Abstract: A method and a quantum circuit operate by: applying, via Hadamard gates of the quantum circuit, Hadamard transforms to qubits in corresponding initial states; sequentially calling, via weighted oracle gates of the quantum circuit, a weighted oracle operator on the qubits to produce a sequence of quantum oracle calls, wherein the weighted oracle operator for the qubits applies an adjustable phase rotation at each of the quantum oracle calls in the sequence of quantum oracle calls and wherein the weighted oracle operator for each one of the qubits is in accordance with a weight associated with the one of the qubits; applying, via diffusion gates of the quantum circuit, diffusion operators; and generating a quantum computing result based on a measurement from the qubits, after having applied the sequence of quantum oracle calls and the diffusion operators.

Abstract: A controlled quantum logic gate implements a replacement for an n?1 qubit controlled X gate function to n qubits, wherein n is greater than 4. The quantum logic gate includes a controlled gate or controlled Z gate equivalent that selectively applies, under control of a first subset of the n qubits, a pi radian Z-axis Bloch sphere rotation or a phase flip to a target qubit of the n qubits. A pair of controlled Hadamard gates selectively conjugate the target qubit under control of a second subset of the n qubits.

Abstract: A controlled quantum logic gate implements a replacement for an n?1 qubit controlled X gate function to n qubits, wherein n is greater than 4. The quantum logic gate includes a controlled gate or controlled Z gate equivalent that selectively applies, under control of a first subset of the n qubits, a pi radian Z-axis Bloch sphere rotation or a phase flip to a target qubit of the n qubits. A pair of controlled Hadamard gates selectively conjugate the target qubit under control of a second subset of the n qubits.

Abstract: A quantum circuit includes a plurality of Hadamard gates apply Hadamard transforms to a plurality of qubits in a corresponding plurality of initial states. A plurality of weighted oracle gates sequentially call a weighted oracle operator on the plurality of qubits to produce a sequence of quantum oracle calls, wherein the weighted oracle operator for the plurality of qubits applies an adjustable phase rotation at each of the quantum oracle calls in the sequence of quantum oracle calls. A plurality of diffusion gates apply a plurality of diffusion operators, wherein a selected one or more of a plurality of diffusion operators is applied after each of the quantum oracle calls in the sequence of quantum oracle calls. A measurement function generates a quantum computing result based on a measurement from the plurality of qubits, after the sequence of quantum oracle calls are applied and after the plurality of diffusion operators are applied.

Abstract: A quantum circuit includes a state preparation circuit, that prepares an n choose k state on n qubits, an oracle, and a microdiffuser circuit. Wherein, for each in a sequence of iterations, the oracle and the microdiffuser circuit are applied, wherein the microdiffuser circuit operates on a subset of n qubits of varying size over the sequence of iterations, wherein for the jth iteration of the sequence of iterations, the microdiffuser circuit operates on a subset of n qubits of size mj, and wherein a measurement is applied to the n qubits.

Abstract: A TDGn quantum circuit on n wires includes a first set of circuits and a plurality of CX gates appended to the first set of circuits to generate a plurality of additional circuits, wherein each of the additional circuits is formed by appending a CX gate of the plurality of CX gates in a corresponding one of a plurality of configurations to one circuit of a first set of circuits. The TDGn quantum circuit further includes a second set of circuits, wherein the second set of circuits is generated by an iterative selection procedure.

Abstract: A controlled quantum logic gate implements a n?1 qubit controlled Z gate function based on n qubits and an ancilla qubit, wherein n is greater than 3. The quantum logic gate includes a plurality of leading gates that operate on the at least one ancilla qubit to generate an ancilla qubit state in response to an initial state of the ancilla bit and each of the n qubits. A measurement operates on the ancilla qubit state to generate a classical ancilla bit state. At least one following gate includes at least one controlled Z gate equivalent that operates under control of at least one of the n qubits and further under control of the classical ancilla bit state to selectively apply a phase adjustment to at least another one of the n qubits.

