Abstract: Methods and systems for solving various computational problems with quantum processors are provided. Such quantum processors comprise a plurality of quantum devices together with a plurality of coupling devices. The quantum processor is initialized by setting states of the quantum devices and coupling devices and allowed to evolve to a final state which approximates a natural ground state of the computational problem. The final state can include values of nodes arranged in a lattice in the quantum processor and can represent a solution to the computational processor. The computational problem can have complexity P, NP, NP-Hard, or NP-Complete and may be mapped to a quantum processor with nearest-neighbor and next-nearest-neighbor couplings. The solution to the computational problem can be read out from the quantum processor and transmitted as a data signal embodied in a carrier wave.

Abstract: Methods and systems represent constraint as an Ising model penalty function and a penalty gap associated therewith, the penalty gap separating a set of feasible solutions to the constraint from a set of infeasible solutions to the constraint; and determines the Ising model penalty function subject to the bounds on the programmable parameters imposed by the hardware limitations of the second processor, where the penalty gap exceeds a predetermined threshold greater than zero. Such may be employed to find quantum binary optimization problems and associated gap values employing a variety of techniques.

Abstract: Quantum annealing may include applying and gradually removing disorder terms to qubits of a quantum processor, for example superconducting flux qubits of a superconducting quantum processor. A problem Hamiltonian may be established by applying control signals to the qubits, an evolution Hamiltonian established by applying disorder terms, and annealing by gradually removing the disorder terms. Change in persistent current in the qubits may be compensated. Multipliers may mediate coupling between various qubits and a global signal line, for example by applying respective scaling factors. Two global signal lines may be arranged in an interdigitated pattern to couple to respective qubits of a communicatively coupled pair of qubits. Pairs of qubits may be communicatively isolated and used to measure a response of one another to defined signals.

Abstract: A structure comprising (i) a first information device, (ii) a second information device, (iii) a first coupling element and (iv) a second coupling element is provided. The first information device has at least a first lobe and a second lobe that are in electrical communication with each other. The second information device and has at least a first lobe and a second lobe that are in electrical communication with each other. The first coupling element inductively couples the first lobe of the first information device to the first lobe of the second information device. The second coupling element inductively couples the first lobe of the first information device to the second lobe of the second information device.

Abstract: A structure comprising (i) a first information device, (ii) a second information device, (iii) a first coupling element and (iv) a second coupling element is provided. The first information device has at least a first lobe and a second lobe that are in electrical communication with each other. The second information device and has at least a first lobe and a second lobe that are in electrical communication with each other. The first coupling element inductively couples the first lobe of the first information device to the first lobe of the second information device. The second coupling element inductively couples the first lobe of the first information device to the second lobe of the second information device.

Abstract: Systems and methods for copying the classical state of a source qubit to a target qubit are provided. These techniques may be used to read out the states of an array of qubits.

Abstract: A structure comprising (i) a first information device, (ii) a second information device, (iii) a first coupling element and (iv) a second coupling element is provided. The first information device has at least a first lobe and a second lobe that are in electrical communication with each other. The second information device and has at least a first lobe and a second lobe that are in electrical communication with each other. The first coupling element inductively couples the first lobe of the first information device to the first lobe of the second information device. The second coupling element inductively couples the first lobe of the first information device to the second lobe of the second information device.

Abstract: A quantum processing apparatus includes a qubit, a superconducting bus, and a controllable coupling mechanism that controllably couples the superconducting bus to the qubit. The controllable coupling mechanism is characterized by a first state in which the superconducting bus and the qubit are capacitively coupled, thereby permitting a coupling operation to be performed between a quantum device, coupled to the superconducting bus, and the qubit. The controllable coupling mechanism is also characterized by a second state in which the superconducting bus and the qubit are capacitively uncoupled such that the qubit and the quantum device are not coupled to each other.

Abstract: Analog processors for solving various computational problems are provided. Such analog processors comprise a plurality of quantum devices, arranged in a lattice, together with a plurality of coupling devices. The analog processors further comprise bias control systems each configured to apply a local effective bias on a corresponding quantum device. A set of coupling devices in the plurality of coupling devices is configured to couple nearest-neighbor quantum devices in the lattice. Another set of coupling devices is configured to couple next-nearest neighbor quantum devices. The analog processors further comprise a plurality of coupling control systems each configured to tune the coupling value of a corresponding coupling device in the plurality of coupling devices to a coupling. Such quantum processors further comprise a set of readout devices each configured to measure the information from a corresponding quantum device in the plurality of quantum devices.

Abstract: The present invention involves a quantum computing apparatus that includes a substrate attached to which is a flux shield upon which is at least one element of circuitry. The flux shield has an aperture. Inside the aperture is a superconducting structure. The superconducting structure and the circuitry interact so that a change in a state of the superconducting structure can be detected by the circuitry. The present invention provides a method for initializing and measuring the state of a superconducting structure by adjusting and measuring the current in an element of circuitry coupled to the structure by a flux shield. The present invention provides a mechanism for coupling qubits. In embodiments of the present invention, qubits are selectively coupled by a coupling circuit that can be on a second substrate. The coupling of the qubit to the coupling circuit is enhanced by the presence of a flux shield.

