Graph state-based link chain structure quantum stabilizer subcode construction method

A technique for stabilizing subcodes and construction methods, applied in the direction of error detection coding, coding, code conversion, etc. that apply multiple parity bits, can solve the problems that are not optimistic, cannot use the advantages of graph theory geometric intuition construction, and are difficult to promote and other issues to achieve the effect of reducing complexity

Active Publication Date: 2016-11-09
易迅通科技有限公司
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  • Abstract
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Problems solved by technology

But its disadvantage is that because the code set search problem is a complete NP problem, it is very pessimistic to rely solely on limited search when faced with building longer and higher-dimensional error correction codes.
But its disadvantage is that it relies on the analytical structure of actual physical quantities, and it is difficult to promote in terms of dimension expansion and increasing input bits.
And when using actual physical quantities for analysis, there are many limitations
When exploring new code structures, the unique geometric intuition construction advantages of graph theory cannot be used

Method used

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  • Graph state-based link chain structure quantum stabilizer subcode construction method
  • Graph state-based link chain structure quantum stabilizer subcode construction method
  • Graph state-based link chain structure quantum stabilizer subcode construction method

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Embodiment 1

[0061] When the number of qubits is arranged in n=5 ring chains, the corresponding graph state is as follows figure 2 , a (5,1) stable subcode can be constructed through the construction method proposed by the present invention. Specific steps are as follows:

[0062] Step 1: According to the graph state of the qubit stabilizer codes arranged in a ring chain, using the unique rotational symmetry of its structure, the main part of the stabilizer can be analytically constructed by establishing the entanglement relationship of the neighborhood. When the number of qubits is n=5, through the construction formula of formula 1, the stable sub-matrix that can be obtained is:

[0063] g 1 :G 1 G 4 = X Z Z X I

[0064] g 2 :G 2 G 5 = I X Z Z X

[0065] g 3 :G 3 G 1 = X I X Z Z

[0066] g 4 :G 4 G 2 = Z X I X Z

[0067] Step 2: Calculation and analysis of the main part of the stable submatrix S that is analytically constructed by establishing the entanglement relationsh...

Embodiment 2

[0076] When the number of qubits is arranged in n=7 ring chains, the corresponding graph state is as follows image 3 , a (7,1) stable subcode can be constructed through the construction method proposed by the present invention. Specific steps are as follows:

[0077] Step 1: According to the graph state of the qubit stabilizer codes arranged in a ring chain, using the unique rotational symmetry of its structure, the main part of the stabilizer can be analytically constructed by establishing the entanglement relationship of the neighborhood. When the number of qubits is n=7, through the construction formula of formula 1, the stable sub-matrix that can be obtained is:

[0078] g 1 :G 1 G 4 =XZZXZIZ

[0079] g 2 :G 2 G 5 =ZXZZXZI

[0080] g 3 :G 3G 6 =IZXZZXZ

[0081] g 4 :G 4 G 7 =ZIZXZZX

[0082] g 5 :G 5 G 1 =XZIZXZZ

[0083] Step 2: Calculation and analysis of the main part of the stable submatrix S that is analytically constructed by establishing the en...

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Abstract

The invention discloses a graph state-based link chain structure quantum stabilizer subcode construction method which is different from a current popular method for constructing a stabilizer subcode through a graph state in ideas. According to the method, specific rotation symmetry of a structure of a graph state of quantum bit subcodes arranged in a link chain manner is adopted, a main part of a stabilizer is analytically constructed by establishing an entanglement relation of neighborhoods, then through calculating and analyzing, a missing part which does not meet an error correction condition is supplemented, and an error correction capability of the stabilizer is ensured by adding a stabilizer sub-operation operator, so that a complete stabilizer subcode is acquired. According to the method for constructing the quantum error-correcting code by establishing the entanglement relation of the neighborhoods through a topological structure and the specific symmetric property of the graph state, excellent promotion significance and application prospects are realized on two aspects of extending a higher dimensional quantum error-correcting code and exploring a new type of quantum error-correcting code.

Description

technical field [0001] The invention relates to the technical field of quantum security communication, in particular to a method for analyzing and constructing a graph-state-based ring-chain structure quantum stable subcode. Background technique [0002] With the development of quantum error-correcting codes, there are many effective methods for constructing stable subcodes. Among them, the method of using graph states to construct stable subcodes has also been proposed, and there are construction advantages that other construction methods do not have. For example, the transformation characteristics of quantum errors, the code family can be controlled in the system of the same size, and the new structure of the code can be discovered by using the geometric structure of the graph, etc. On the basis of two-dimensional graph state and high-dimensional graph state, the construction of quantum error-correcting codes has been realized and fully verified. [0003] Document 1: "Qu...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H03M13/11H04L9/08
CPCH03M13/1111H04L9/0858
Inventor 曹正文张爽浩彭进业曾贵华杨涛柴庚
Owner 易迅通科技有限公司
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