The Code Family `Toric`

The famous toric code, the first topological code. Terrible rate, ok-ish distance, awesome locality – a tradeoff that will turn out to be fundamental to codes with only 2D connectivity.

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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Toric(3, 3)

Parity Check Tableau

the parity check tableau of the Toric(3, 3) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Toric(3, 3) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the Toric(3, 3) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

the Shor syndrome extraction circuit of the Toric(3, 3) instance of this code family

Toric(4, 4)

Parity Check Tableau

the parity check tableau of the Toric(4, 4) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Toric(4, 4) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the Toric(4, 4) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

the Shor syndrome extraction circuit of the Toric(4, 4) instance of this code family

Toric(6, 6)

Parity Check Tableau

the parity check tableau of the Toric(6, 6) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Toric(6, 6) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the Toric(6, 6) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

the Shor syndrome extraction circuit of the Toric(6, 6) instance of this code family

Toric(8, 8)

Parity Check Tableau

the parity check tableau of the Toric(8, 8) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Toric(8, 8) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the Toric(8, 8) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

the Shor syndrome extraction circuit of the Toric(8, 8) instance of this code family

Toric(10, 10)

Parity Check Tableau

the parity check tableau of the Toric(10, 10) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Toric(10, 10) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the Toric(10, 10) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

the Shor syndrome extraction circuit of the Toric(10, 10) instance of this code family

Toric(12, 12)

Parity Check Tableau

the parity check tableau of the Toric(12, 12) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Toric(12, 12) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the Toric(12, 12) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

the Shor syndrome extraction circuit of the Toric(12, 12) instance of this code family

Performance of Specific Decoders

TODO