The Code Family `Triangular666`

The 6.6.6 Honeycomb color code, defined on a hexagonal lattice. Each hexagon has an X and Z check on all the qubits on its vertices. A code of odd distance 𝑑 has either (3𝑑² + 1)/4 or (3𝑑 - 1)²/4 physical qubits.

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

Triangular666(3)

Parity Check Tableau

the parity check tableau of the Triangular666(3) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Triangular666(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 Triangular666(3) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

Triangular666(5)

Parity Check Tableau

the parity check tableau of the Triangular666(5) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Triangular666(5) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the Triangular666(5) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

Triangular666(7)

Parity Check Tableau

the parity check tableau of the Triangular666(7) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Triangular666(7) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the Triangular666(7) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

Triangular666(9)

Parity Check Tableau

the parity check tableau of the Triangular666(9) instance of this code family

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Triangular666(9) instance of this code family

Naive Syndrome Extraction Circuit

can be generated with QuantumClifford.naive_syndrome_circuit

the naive syndrome extraction circuit of the Triangular666(9) instance of this code family

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

Performance of Specific Decoders

TODO