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 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 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 method is presented for use with a quantum circuit and a quantum register having a plurality of qubits. The method includes: sequentially calling, via a plurality of oracle gates of the quantum circuit, a quantum oracle operator on a plurality of qubit states to produce a sequence of quantum oracle calls; applying, via a plurality of diffusion gates of the quantum circuit, 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 oracle calls; and generating a quantum computing result based on a measurement from the plurality of qubits, after having applied the sequence of oracle calls and the plurality of diffusion operators.