least a first optical output, at least an optical matrix multiplier configured to perform at least two matrix multiplications, a first matrix multiplication as a function of the first optical output and a second matrix multiplication as a function of the second optical output, and at least a photodetector configured to measure the at least a first optical output and the at least a second optical output.

Systems and methods that include: providing input information in an electronic format; converting at least a part of the electronic input information into an optical input vector; optically transforming the optical input vector into an optical output vector based on an optical matrix multiplication; converting the optical output vector into an electronic format; and electronically applying a non-linear transformation to the electronically converted optical output vector to provide output information in an electronic format. In some examples, a set of multiple input values are encoded on respective optical signals carried by optical waveguides. For each of at least two subsets of one or more optical signals, a corresponding set of one or more copying modules splits the subset of one or more optical signals into two or more copies of the optical signals. For each of at least two copies of a first subset of one or more optical signals, a corresponding multiplication module multiplies the one or more optical signals of the first subset by one or more matrix element values using optical amplitude modulation. For results of two or more of the multiplication modules, a summation module produces an electrical signal that represents a sum of the results of the two or more of the multiplication modules.

An optoelectronic computing system includes a first semiconductor die having a photonic integrated circuit (PIC) and a second semiconductor die having an electronic integrated circuit (EIC). The PIC includes optical waveguides, in which input values are encoded on respective optical signals carried by the optical waveguides. The PIC includes an optical copying distribution network having optical splitters. The PIC includes an array of optoelectronic circuitry sections, each receiving an optical wave from one of the output ports of the optical copying distribution network, and each optoelectronic circuitry section includes: at least one photodetector detecting at least one optical wave from the optoelectronic operation. The EIC includes electrical input ports receiving respective electrical values. The first semiconductor die and the second semiconductor die are electrically coupled in a controlled collapse chip connection, with the electrical output port of the PIC connected to one of the electrical input ports of the EIC.

A quantum information processing system comprises a light source, a detector, at least one spatial light modulator and at least one optical lens. The light source is configured to provide a beam of entangled photons. The at least one optical lens is configured to project the resultant beam onto the spatial light modulator, either by direct imaging or by performing a full or partial optical Fourier transform. Said spatial light modulator includes a plurality of discrete pixels and is configured to select one or more of the plurality of discrete pixels to generate a resultant beam from said beam of entangled photons. The resultant beam from said spatial light modulator is projected onto the detector. For optical computation, such as search algorithms, the configuration and projections are repeated to find the optimal solution.

A quantum information processing system comprises a light source, a detector, at least one spatial light modulator and at least one optical lens. The light source is configured to provide a beam of entangled photons. The at least one optical lens is configured to project the resultant beam onto the spatial light modulator, either by direct imaging or by performing a full or partial optical Fourier transform. Said spatial light modulator includes a plurality of discrete pixels and is configured to select one or more of the plurality of discrete pixels to generate a resultant beam from said beam of entangled photons. The resultant beam from said spatial light modulator is projected onto the detector. For optical computation, such as search algorithms, the configuration and projections are repeated to find the optimal solution.

Systems and methods that include: providing input information in an electronic format; converting at least a part of the electronic input information into an optical input vector; optically transforming the optical input vector into an optical output vector based on an optical matrix multiplication; converting the optical output vector into an electronic format; and electronically applying a non-linear transformation to the electronically converted optical output vector to provide output information in an electronic format. In some examples, a set of multiple input values are encoded on respective optical signals carried by optical waveguides. For each of at least two subsets of one or more optical signals, a corresponding set of one or more copying modules splits the subset of one or more optical signals into two or more copies of the optical signals. For each of at least two copies of a first subset of one or more optical signals, a corresponding multiplication module multiplies the one or more optical signals of the first subset by one or more matrix element values using optical amplitude modulation. For results of two or more of the multiplication modules, a summation module produces an electrical signal that represents a sum of the results of the two or more of the multiplication modules.