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 solid-state quantum computing structure includes a d-wave superconductor in sets of islands that clean Josephson junctions separate from a first superconducting bank. The d-wave superconductor causes the ground state for the supercurrent at each junction to be doubly degenerate, with two supercurrent ground states having distinct magnetic moments. These quantum states of the supercurrents at the junctions create qubits for quantum computing. The quantum states can be uniformly initialized from the bank, and the crystal orientations of the islands relative to the bank influence the initial quantum state and tunneling probabilities between the ground states. A second bank, which a Josephson junction separates from the first bank, can be coupled to the islands through single electron transistors for selectably initializing one or more of the supercurrents in a different quantum state. Single electron transistors can also be used between the islands to control entanglements while the quantum states evolve.

Abstract: A structure comprising a tank circuit inductively coupled to a flux qubit or a phase qubit. In some embodiments, a low temperature preamplifier is in electrical communication with the tank circuit. The tank circuit comprises an effective capacitance and an effective inductance that are in parallel or in series. In some embodiments, the effective inductance comprises a multiple winding coil of wire. A method that includes the steps of (i) providing a tank circuit and a phase qubit that are inductively coupled, (ii) reading out a state of the phase qubit, (iii) applying a flux to the phase qubit that approaches a net zero flux, (iv) increasing a level of flux applied to the phase qubit, and (v) observing a response of the tank circuit in a readout device.

Abstract: A solid-state quantum computing qubit includes a multi-terminal junction coupled to a superconducting loop where the superconducting loop introduces a phase shift to the superconducting order parameter. The ground state of the supercurrent in the superconducting loop and multi-terminal junction is doubly degenerate, with two supercurrent ground states having distinct magnetic moments. These quantum states of the supercurrents in the superconducting loop create qubits for quantum computing. The quantum states can be initialized by applying transport currents to the external leads. Arbitrary single qubit operations may be performed by varying the transport current and/or an externally applied magnetic field. Read-out may be performed using direct measurement of the magnetic moment of the qubit state, or alternatively, radio-frequency single electron transistor electrometers can be used as read-out devices when determining a result of the quantum computing.

Abstract: A superconducting structure that can operate, for example, as a qubit or a superconducting switch is presented. The structure includes a loop formed from two parts. A first part includes two superconducting materials separated by a junction. The junction can, for example, be a 45° grain boundary junction. The second part can couple the two superconducting materials across the junction. The second part includes a superconducting material coupled to each of the two superconducting materials of the first part through c-axis junctions. Further embodiments of the invention can be as a coherent unconventional superconducting switch, or a variable phase shift unconventional superconductor junction device.

Abstract: A circuit comprising a superconducting qubit and a resonant control system that is characterized by a resonant frequency. The resonant frequency of the control system is a function of a bias current. The circuit further includes a superconducting mechanism having a capacitance or inductance. The superconducting mechanism coherently couples the superconducting qubit to the resonant control system. A method for entangling a quantum state of a first qubit with the quantum state of a second qubit. In the method, a resonant control system, which is capacitively coupled to the first and second qubit, is tuned to a first frequency that corresponds to the energy differential between the lowest two potential energy levels of the first qubit. The resonant control system is then adjusted to a second frequency corresponding to energy differential between the lowest two potential energy levels of the second qubit.

Abstract: A method for quantum computing with a quantum system comprising a first energy level, a second energy level, and a third energy level. The first energy level and said second energy level are capable of being degenerate with respect to each other. In the method a signal is applied to the quantum system. The signal has an alternating amplitude at an associated frequency such that (i) the frequency of the signal correlates with an energy level separation between the first energy level and the third energy level or (ii) the frequency of the signal correlates with an energy level separation between the second energy level and the third energy level. The signal induces an oscillation in the state of the quantum system between the first energy level and the second energy level.

Abstract: A control system for an array of qubits is disclosed. The control system according to the present invention provides currents and voltages to qubits in the array of qubits in order to perform functions on the qubit. The functions that the control system can perform include read out, initialization, and entanglement. The state of a qubit can be determined by grounding the qubit, applying a current across the qubit, measuring the resulting potential drop across the qubit, and interpreting the potential drop as a state of the qubit. A qubit can be initialized by grounding the qubit and applying a current across the qubit in a selected direction for a time sufficient that the quantum state of the qubit can relax into the selected state. In some embodiments, the qubit can be initialized by grounding the qubit and applying a current across the qubit in a selected direction and then ramping the current to zero in order that the state of the qubit relaxes into the selected state.

Abstract: A method is provided for entangling a quantum state of a qubit with a quantum state of a resonant control system. The method comprises tuning the resonant control system, which is capacitively or inductively coupled to the qubit, to a resonant frequency for a period of time. The resonant frequency corresponds to an energy difference between a first energy level of the qubit and a second energy level of the qubit. The act of tuning entangles the quantum state of the qubit with the quantum state of the resonant control system. A representative resonant control system includes a Josephson junction. A method is also provided for entangling a quantum state of a qubit, within a plurality of qubits, with a quantum state of a resonant control system.

Abstract: A solid-state quantum computing qubit includes a multi-terminal junction coupled to a superconducting loop where the superconducting loop introduces a phase shift to the superconducting order parameter. The ground state of the supercurrent in the superconducting loop and multi-terminal junction is doubly degenerate, with two supercurrent ground states having distinct magnetic moments. These quantum states of the supercurrents in the superconducting loop create qubits for quantum computing. The quantum states can be initialized by applying transport currents to the external leads. Arbitrary single qubit operations may be performed by varying the transport current and/or an externally applied magnetic field. Read-out may be performed using direct measurement of the magnetic moment of the qubit state, or alternatively, radio-frequency single electron transistor electrometers can be used as read-out devices when determining a result of the quantum computing.