Abstract: A controlled quantum logic gate implements a n?1 qubit controlled Z gate function based on n qubits and an ancilla qubit, wherein n is greater than 3. The quantum logic gate includes a plurality of leading gates that operate on the at least one ancilla qubit to generate an ancilla qubit state in response to an initial state of the ancilla bit and each of the n qubits. A measurement operates on the ancilla qubit state to generate a classical ancilla bit state. At least one following gate includes at least one controlled Z gate equivalent that operates under control of at least one of the n qubits and further under control of the classical ancilla bit state to selectively apply a phase adjustment to at least another one of the n qubits.

Abstract: A controlled quantum logic gate implements a replacement for an n?1 qubit controlled X gate function to n qubits, wherein n is greater than 4. The quantum logic gate includes a controlled gate or controlled Z gate equivalent that selectively applies, under control of a first subset of the n qubits, a pi radian Z-axis Bloch sphere rotation or a phase flip to a target qubit of the n qubits. A pair of controlled Hadamard gates selectively conjugate the target qubit under control of a second subset of the n qubits.

Abstract: Sampling of a plurality of qubits arranged in a grid topology with N columns is emulated by: producing final weights and variable assignments for the N columns based on N iterative passes through the grid topology, wherein the final weights and variable assignments for a selected column of the N columns is based on preliminary weights and variable assignments generated for a column adjacent to the selected column of the N columns; and emulating a sample the plurality of qubits based on the final weights and variable assignments for each of the N columns.

Abstract: A system is presented for emulating sampling of a quantum computer having a plurality of qubits arranged in a grid topology with N columns. The system includes a classical processor that is configured by operational instructions to perform operations that include producing final weights and variable assignments for the N columns based on N iterative passes through the grid topology, wherein each of the N iterative passes generates preliminary weights and variable assignments for a corresponding subset of the N columns, wherein the preliminary weights and variable assignments for a selected column of the corresponding subset based on the preliminary weights and variable assignments generated for a column adjacent to the selected column of the corresponding subset, and wherein the sampling of the quantum computer having the plurality of qubits is emulated by producing a plurality of samples from the N iterative passes based on the final weights and variable assignments for each of the N columns.

Abstract: A system is presented for emulating sampling of a quantum computer having a plurality of qubits arranged in a grid topology with N columns. The system includes a classical processor that is configured by operational instructions to perform operations that include producing final weights and variable assignments for the N columns based on N iterative passes through the grid topology, wherein each of the N iterative passes generates preliminary weights and variable assignments for a corresponding subset of the N columns, wherein the preliminary weights and variable assignments for a selected column of the corresponding subset based on the preliminary weights and variable assignments generated for a column adjacent to the selected column of the corresponding subset, and wherein the sampling of the quantum computer having the plurality of qubits is emulated by producing a plurality of samples from the N iterative passes based on the final weights and variable assignments for each of the N columns.

Abstract: A system is presented for emulating sampling of a quantum computer having a plurality of qubits arranged in a grid topology with N columns. The system includes a classical processor that is configured by operational instructions to perform operations that include producing final weights and variable assignments for the N columns based on N iterative passes through the grid topology, wherein each of the N iterative passes generates preliminary weights and variable assignments for a corresponding subset of the N columns, wherein the preliminary weights and variable assignments for a selected column of the corresponding subset based on the preliminary weights and variable assignments generated for a column adjacent to the selected column of the corresponding subset, and wherein the sampling of the plurality of qubits is emulated by a sample based on the final weights and variable assignments for each of the N columns.

Abstract: A system is presented for emulating sampling of a quantum computer having a plurality of qubits arranged in a grid topology with N columns. The system includes a classical processor that is configured by operational instructions to perform operations that include producing final weights and variable assignments for the N columns based on N iterative passes through the grid topology, wherein each of the N iterative passes generates preliminary weights and variable assignments for a corresponding subset of the N columns, wherein the preliminary weights and variable assignments for a selected column of the corresponding subset based on the preliminary weights and variable assignments generated for a column adjacent to the selected column of the corresponding subset, and wherein the sampling of the plurality of qubits is emulated by a sample based on the final weights and variable assignments for each of the N columns.