A hybrid computing system for solving a computational problem includes a digital processor, a quantum processor having qubits and coupling devices that together define a working graph of the quantum processor, and at least one nontransitory processor-readable medium communicatively coupleable to the digital processor which stores at least one of processor-executable instructions or data. The digital processor receives a computational problem, and programs the quantum processor with a first set of bias fields and a first set of coupling strengths. The quantum processor generates samples as potential solutions to an approximation of the problem. The digital processor updates the approximation by determining a second set of bias fields based at least in part on the first set of bias fields and a first set of mean fields that are based at least in part on the first set of samples and coupling strengths of one or more virtual coupling devices.

A hybrid computing system for solving a computational problem includes a digital processor, a quantum processor having qubits and coupling devices that together define a working graph of the quantum processor, and at least one nontransitory processor-readable medium communicatively coupleable to the digital processor which stores at least one of processor-executable instructions or data. The digital processor receives a computational problem, and programs the quantum processor with a first set of bias fields and a first set of coupling strengths. The quantum processor generates samples as potential solutions to an approximation of the problem. The digital processor updates the approximation by determining a second set of bias fields based at least in part on the first set of bias fields and a first set of mean fields that are based at least in part on the first set of samples and coupling strengths of one or more virtual coupling devices.

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.

Embodiments relate to a method for estimating an amplitude of a unitary operator U to within an error ε by using a quantum processor configurable to implement the unitary operator U on a quantum circuit. The quantum circuit has a maximum depth S can implement the unitary operator no more than D times in a single run. A schedule of iterations n=1 to N based on the error ε and number D is determined. Each iteration n characterized by a schedule parameter kn. kn≤D for all n and kn increases at a rate that is less than exponential. The iterations n may be sequentially executed. In each iteration, the quantum processor is configured to sequentially apply and execute the unitary operator U kn times on the quantum circuit. A non-quantum processor then estimates the amplitude of the unitary operator U based on the measured resulting states.

A conversion method according to the present disclosure, is a method of converting an objective function of combinatorial optimization related to encoding and decoding into a form of an Ising model, the conversion of the objective function into the form of the Ising model being performed by the conversion method, and the method includes: removing a modulo 2 operation from the objective function by using first transformation; replacing a first variable to be optimized included in the objective function with a second variable corresponding to an Ising spin by using second transformation; and reducing a degree related to the second variable of the objective function by using third transformation.

A conversion method according to the present disclosure, is a method of converting an objective function of combinatorial optimization related to encoding and decoding into a form of an Ising model, the conversion of the objective function into the form of the Ising model being performed by the conversion method, and the method includes: removing a modulo 2 operation from the objective function by using first transformation; replacing a first variable to be optimized included in the objective function with a second variable corresponding to an Ising spin by using second transformation; and reducing a degree related to the second variable of the objective function by using third transformation.

A system and method for mitigating flux trapping in a superconducting integrated circuit. A first metal layer is formed having a first critical temperature and a first device, and a flux directing layer is formed having a second critical temperature. The flux directing layer is positioned in communication with an aperture location, and the aperture location is spaced from the first device to isolate the first device from flux trapped in the aperture. The superconducting integrated circuit is cooled from a first temperature that is above both the first and second critical temperatures to a second temperature that is less than both the first and second critical temperatures by a cryogenic refrigerator. A relative temperature difference between the first and second critical temperatures causes the flux directing layer to direct flux away from the first device and trap flux at the aperture location.

In a quantum computer, quantum algorithms are performed by a qubit interacting with multiple quantum control pulses. The quantum control pulses are electromagnetic RF signals that are generated digitally at baseband and sent, via asynchronous ports, to DACs that feed an RF upconversion circuit. For synchronization, each asynchronous port is coupled to a multi-tap delay line. The setting of the multi-tap delay line is determined by a function of the port's setup-and-hold time. This function is trained, via machine learning, to be applicable across a variety of ports.

In a quantum computer, quantum algorithms are performed by a qubit interacting with multiple quantum control pulses. The quantum control pulses are electromagnetic RF signals that are generated digitally at baseband and sent, via asynchronous ports, to DACs that feed an RF upconversion circuit. For synchronization, each asynchronous port is coupled to a multi-tap delay line. The setting of the multi-tap delay line is determined by a function of the port's setup-and-hold time. This function is trained, via machine learning, to be applicable across a variety of ports.

Methods, systems, and apparatus for solving computational tasks using quantum computing resources. In one aspect a method includes receiving, at a quantum formulation solver, data representing a computational task to be performed; deriving, by the quantum formulation solver, a formulation of the data representing the computational task that is formulated for a selected type of quantum computing resource; routing, by the quantum formulation solver, the formulation of the data representing the computational task to a quantum computing resource of the selected type to obtain data representing a solution to the computational task; generating, at the quantum formulation solver, output data including data representing a solution to the computational task; and receiving, at a broker, the output data and generating one or more actions to be taken based on the output data.