Apparatus and method for decoding quantum low-density parity-check code

Patent metadata

Field	Value
Publication number	US-12346774-B2
Application number	US-202418407498-A
Country	US
Kind code	B2
Filing date	Jan 9, 2024
Priority date	Jul 11, 2023
Publication date	Jul 1, 2025
Grant date	Jul 1, 2025

Abstract

An apparatus and method for decoding a quantum low density parity-check code using quantum channel information whereby the apparatus and method provide a technique of performing iterative decoding initially using a first error correction and when error correction fails using a second error correction, in a process decoding a quantum low-density parity-check code based on a belief propagation algorithm.

First claim

What is claimed is:

1. A method for decoding a quantum low-density parity-check code, the method comprising:
initializing quantum channel information;
performing a first error correction based on a belief propagation algorithm, by using the initialized quantum channel information;
if the first error correction fails, determining the directivity of the quantum channel for a variable node connected to an unsatisfied check node, based on the connection relationship between the unsatisfied check node and the variable node;
reconfiguring the quantum channel information for the variable node based on the determined directivity of the quantum channel; and
performing a second error correction based on the belief propagation algorithm, by using the reconfigured quantum channel information.

2. The method of claim 1 , wherein, in the determining of the directivity of the quantum channel for the variable node, the directivity of the quantum channel for the variable node is determined, based on syndrome information and stabilizer operator information of the unsatisfied check node with respect to the variable node.

3. The method of claim 1 , wherein the quantum channel information includes the error rate of the quantum channel and the probabilities of quantum error operators, and
the directivity of the quantum channel includes the error rate and the probabilities of error operators, which are required for correcting the quantum channel information corresponding to the variable node.

4. The method of claim 3 , wherein, in the determining of the directivity of the quantum channel for the variable node, if the variable node is connected to a plurality of unsatisfied check nodes, the directivity of the quantum channel is determined by normalizing the products of the error rate of each of the unsatisfied check nodes multiplied by the probabilities of error operators.

5. The method of claim 1 , wherein, in the initializing of quantum channel information, the quantum channel information is initialized by using a depolarizing channel.

6. The method of claim 1 , wherein, in the determining of the directivity of the quantum channel for the variable node, syndrome information of each of a plurality of check nodes is calculated based on an estimated error and a stabilizer operator, the calculated syndrome information and actual syndrome information are compared, and the first error correction is deemed a failure if the unsatisfied check code occurs in which the calculated syndrome information does not match the actual syndrome information.

7. The method of claim 1 , further comprising, if a plurality of variable nodes are connected to the unsatisfied check node, determining at least one variable node whose quantum channel information will be reconfigured, based on the number of unsatisfied check nodes connected to each of the variable nodes and the number of satisfied check nodes connected thereto.

8. A method for decoding a quantum low-density parity-check code, the method comprising:
initializing quantum channel information;
performing a first error correction based on a belief propagation algorithm, by using the initialized quantum channel information;
if the first error correction fails, determining the priority of variable nodes whose quantum channel information will be reconfigured, based on the number of unsatisfied check nodes connected to each of the variable nodes and the number of satisfied check nodes connected thereto;
reconfiguring the quantum channel information for the variable nodes based on the determined priority; and
performing a second error correction based on the belief propagation algorithm, by using the reconfigured quantum channel information.

9. An apparatus for decoding a quantum low-density parity-check code, the apparatus comprising:
a memory including an instruction; and
a processor that initializes quantum channel information by executing the instruction, that performs a first error correction based on a belief propagation algorithm, by using the initialized quantum channel information, that, if the first error correction fails, determines the directivity of the quantum channel for a variable node connected to an unsatisfied check node, based on the connection relationship between the unsatisfied check node and the variable node, that reconfigures the quantum channel information for the variable node based on the determined directivity of the quantum channel, and that performs a second error correction based on the belief propagation algorithm, by using the reconfigured quantum channel information.

10. The apparatus of claim 9 , wherein the processor determines the directivity of the quantum channel for the variable node, based on syndrome information and stabilizer operator information of the unsatisfied check node with respect to the variable node.

11. The apparatus of claim 9 , wherein the quantum channel information includes the error rate of the quantum channel and the probabilities of quantum error operators, and
the directivity of the quantum channel includes the error rate and the probabilities of error operators, which are required for correcting the quantum channel information corresponding to the variable node.

12. The apparatus of claim 11 , wherein, if the variable node is connected to a plurality of unsatisfied check nodes, the processor determines the directivity of the quantum channel by normalizing the products of the error rate of each of the unsatisfied check nodes multiplied by the probabilities of error operators.

13. The apparatus of claim 9 , wherein the processor initializes the quantum channel information is configured by using a depolarizing channel.

14. The apparatus of claim 9 , wherein the processor calculates syndrome information of each of a plurality of check nodes based on an estimated error and a stabilizer operator, compares the calculated syndrome information and actual syndrome information, and deems the first error correction a failure if the unsatisfied check code occurs in which the calculated syndrome information does not match the actual syndrome information.

15. The apparatus of claim 9 , wherein, if a plurality of variable nodes are connected to the unsatisfied check node, the processor determines at least one variable node whose quantum channel information will be reconfigured, based on the number of unsatisfied check nodes connected to each of the variable nodes and the number of satisfied check nodes connected thereto.

Assignees

• Korea Advanced Inst Sci & Tech

Inventors

• Ha Jeongseok
• Kim Jaemin
• Jung Hyunwoo

Classifications

• H03M13/615

  Use of computational or mathematical techniques · CPC title

• H03M13/1131

  Scheduling of bit node or check node processing · CPC title

• G06N10/70 Primary

  Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation · CPC title

• H03M13/1111 Primary

  Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms · CPC title