The Code Family `GeneralizedBicycle`

The generalized bicycle codes (GBCs) extend the original bicycle codes by using two commuting square n × n binary matrices A and B, satisfying AB + BA = 0. The code is defined using the generator matrices: GX = (A, B), GZ = (Bᵀ, Aᵀ). See Table I in Lin and Pryadko (2023) for the subscripts.

summary of all evaluations that have been executed for this code family

References

ECC Zoo entry
QuantumClifford.jl docs

A Few Examples from this Family

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GeneralizedBicycle(C₂₇)

Parity Check Tableau

the parity check tableau of the GeneralizedBicycle(C₂₇) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the GeneralizedBicycle(C₂₇) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the GeneralizedBicycle(C₂₇) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

GeneralizedBicycle(C₂₇)

Parity Check Tableau

the parity check tableau of the GeneralizedBicycle(C₃₀) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the GeneralizedBicycle(C₃₀) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the GeneralizedBicycle(C₃₀) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

GeneralizedBicycle(C₂₇)

Parity Check Tableau

the parity check tableau of the GeneralizedBicycle(C₃₅) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the GeneralizedBicycle(C₃₅) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the GeneralizedBicycle(C₃₅) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

GeneralizedBicycle(C₂₇)

Parity Check Tableau

the parity check tableau of the GeneralizedBicycle(C₃₆) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the GeneralizedBicycle(C₃₆) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the GeneralizedBicycle(C₃₆) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

GeneralizedBicycle(C₃₆K₁₀)

Parity Check Tableau

the parity check tableau of the GeneralizedBicycle(C₃₆K₁₀) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the GeneralizedBicycle(C₃₆K₁₀) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the GeneralizedBicycle(C₃₆K₁₀) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

Performance of Specific Decoders

TODO