MAXIMUM-LIKELIHOOD DECODING OF QUANTUM CODES

Abstract

Techniques regarding quantum error correction are provided. For example, one or more embodiments described herein can comprise a system, which can comprise a memory that can store computer executable components. The system can also comprise a processor, operably coupled to the memory, and that can execute the computer executable components stored in the memory. The computer executable components can comprise a maximum-likelihood decoder component that executes a maximum-likelihood decoding algorithm to determine an error correction based on a decoding hypergraph that characterizes error-sensitive events associated with a quantum error-correcting code executed on a quantum circuit.

Description

Claims

1. A system, comprising: a memory that stores computer executable components; anda processor, operably coupled to the memory, and that executes the computer executable components stored in the memory, wherein the computer executable components comprise: a hypergraph component that: executes, using a quantum processor comprising qubits, a quantum error-correcting code on a quantum circuit, andgenerates a decoding hypergraph by mapping error-sensitive events associated with the executing of the quantum error-correcting code on the quantum circuit to faults of the quantum circuit.

2. The system of claim 1, wherein the decoding hypergraph comprises: nodes respectively corresponding to the error sensitive events, andhyperedges connecting the nodes, and wherein the respective hyperedges correlate the error sensitive events to one or more of the faults that are potential causes of the error sensitive events.

3. The system of claim 2, further comprising: a probability distribution component that assigns probability values to the hyperedges and generates a probability distribution based on the probability values.

4. The system of claim 1, further comprising: an error-sensitive event component that identifies the error-sensitive events by performing a Gottesman-Knill simulation of the quantum circuit.

5. The system of claim 1, further comprising: an error-sensitive event component that identifies the error-sensitive events by employing flag qubits associated with high-weight errors originating from low-weight errors.

6. The system of claim 1, wherein the error-sensitive events comprise linear combinations of syndrome measurement bits that would equate to zero in an ideal quantum circuit operation.

7. The system of claim 1, wherein the error-sensitive events depend on a topology of the quantum circuit.

8. A computer-implemented method, comprising: executing, by a system operatively coupled to a processor, using a quantum processor comprising qubits, a quantum error-correcting code on a quantum circuit; andgenerating, by the system, a decoding hypergraph by mapping error-sensitive events associated with the executing of the quantum error-correcting code on the quantum circuit to faults of the quantum circuit.

9. The computer-implemented method of claim 8, wherein the decoding hypergraph comprises: nodes respectively corresponding to the error sensitive events, andhyperedges connecting the nodes, and wherein the respective hyperedges correlate the error sensitive events to one or more of the faults that are potential causes of the error sensitive events.

10. The computer-implemented method of claim 9, further comprising: assigning, by the system, probability values to the hyperedges; and generating, by the system, a probability distribution based on the probability values.

11. The computer-implemented method of claim 8, further comprising: identifying, by the system, the error-sensitive events by performing a Gottesman-Knill simulation of the quantum circuit.

12. The computer-implemented method of claim 8, further comprising: identifying, by the system, the error-sensitive events by employing flag qubits associated with high-weight errors originating from low-weight errors.

13. The computer-implemented method of claim 8, wherein the error-sensitive events comprise linear combinations of syndrome measurement bits that would equate to zero in an ideal quantum circuit operation.

14. The computer-implemented method of claim 8, wherein the error-sensitive events depend on a topology of the quantum circuit.

15. A computer program product for quantum error correction, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause the processor to: execute, using a quantum processor comprising qubits, a quantum error-correcting code on a quantum circuit; andgenerate a decoding hypergraph by mapping error-sensitive events associated with the executing of the quantum error-correcting code on the quantum circuit to faults of the quantum circuit.

16. The computer program product of claim 15, wherein the decoding hypergraph comprises: nodes respectively corresponding to the error sensitive events, andhyperedges connecting the nodes, and wherein the respective hyperedges correlate the error sensitive events to one or more of the faults that are potential causes of the error sensitive events.

17. The computer program product of claim 16, wherein the program instructions further cause the processor to: assign probability values to the hyperedges; andgenerate a probability distribution based on the probability values.

18. The computer program product of claim 15, wherein the program instructions further cause the processor to: identify the error-sensitive events by performing a Gottesman-Knill simulation of the quantum circuit.

19. The computer program product of claim 15, wherein the program instructions further cause the processor to: identify the error-sensitive events by employing flag qubits associated with high-weight errors originating from low-weight errors.

20. The computer program product of claim 15, wherein the error-sensitive events comprise linear combinations of syndrome measurement bits that would equate to zero in an ideal quantum circuit operation.