Abstract: A computing system includes: a computational engine having a plurality of processing elements arrayed in accordance with a grid topology, wherein each of the plurality of processing elements is configured to perform one of a plurality of processing functions, and wherein the plurality of processing functions include a principal function, a kernel function, a routing function, and a reducer function; and a host processor having at least one processing circuit and at least one memory that stores operational instructions that, when executed by the at least one processing circuit, cause the at least one processor to: receive a task input; and control the computational engine in accordance with an iterative reduce-broadcast-apply process to generate a task output that is based on the task input.

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: 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 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.

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.