Multi-pass system for emulating a quantum computer and methods for use therewith

1. A system for emulating sampling of a quantum computer having a plurality of qubits arranged in a grid topology with N columns, the system comprising:

a memory that stores operational instructions;

at least one classical processor that is configured by the operational instructions to perform operations, the operations including:

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, and wherein the preliminary weights and variable assignments for a selected column of the corresponding subset of the N columns is based on the preliminary weights and variable assignments generated for a column adjacent to the selected column of the corresponding subset of the N columns;

wherein the sampling of the quantum computer having the plurality of qubits is emulated by a sample based on the final weights and variable assignments for each of the N columns.

2. The system of claim 1 , wherein a first iterative pass of the N iterative passes generates the final weights and variable assignments for an Nth column of the N columns, based on the preliminary weights and variable assignments generated for a (N−1)st column of the N columns.

3. The system of claim 2 , wherein the corresponding subset of the N columns associated with the first iterative pass of the N iterative passes includes all columns of the N columns in a range between a second column of the N columns and the (N−1)st column of the N columns.

4. The system of claim 2 , wherein the first iterative pass of the N iterative passes generates the preliminary weights and variable assignments for a first column of the N columns, based on null weights corresponding to a null column.

5. The system of claim 2 , wherein the last iterative pass of the N iterative passes generates the final weights and variable assignments for a first column of the N columns, based on the final weights and variable assignments for a second column of the N columns.

6. The system of claim 1 , wherein each of the N iterative passes generates the final weights and variable assignments for a corresponding one of the N columns.

7. The system of claim 1 , wherein a pth iterative pass of the N iterative passes generates the final weights and variable assignments for an (N−p+1)st column of the N columns, based on the preliminary weights and variable assignments generated for a (N−p)th column of the N columns.

8. The system of claim 7 , wherein the corresponding subset of the N columns associated with the pth iterative pass of the N iterative passes includes all columns of the N columns in a range between a second column of the N columns and the (N−p)th column of the N columns.

9. The system of claim 1 , wherein the grid topology corresponds to a quadratic unconstrained binary optimization (QUBO) model.

10. The system of claim 1 , wherein the sample corresponds to a Boltzmann distribution.

11. A system for emulating sampling of a quantum computer having a plurality of qubits arranged in a grid topology with N columns, the system comprising:

a memory that stores operational instructions;

at least one classical processor that is configured by the operational instructions to perform operations, the operations including:

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 number of columns of the N columns based on preliminary weights and variable assignments generated for an adjacent column for each of the number of columns, wherein final weights and variable assignments are generated for a final column of the N columns for each of the N iterative passes based on the preliminary weights and variable assignments generated for a column of the N columns adjacent to the final column of the N columns, wherein the final weights and variable assignments for the final column of the N columns are used in a next successive pass of the N iterative passes to reduce the number of columns of the N columns where the preliminary weights and variable assignments are regenerated until the N iterative passes are complete and final weights and variable assignments for each of the N columns have been generated;

wherein the sampling of the quantum computer having the plurality of qubits is emulated by a sample based on the final weights and variable assignments for each of the N columns.

12. The system of claim 11 , wherein producing the preliminary weights and variable assignments for the N columns based on the N iterative passes includes:

performing a first pass of the N iterative passes through the grid topology wherein a Nth column of the N columns corresponds to the final column, and wherein the number of columns of the N columns where preliminary weights and variable assignments are generated is equal to N−1.

13. The system of claim 12 , wherein producing the preliminary weights and variable assignments for the N columns based on the N iterative passes includes:

performing N−1 other passes of the N iterative passes through the grid topology by:

(a) setting p=2;

(b) performing an pth pass through the grid topology, wherein the (N−p+1)th column of the N columns corresponds to the final column, and wherein the number of columns of the N columns where preliminary weights and variable assignments are regenerated is equal to (N−p);

(c) incrementing p; and

(d) repeating steps (b) and (c) until p=N.

14. The system of claim 12 , wherein the first pass of the N iterative passes through the grid topology includes generating the preliminary weights and variable assignments for a first column of the N columns based on null weights corresponding to a null column.

15. The system of claim 11 , wherein the grid topology corresponds to a quadratic unconstrained binary optimization (QUBO) model.

16. The system of claim 11 , wherein the sample corresponds to a Boltzmann distribution.

17. A method for emulating sampling of a quantum computer having a plurality of qubits arranged in a grid topology with N columns, the method comprising:

performing a first iterative pass through the grid topology to produce final weights and variable assignments for a Nth column of the N columns, by generating preliminary weights and variable assignments for N−1 columns of the N columns based on preliminary weights and variable assignments generated for an adjacent column for each of the N−1 columns, wherein the final weights and variable assignments are generated for the Nth column based on the preliminary weights and variable assignments generated for an (N−1)st column of the N columns adjacent to the Nth column;

performing N−1 other iterative passes of N iterative passes through the grid topology by:

(a) setting p=2;

(b) performing an pth pass through the grid topology, to produce final weights and variable assignments for the (N−p+1)st column of the N columns, by regenerating preliminary weights and variable assignments for N−p columns of the N columns based on preliminary weights and variable assignments regenerated for an adjacent column for each of the N−p columns, wherein the final weights and variable assignments are generated for the (N−p+1)st column based on the preliminary weights and variable assignments regenerated for an (N−p)th column of the N columns adjacent to the (N−p+1)st column and the final weights and variable assignments generated for the (N−p+2)nd column;

(c) incrementing p;

(d) repeating steps (b) and (c) until p=N; and

(e) performing a final pass through the grid topology, to produce final weights and variable assignments for a first column of the N columns, based on the final weights and variable assignments generated for a second column of the N columns;

wherein the sampling of the quantum computer having the plurality of qubits is emulated by a sample based on the final weights and variable assignments for each of the N columns.

18. The method of claim 17 , wherein the first iterative pass of the N iterative passes through the grid topology includes generating the preliminary weights and variable assignments for the first column of the N columns based on null weights corresponding to a null column adjacent to the first column of the N columns.

19. The method of claim 17 , wherein the grid topology corresponds to a quadratic unconstrained binary optimization (QUBO) model.

20. The method of claim 17 , wherein the sample corresponds to a Boltzmann distribution.