The Code Family Concat
Concatenated codes recursively encode the logical qubits of an outer code using an inner code. For outer code [[n₁, k₁, d₁]] and inner code [[n₂, k₂, d₂]], the result is [[n₁n₂, k₁k₂, d₁d₂]].
References
A Few Examples from this Family
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Concat(QECCore.Perfect5(), QECCore.Perfect5())
Parity Check Tableau
, QECCore.Perfect5()).png)
Encoding Circuit
can be generated with
QuantumClifford.naive_encoding_circuit, QECCore.Perfect5())_encoding.png)
Naive Syndrome Extraction Circuit
can be generated with
QuantumClifford.naive_syndrome_circuit, QECCore.Perfect5())_naive_syndrome.png)
Shor Syndrome Extraction Circuit
can be generated with
QuantumClifford.shor_syndrome_circuit
Concat(QECCore.Perfect5(), QECCore.Steane7())
Parity Check Tableau
, QECCore.Steane7()).png)
Encoding Circuit
can be generated with
QuantumClifford.naive_encoding_circuit, QECCore.Steane7())_encoding.png)
Naive Syndrome Extraction Circuit
can be generated with
QuantumClifford.naive_syndrome_circuit, QECCore.Steane7())_naive_syndrome.png)
Shor Syndrome Extraction Circuit
can be generated with
QuantumClifford.shor_syndrome_circuit
Concat(QECCore.Steane7(), QECCore.Cleve8())
Parity Check Tableau
, QECCore.Cleve8()).png)
Encoding Circuit
can be generated with
QuantumClifford.naive_encoding_circuit, QECCore.Cleve8())_encoding.png)
Naive Syndrome Extraction Circuit
can be generated with
QuantumClifford.naive_syndrome_circuit, QECCore.Cleve8())_naive_syndrome.png)
Shor Syndrome Extraction Circuit
can be generated with
QuantumClifford.shor_syndrome_circuit
Concat(QECCore.Toric(2, 2), QECCore.Shor9())
Parity Check Tableau
, QECCore.Shor9()).png)
Encoding Circuit
can be generated with
QuantumClifford.naive_encoding_circuit, QECCore.Shor9())_encoding.png)
Naive Syndrome Extraction Circuit
can be generated with
QuantumClifford.naive_syndrome_circuit, QECCore.Shor9())_naive_syndrome.png)
Shor Syndrome Extraction Circuit
can be generated with
QuantumClifford.shor_syndrome_circuitPerformance of Specific Decoders
TODO