Local prematching path for correlation decoding of quantum error correction code

Abstract

A method, system, and apparatus for predicting the occurrence of errors in quantum computing. In one embodiment, the method includes updating the edge weights of a second quantum error correction detector graph by performing a local search of a first quantum error correction detector graph, wherein the local search includes, for each detection event in the first quantum error correction detector graph, reweighting complementary edges in the second quantum error correction detector graph using a single edge error on the edge connecting the detection event to the nearest other detection event; and performing a decoding process on the second quantum error correction detector graph to compute a decode output of the decoding process, wherein the decode output predicts the occurrence of errors in quantum computing.

Claims

1. A method implemented in a computer, Obtaining measurement data from a quantum computer that performs quantum computations, The method involves generating a first detector graph using the aforementioned measurement data, wherein the first detector graph labels a first set of detection events occurring within the measurement data, and assigns weights to each edge in the first detector graph. The method involves generating a second detector graph using the aforementioned measurement data, wherein the second detector graph labels a second set of detection events occurring within the measurement data, and the second set of detection events differs from the first set of detection events, with each edge in the second detector graph being weighted accordingly. For each detection event in the first detector graph, Identify one or more edges in the first detector graph associated with the detection event, and Processing one or more identified edges sequentially, including labeling each edge associated with the detection event and connected to another detection event as a candidate error mechanism; For each edge labeled as a candidate error mechanism, the weights of one or more complementary edges in the second detector graph are updated in order to generate an updated second detector graph. A method comprising performing the decoding process on the updated second detector graph in order to compute the decoded output of the decoding process, wherein the decoded output predicts the occurrence of errors in the quantum computation.

2. The method according to claim 1, wherein the first detector graph and the second detector graph are generated from a hypergraph representing the measurement data.

3. The method according to claim 2, wherein when the edges of the first detector graph and the edges of the second detector graph are combined to form a single hyperedge of the hypergraph, one or more edges in the second detector graph are complementary edges to the edges in the first detector graph.

4. Generating the first detector graph and generating the second detector graph are performed by To generate a hypergraph representing the aforementioned measurement data, The method according to any one of claims 1 to 3, comprising decomposing the hypergraph into a first detector graph and a second detector graph, wherein the first detector graph and the second detector graph are relatively prime graphs.

5. The method according to any one of claims 1 to 4, wherein updating the weights of one or more complementary edges in the second detector graph includes performing Bayesian reweighting of the complementary edges in the second detector graph.

6. The method according to any one of claims 1 to 5, wherein the first set of detected events includes a first type of Pauli error, and the second set of detected events includes a second type of Pauli error, the first type being different from the second type.

7. The method according to claim 6, wherein the first type includes an X or Z error, and the second type includes a Z or X error.

8. The method according to claim 6 or 7, wherein the first detector graph and the second detector graph are generated from a hypergraph representing the measurement data, and the hypergraph represents a third type of Pauli error which is decomposed into a first type of Pauli error and a second type of Pauli error.

9. The method according to claim 8, wherein the third type of Pauli error includes a Y error.

10. The method according to any one of claims 1 to 9, wherein generating the first detector graph and the second detector graph includes associating each edge in the first detector graph and each edge in the second detector graph with equal initial weights.

11. The method according to any one of claims 1 to 10, wherein sequentially processing the identified one or more edges includes processing the identified one or more edges in ascending order of weight.

12. The method according to any one of claims 1 to 11, wherein sequentially processing the identified one or more edges further comprises processing subsequent edges of the identified one or more edges for each edge that is a detector graph boundary edge and is associated with the detection event.

13. The method according to any one of claims 1 to 12, wherein sequentially processing the identified one or more edges further comprises processing subsequent edges of the identified one or more edges for each edge associated with the detection event and connected to another node not corresponding to the detection event.

14. The method according to any one of claims 1 to 13, wherein the decoding process includes a minimum weight perfect matching decoding process or a union-found decoding process.

15. The method according to any one of claims 1 to 14, wherein labeling an edge as a candidate error mechanism indicates that an error related to the error mechanism has occurred.

