The Code Family `TwoBlockGroupAlgebra`

The two-block group algebra (2BGA) codes extend the generalized bicycle (GB) codes by replacing the cyclic group with a general finite group, which can be non-abelian. The stabilizer generator matrices are defined using commuting square matrices derived from elements of a group algebra: HX = (A, B), HZ^T = [B; -A] where A and B are commuting ℓ × ℓ matrices, ensuring the CSS orthogonality condition.

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

Click on the ▶ marker to expand

TwoBlockGroupAlgebra(A1, B1)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A1, B1) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A1, B1) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A1, B1) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

TwoBlockGroupAlgebra(A2, B2)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A2, B2) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A2, B2) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A2, B2) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

TwoBlockGroupAlgebra(A3, B3)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A3, B3) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A3, B3) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A3, B3) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

TwoBlockGroupAlgebra(A4, B4)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A4, B4) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A4, B4) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A4, B4) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

TwoBlockGroupAlgebra(A5, B5)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A5, B5) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A5, B5) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A5, B5) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

TwoBlockGroupAlgebra(A6, B6)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A6, B6) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A6, B6) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A6, B6) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

TwoBlockGroupAlgebra(A₇₂, B₇₂)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A₇₂, B₇₂) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A₇₂, B₇₂) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A₇₂, B₇₂) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

TwoBlockGroupAlgebra(A₇₂, B₇₂)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A₁₉₆, B₁₉₆) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A₁₉₆, B₁₉₆) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A₁₉₆, B₁₉₆) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

TwoBlockGroupAlgebra(A₇₂, B₇₂)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A₂₈₈, B₂₈₈) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A₂₈₈, B₂₈₈) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A₂₈₈, B₂₈₈) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

TwoBlockGroupAlgebra(A₇₂, B₇₂)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A₁₀₈, B₁₀₈) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A₁₀₈, B₁₀₈) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A₁₀₈, B₁₀₈) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

TwoBlockGroupAlgebra(A₇₂, B₇₂)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A₃₆₀, B₃₆₀) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A₃₆₀, B₃₆₀) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A₃₆₀, B₃₆₀) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

TwoBlockGroupAlgebra(A₇₂, B₇₂)

Parity Check Tableau

the parity check tableau of the TwoBlockGroupAlgebra(A₇₅₆, B₇₅₆) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the TwoBlockGroupAlgebra(A₇₅₆, B₇₅₆) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the TwoBlockGroupAlgebra(A₇₅₆, B₇₅₆) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

Performance of Specific Decoders

TODO