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
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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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