16. It is a system, One or more data processing devices, A non-temporary computer-readable storage medium that communicates with the one or more data processing devices and stores instructions that, when executed by the one or more data processing devices, cause the one or more data processing devices to perform an operation to decode measurement data received from a quantum computer that performs quantum computation, wherein the operation is Obtaining measurement data from a quantum computer that performs quantum computations, The method involves generating a first detector graph using the aforementioned measurement data, wherein the first detector graph labels a first set of detection events occurring within the measurement data, and assigns weights to each edge in the first detector graph. The method involves generating a second detector graph using the aforementioned measurement data, wherein the second detector graph labels a second set of detection events occurring within the measurement data, and the second set of detection events differs from the first set of detection events, with each edge in the second detector graph being weighted accordingly. For each detection event in the first detector graph, Identify one or more edges in the first detector graph associated with the detection event, and Processing one or more identified edges sequentially, including labeling each edge associated with the detection event and connected to another detection event as a candidate error mechanism; For each edge labeled as a candidate error mechanism, the weights of one or more complementary edges in the second detector graph are updated in order to generate an updated second detector graph. A system comprising: performing the decoding process on the updated second detector graph in order to compute the decoded output of the decoding process, wherein the decoded output predicts the occurrence of errors in the quantum computation.

17. A computer-readable storage medium that is executable by a processing unit and stores instructions that cause the processing unit to perform an operation to decode measurement data received from a quantum computer performing quantum computation, wherein the operation is: Obtaining measurement data from a quantum computer that performs quantum computations, The method involves generating a first detector graph using the aforementioned measurement data, wherein the first detector graph labels a first set of detection events occurring within the measurement data, and assigns weights to each edge in the first detector graph. The method involves generating a second detector graph using the aforementioned measurement data, wherein the second detector graph labels a second set of detection events occurring within the measurement data, and the second set of detection events differs from the first set of detection events, with each edge in the second detector graph being weighted accordingly. For each detection event in the first detector graph, Identify one or more edges in the first detector graph associated with the detection event, and Processing one or more identified edges sequentially, including labeling each edge associated with the detection event and connected to another detection event as a candidate error mechanism; For each edge labeled as a candidate error mechanism, the weights of one or more complementary edges in the second detector graph are updated in order to generate an updated second detector graph. A computer-readable storage medium comprising: performing the decoding process on the updated second detector graph in order to compute the decoded output of the decoding process, wherein the decoded output predicts the occurrence of errors in the quantum computation.

18. A method for computer implementation to predict the occurrence of errors in quantum computing, wherein the method is Updating the edge weights of a second quantum error correction detector graph by performing a local search of a first quantum error correction detector graph, wherein the local search includes, for each detection event in the first quantum error correction detector graph, reweighting complementary edges in the second quantum error correction detector graph using a single edge error on an edge connecting the detection event to the nearest other detection event. A method comprising performing the decoding process on the second quantum error correction detector graph in order to compute the decode output of the decoding process, wherein the decode output predicts the occurrence of the error in the quantum computation.

19. It is a system, One or more data processing devices, The system includes a non-temporary computer-readable storage medium that communicates with the one or more data processing devices and stores instructions that, when executed by the one or more data processing devices, cause the one or more data processing devices to perform an operation to predict the occurrence of an error in quantum computation, wherein the operation is: Updating the edge weights of a second quantum error correction detector graph by performing a local search of a first quantum error correction detector graph, wherein the local search includes, for each detection event in the first quantum error correction detector graph, reweighting complementary edges in the second quantum error correction detector graph using a single edge error on an edge connecting the detection event to the nearest other detection event. A system comprising: performing the decoding process on the second quantum error correction detector graph in order to compute the decode output of the decoding process, wherein the decode output predicts the occurrence of the error in the quantum computation.

20. A computer-readable storage medium that is executable by a processing unit and stores instructions that cause the processing unit to perform an operation to predict the occurrence of errors in quantum computation, wherein the operation is: Updating the edge weights of a second quantum error correction detector graph by performing a local search of a first quantum error correction detector graph, wherein the local search includes, for each detection event in the first quantum error correction detector graph, reweighting complementary edges in the second quantum error correction detector graph using a single edge error on an edge connecting the detection event to the nearest other detection event. A computer-readable storage medium comprising: performing the decoding process on a second quantum error correction detector graph in order to compute the decoded output of the decoding process, wherein the decoded output predicts and performs the occurrence of the error in the quantum computation.

21. It is a system, One or more data processing devices, A system comprising: a non-temporary computer-readable storage medium that communicates with one or more data processing devices and stores instructions, when executed by one or more data processing devices, that cause one or more data processing devices to perform the method described in any one of claims 1 to 15 or 18.

22. A computer-readable storage medium that is executable by a processing device and stores instructions that cause the processing device to perform the method according to any one of claims 1 to 15 or 18 during execution.

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