EP-4736083-A1 - QUANTUM DECODER

EP4736083A1EP 4736083 A1EP4736083 A1EP 4736083A1EP-4736083-A1

Abstract

A quantum error correction method and apparatus are disclosed. A decoder of a quantum computer system receives syndrome data representative of an error state of qubits in the quantum computer system, the syndrome data comprising defects each associated with a location in a decoding graph. The decoder initialises a size value of a region surrounding each defect in the decoding graph. The decoder then identifies clusters of defects and increases the size values of identified defects. A correction for the error state is determined based on the clusters of defects.

Inventors

BARNES, Kenton
BARBER, BEN
SKORIC, LUKA

Assignees

Riverlane Ltd

Dates

Publication Date: 20260506
Application Date: 20230726

Claims (8)

1. A computer-implemented quantum error correction method comprising: (a) receiving, at a decoder of a quantum computer system, syndrome data representative of an error state of qubits in the quantum computer system, the syndrome data comprising a plurality of defects, each defect of the plurality of defects associated with a respective location in a decoding graph; (b) initialising, at the decoder, a respective size value associated with each respective defect of the plurality of defects, the respective size value representative of a respective size of a respective region surrounding the respective defect in the decoding graph; (c) identifying, at the decoder, clusters of defects, wherein a pair of defects of the plurality of defects is included in a same cluster if a shortest distance between the pair of defects in the decoding graph is less than a sum of the respective size values associated with each respective defect of the pair of defects; (d) identifying, at the decoder, defects in clusters that (i) contain an odd total number of defects and (ii) do not contain any respective defects having a respective size value larger than a shortest distance between the respective defect and any boundary of the decoding graph; (e) if any defects are identified in step (d): determining, at the decoder, an increment value based on a minimum distance between the respective region surrounding any respective identified defect and one of (i) any boundary of the decoding graph, and (ii) the respective region surrounding another defect in a different cluster; and, increasing, at the decoder, the respective size value associated with each identified defect by the increment value and repeating steps (c), (d) and (e); (f) otherwise, determining, at the decoder and based on the clusters of defects, a correction for the error state.
2. The method of claim 1, further comprising obtaining, at a quantum processing unit (QPU) of the quantum computer system, the syndrome data by measuring a plurality of syndrome qubits of the QPU.
3. The method of claim 1 or claim 2, wherein the quantum error correction method is a surface code error correction procedure.
4. The method of any preceding claim, wherein identifying the correction for the error state comprises: identifying a logical operator for the quantum error correction method involving physical qubits of the quantum computer system that are associated with the boundary of the decoding graph; determining a parity of a total number of clusters that the logical operator intersects that contain an odd total number of defects, wherein an even parity indicates that the logical operator is in a correct logical state and an odd parity indicates that the logical operator is in an incorrect logical state.
5. The method of any preceding claim, wherein determining the increment value comprises: determining a minimum cluster separation value of the identified defects, wherein the minimum cluster separation value is equal to the minimum value of: (i) half of a shortest distance between the respective regions of any two defects identified in step (d) that are not in same cluster, (ii) a shortest distance from the respective region of any defect identified in step (d) to the respective region of any defect not identified in step (d), and (iii) a shortest distance from any defect identified in step (d) to any boundary of the decoding graph; and setting the increment value to at least the minimum cluster separation value.
6. A computer program product comprising instructions which, when the program is executed by a decoder of a quantum computing system, cause the decoder to carry out the method of any preceding claim.
7. A computer-readable medium comprising the computer program product of claim 6.
8. A quantum computing system comprising a decoder configured to perform the method of any of claims 1 to 5.

Description

QUANTUM DECODER BACKGROUND The present disclosure relates to apparatus, systems, methods and data structures for use in decoding quantum error correction codes. SUMMARY OF THE INVENTION According to a first aspect of the invention, there is provided a computer-implemented quantum error correction method comprising: (a) receiving, at a decoder of a quantum computer system, syndrome data representative of an error state of qubits in the quantum computer system, the syndrome data comprising a plurality of defects, each defect of the plurality of defects associated with a respective location in a decoding graph; (b) initialising, at the decoder, a respective size value associated with each respective defect of the plurality of defects, the respective size value representative of a respective size of a respective region surrounding the respective defect in the decoding graph; (c) identifying, at the decoder, clusters of defects, wherein a pair of defects of the plurality of defects is included in a same cluster if a shortest distance between the pair of defects in the decoding graph is less than a sum of the respective size values associated with each respective defect of the pair of defects; (d) identifying, at the decoder, defects in clusters that (i) contain an odd total number of defects (this may include defects that are not in any cluster yet, i.e. isolated defects may be treated as a cluster containing a single defect) and (ii) do not contain any respective defects having a respective size value larger than a shortest distance between the respective defect and any boundary of the decoding graph (the method is applicable to decoding graphs with no boundary, e.g. toric code decoding graphs: if the decoding graph does not have a boundary, none of the defects will have a size value larger than a shortest distance between the respective defect and any boundary of the decoding graph); (e) if any defects are identified: determining, at the decoder, an increment value based on a minimum distance between the respective region surrounding any respective identified defect and one of (i) any boundary of the decoding graph (if the decoding graph has a boundary), and (ii) the respective region surrounding another defect in a different cluster ; and, increasing, at the decoder, the respective size value associated with each identified defect by the increment value and repeating steps (c), (d) and (e) (until no defects are identified in step (d)); (f) otherwise, determining, at the decoder and based on the clusters of defects, a correction for the error state. The present invention provides an improved implementation of union-find decoding (an introduction to union-find decoding can be found in Delfosse & Nickerson, arXiv: 1709.06218v3 [quant-ph]). Quantum error correction codes generally involve decoding a "syndrome", which can be considered to be a signature associated with an error state of the physical qubits in the code (two different errors can potentially have the same syndrome). A "decoder" is then used to identify an error which could have caused the syndrome (or possibly instead just a correction operation that can be used to correct logical qubit states encoded in the code, e.g. a single bit representing whether the eventual logical measurement outcome needs to be flipped). In certain error correction codes, such as topological error correction codes including the surface code, a "decoding graph" can be used to facilitate decoding of the syndrome by pairing "defects" in the syndrome (these defects generally provide an indication of end points of chains of errors on physical data qubits in the error correction code). Union find algorithms decode syndromes by clustering defects into groups. A cluster of decoding graph edges is formed around each defect (defects are located at a subset of nodes of the decoding graph), and these clusters are grown by including additional edges until all defects are included in a cluster containing an even number of defects (or the cluster touches a boundary of the decoding graph), with overlapping clusters being merged after each growth stage. Correction(s) to the encoded logical state can then be determined based on the clustering of defects. Conventional union-find decoding methods track all of the decoding graph edges contained in each cluster. Fault-tolerant quantum computation will likely involve millions of physical data qubits, with the number of edges in the decoding graph being orders or magnitude larger still. The size of the decoding graph therefore imposes extremely high memory requirements upon the decoding hardware (potentially prohibitively high), and there is therefore a need to reduce this memory overhead. The present invention overcomes this memory problem by implementing union-find decoding (and therefore operating the quantum computer as a whole) in a new way. Rather than tracking the edges that form each cluster in the decoding graph, the present invention i