Method and apparatus for generating quantum error correction code using graph state

Patent metadata

Field	Value
Publication number	US-10911067-B2
Application number	US-201616309281-A
Country	US
Kind code	B2
Filing date	Jun 24, 2016
Priority date	Jun 13, 2016
Publication date	Feb 2, 2021
Grant date	Feb 2, 2021

Abstract

Provided is a quantum error correction code generating method using a graph state. According to the exemplary embodiment of the present invention, a quantum error correction code generating method using a graph state: includes: generating a graph state representing an adjacency relationship between a plurality of qubits including at least one entangled qubit (ebit); generating a first stabilizer generator which corresponds to the graph state and is configured by a plurality of stabilizers for detecting errors of the plurality of qubits; and generating at least one logical Z operator used for a phase flip operation of a codeword, at least one logical X operator used for a bit flip operation of a codeword, and a second stabilizer generator which is a sub set of the first stabilizer generator, based on the first stabilizer generator and the at least one entangled qubit.

First claim

The invention claimed is:

1. A quantum error correction code generating method using a graph state, the quantum error correction code generating method executed by an electronic device including a processor, the quantum error correction code generating method comprising:
generating a graph state representing an adjacency relationship between a plurality of qubits including an entangled qubit;
generating a first stabilizer generator which corresponds to the graph state received from a graph unit and is configured by a plurality of stabilizers for detecting errors of the plurality of qubits; and
generating a logical Z operator used for a phase flip operation of a codeword, a logical X operator used for a bit flip operation of the codeword, and a second stabilizer generator which is a sub set of the first stabilizer generator, based on the first stabilizer generator and the entangled qubit,
wherein the generating of the second stabilizer generator includes:
based on the entangled qubit, determining a first stabilizer of the plurality of stabilizers as the logical Z operator and generating the second stabilizer generator comprising the other stabilizers excluding the first stabilizer from the plurality of stabilizers; and
generating the logical X operator using the logical Z operator and the second stabilizer generator,
wherein the first stabilizer, as the logical Z operator, includes an X operator used for a bit flip operation of a qubit, and
wherein the X operator of the first stabilizer is placed in the first stabilizer at a position corresponding to the entangled qubit placed in the graph state;

and
transmitting the codeword to a receiver.

2. The quantum error correction code generating method of claim 1 , wherein the generating of the logical X operator includes:
generating a candidate operator in which the X operator included in the logical Z operator is replaced with a Z operator used for a phase flip operation of a qubit; and
generating the logical X operator using the candidate operator and a second stabilizer including the Z operator placed in the same position in the second stabilizer generator as the replaced Z operator placed in the candidate operator.

3. The quantum error correction code generating method of claim 2 , wherein the logical X operator is calculated by Equation 1:
X =X j Z r i |I for i= 1, . . . , k ( k=c )  Equation 1

where X is the logical X operator, X is the X operator, Z is the Z operator, I is an identity operator, i is an index of the entangled qubit, r i is an i-th row corresponding to the entangled qubit in an adjacency matrix corresponding to the graph state, k and c are the numbers of the entangled qubits, and n is the number of logical qubits among the plurality of qubits, j is a value defined as i+(n−c).

4. The quantum error correction code generating method of claim 1 , wherein the generating of a first stabilizer generator includes:
generating an adjacency matrix indicating whether the plurality of qubits is adjacent to each other, based on the graph state;
calculating the plurality of stabilizers which is configured by a Pauli operator and corresponds to each row of the adjacency matrix; and
generating the first stabilizer generator including the plurality of stabilizers.

5. The quantum error correction code generating method of claim 4 , wherein the first stabilizer generator is calculated by Equation 2:

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Assignees

• Univ Korea Res & Bus Found

Inventors

• Heo Jun
• Sohn Il Kwon

Classifications

• G06N5/01 Primary

  Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound · CPC title

• G06N10/70

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

• H03M13/615

  Use of computational or mathematical techniques · CPC title

• G06F17/10

  Complex mathematical operations {(function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544)} · CPC title

• H03M13/1191

  Codes on graphs other than LDPC codes · CPC title