Abstract: An optimally stopped heuristic optimizer includes a processor. The processor heuristically generates a sequence of proposed solutions for solving a discrete optimization problem associated with an objective function, and for each additional proposed solution of the sequence, derives an estimate of a quality distribution that is based on the sequence including the additional proposed solution. The quality distribution assigns a probability to each of the proposed solutions according to quality of the proposed solution. The processor further, responsive to a most recent additional proposed solution of the sequence having quality better than a quality threshold that is defined by the estimate corresponding to the sequence including the most recent additional proposed solution, commands a stop such that further proposed solutions to the discrete optimization problem are no longer generated, and identifies and outputs a selected one of the sequence having best quality.

Abstract: Systems and methods of processing using a quantum processor are described. A method includes obtaining a problem Hamiltonian and defining a nested Hamiltonian with a plurality of logical qubits by embedding a logical KN representing the problem Hamiltonian into a larger KC×N, where N represents a number of the logical qubits and C represents a nesting level defining the amount of hardware resources for the nest Hamiltonian. The method also includes encoding the nested Hamiltonian into the plurality of physical qubits of the quantum processor; and performing a quantum annealing process with the quantum processor after the encoding.

Abstract: An optimally stopped heuristic optimizer includes a processor. The processor heuristically generates a sequence of proposed solutions for solving a discrete optimization problem associated with an objective function, and for each additional proposed solution of the sequence, derives an estimate of a quality distribution that is based on the sequence including the additional proposed solution. The quality distribution assigns a probability to each of the proposed solutions according to quality of the proposed solution. The processor further, responsive to a most recent additional proposed solution of the sequence having quality better than a quality threshold that is defined by the estimate corresponding to the sequence including the most recent additional, proposed solution, commands a stop such that further proposed solutions to the discrete optimization problem are no longer generated, and identifies and outputs a selected one of the sequence having best quality.

Abstract: Systems and methods of processing using a quantum processor are described. A method includes obtaining a problem Hamiltonian and defining a nested Hamiltonian with a plurality of logical qubits by embedding a logical KN representing the problem Hamiltonian into a larger KC×N, where N represents a number of the logical qubits and C represents a nesting level defining the amount of hardware resources for the nest Hamiltonian. The method also includes encoding the nested Hamiltonian into the plurality of physical qubits of the quantum processor; and performing a quantum annealing process with the quantum processor after the encoding.

Abstract: A quantum computing method comprising constructing a dressing transformation V between a physical Hamiltonian H and an ideal Hamiltonian HID. The physical Hamiltonian H describes a physical quantum computer that comprises a plurality of qubits, including interactions between the plurality of qubits and a continuum. The ideal Hamiltonian HID describes the universal quantum computer that corresponds to the physical quantum computer. Each qubit in the plurality of qubits is initialized and quantum calculations are performed using the plurality of qubits. Measurement of the plurality of qubits is performed in the dressed state.

Abstract: The present invention involves a quantum computing structure, comprising: one or more logical qubits, which is encoded into a plurality of superconducting qubits; and each of the logical qubits comprises at least one operating qubit and at least one ancilla qubit. Also provided is a method of quantum computing, comprising: performing encoded quantum computing operations with logical qubits that are encoded into superconducting operating qubits and superconducting ancilla qubits. The present invention further involves a method of error correction for a quantum computing structure comprising: presenting a plurality of logical qubits, each of which comprises an operating physical qubit and an ancilla physical qubit, wherein the logical states of the plurality of logical qubits are formed from a tensor product of the states of the operating and ancilla qubits; and wherein the states of the ancilla physical qubits are suppressed; and applying strong pulses to the grouping of logical qubits.

Abstract: The invention includes systems for and methods of performing quantum computation. The method of quantum computation includes preparing a set of one or more qubits capable of storing quantum information in 2n possible states, wherein the number of qubits n?1. The qubit set is subject to a decoherence mechanism that could cause a loss of quantum information stored in some but not all of the qubit states. The method also includes determining, via a quantum measurement of the qubit system or just by analyzing the decoherence of the qubit states, which of the 2n states or their superposition is/are not susceptible to decoherence. The method further includes encoding and processing quantum information in one or more of the decoherence-free states by controlling qubit-qubit interactions or via an electromagnetic interaction with the set of qubits.

Abstract: A method for performing a single-qubit gate on an arbitrary quantum state. An ancillary qubit is set to an initial state |I>. The data qubit is coupled to an ancillary qubit. The state of the ancillary qubit is measured, and the data qubit and the ancillary qubit are coupled for a first period of time. A method for applying a single-qubit gate to an arbitrary quantum state. A state of a first and second ancillary qubit are set to an entangled initial state |I>. A state of a data qubit and the first ancillary qubit are measured thereby potentially performing a single qubit operation on the arbitrary quantum state. A first result is determined. The first result indicates whether the single qubit operation applied the single qubit gate to the arbitrary quantum state.

Abstract: A quantum computing method comprising constructing a dressing transformation V between a physical Hamiltonian H and an ideal Hamiltonian HID. The physical Hamiltonian H describes a physical quantum computer that comprises a plurality of qubits, including interactions between the plurality of qubits and a continuum. The ideal Hamiltonian HID describes the universal quantum computer that corresponds to the physical quantum computer. Each qubit in the plurality of qubits is initialized and quantum calculations are performed using the plurality of qubits. Measurement of the plurality of qubits is performed in the dressed state.

Abstract: The present invention involves a quantum computing structure, comprising: one or more logical qubits, which is encoded into a plurality of superconducting qubits; and each of the logical qubits comprises at least one operating qubit and at least one ancilla qubit. Also provided is a method of quantum computing, comprising: performing encoded quantum computing operations with logical qubits that are encoded into superconducting operating qubits and superconducting ancilla qubits. The present invention further involves a method of error correction for a quantum computing structure comprising: presenting a plurality of logical qubits, each of which comprises an operating physical qubit and an ancilla physical qubit, wherein the logical states of the plurality of logical qubits are formed from a tensor product of the states of the operating and ancilla qubits; and wherein the states of the ancilla physical qubits are suppressed; and applying strong pulses to the grouping of logical qubits.

Abstract: The invention provides a system and method for quantum computation comprising the steps of defining a Hilbert space to represent a physical quantum mechanical system; selecting a set of quantum observables for said system; selecting a subspace of said Hilbert space in which all states representing said quantum mechanical system have the same eigenvalue; and storing information in or processing information using said subspace. In addition, the invention provides a system and method for quantum computation, comprising defining a Hilbert space to represent a physical quantum mechanical system; selecting a subspace of said Hilbert space in which the quantum mechanical state of the physical system is decoherence free; and processing quantum information using the quantum mechanical system by controlling only multi body interactions.