Abstract: In methods and systems for estimating a gradient, a time-dependent unitary U and its derivative are computed with respect to a free parameter ?i within a time interval for a pulse program for a quantum system, ?i characterizing at least one of the pulse's shape, amplitude, phase, start time, and end time. The linear equation system ??iU=U*i? is solved for the effective generator ? that is an element of the dynamical Lie algebra generated by the evolution under the time-dependent unitary U. ? is decomposed into a sum of operators Pk, and the gradient of the circuit expectation value of the quantum system is computed with respect to ?i for each operator Pk using a parameter-shift method. In a method for constructing a pulse program, a candidate pulse is added if its evolution generator commutes with all generators of all dynamical Lie algebras during the same time interval.

Abstract: An apparatus includes a plurality of processing layers coupled in series. Each processing layer in the plurality of processing layers includes a Gaussian unit configured to perform a linear transformation on an input signal including a plurality of optical modes. The Gaussian unit includes a network of interconnected beamsplitters and phase shifters and a plurality of squeezers operatively coupled to the network of interconnected beamsplitters and phase shifters. Each processing layer also includes a plurality of nonlinear gates operatively coupled to the Gaussian unit and configured to perform a nonlinear transformation on the plurality of optical modes. The apparatus also includes a controller operatively coupled to the plurality of processing layers and configured to control a setting of the plurality of processing layers.

Abstract: An apparatus includes a light source to provide a plurality of input optical modes in a squeezed state. The apparatus also includes a network of interconnected reconfigurable beam splitters (RBSs) configured to perform a unitary transformation of the plurality of input optical modes to generate a plurality of output optical modes. An array of photon counting detectors is in optical communication with the network of interconnected RBSs and configured to measure the number of photons in each mode of the plurality of the output optical modes after the unitary transformation. The apparatus also includes a controller operatively coupled to the light source and the network of interconnected RBSs. The controller is configured to control at least one of the squeezing factor of the squeezed state of light, the angle of the unitary transformation, or the phase of the unitary transformation.

Abstract: A system, method, and computer program product for optimizing quantum computer programs using multi-level intermediate representations are provided. An intermediate representation of a high-level quantum program defined in a high-level programming language can be determined. An optimized version of the intermediate representation can be generated according to optimization transformations. The optimization transformations can be associated with an intermediate numerical representation or an intermediate quantum representation. The optimized versions of the intermediate representations can then be used to generate a compiled quantum program that can be used for execution by quantum hardware and/or a quantum simulator.

Abstract: An apparatus includes a light source to provide a plurality of input optical modes in a squeezed state. The apparatus also includes a network of interconnected reconfigurable beam splitters (RBSs) configured to perform a unitary transformation of the plurality of input optical modes to generate a plurality of output optical modes. An array of photon counting detectors is in optical communication with the network of interconnected RBSs and configured to measure the number of photons in each mode of the plurality of the output optical modes after the unitary transformation. The apparatus also includes a controller operatively coupled to the light source and the network of interconnected RBSs. The controller is configured to control at least one of the squeezing factor of the squeezed state of light, the angle of the unitary transformation, or the phase of the unitary transformation.

Abstract: An apparatus includes a plurality of processing layers coupled in series. Each processing layer in the plurality of processing layers includes a Gaussian unit configured to perform a linear transformation on an input signal including a plurality of optical modes. The Gaussian unit includes a network of interconnected beamsplitters and phase shifters and a plurality of squeezers operatively coupled to the network of interconnected beamsplitters and phase shifters. Each processing layer also includes a plurality of nonlinear gates operatively coupled to the Gaussian unit and configured to perform a nonlinear transformation on the plurality of optical modes. The apparatus also includes a controller operatively coupled to the plurality of processing layers and configured to control a setting of the plurality of processing layers.

Abstract: An apparatus includes a light source to provide a plurality of input optical modes in a squeezed state. The apparatus also includes a network of interconnected reconfigurable beam splitters (RBSs) configured to perform a unitary transformation of the plurality of input optical modes to generate a plurality of output optical modes. An array of photon counting detectors is in optical communication with the network of interconnected RBSs and configured to measure the number of photons in each mode of the plurality of the output optical modes after the unitary transformation. The apparatus also includes a controller operatively coupled to the light source and the network of interconnected RBSs. The controller is configured to control at least one of the squeezing factor of the squeezed state of light, the angle of the unitary transformation, or the phase of the unitary transformation.

Abstract: An apparatus includes a plurality of processing layers coupled in series. Each processing layer in the plurality of processing layers includes a Gaussian unit configured to perform a linear transformation on an input signal including a plurality of optical modes. The Gaussian unit includes a network of interconnected beamsplitters and phase shifters and a plurality of squeezers operatively coupled to the network of interconnected beamsplitters and phase shifters. Each processing layer also includes a plurality of nonlinear gates operatively coupled to the Gaussian unit and configured to perform a nonlinear transformation on the plurality of optical modes. The apparatus also includes a controller operatively coupled to the plurality of processing layers and configured to control a setting of the plurality of processing layers.

Abstract: An apparatus includes a light source to provide a plurality of input optical modes in a squeezed state. The apparatus also includes a network of interconnected reconfigurable beam splitters (RBSs) configured to perform a unitary transformation of the plurality of input optical modes to generate a plurality of output optical modes. An array of photon counting detectors is in optical communication with the network of interconnected RBSs and configured to measure the number of photons in each mode of the plurality of the output optical modes after the unitary transformation. The apparatus also includes a controller operatively coupled to the light source and the network of interconnected RBSs. The controller is configured to control at least one of the squeezing factor of the squeezed state of light, the angle of the unitary transformation, or the phase of the unitary transformation.

Abstract: An apparatus includes a plurality of processing layers coupled in series. Each processing layer in the plurality of processing layers includes a Gaussian unit configured to perform a linear transformation on an input signal including a plurality of optical modes. The Gaussian unit includes a network of interconnected beamsplitters and phase shifters and a plurality of squeezers operatively coupled to the network of interconnected beamsplitters and phase shifters. Each processing layer also includes a plurality of nonlinear gates operatively coupled to the Gaussian unit and configured to perform a nonlinear transformation on the plurality of optical modes. The apparatus also includes a controller operatively coupled to the plurality of processing layers and configured to control a setting of the plurality of processing layers.