The Code Family `Gottesman`

The [[2ʲ, 2ʲ - j - 2, 3]] family of codes, the quantum equivalent of the Hamming codes, capable of correcting any single-qubit error.

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

Gottesman(3)

Parity Check Tableau

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

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

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

Gottesman(4)

Parity Check Tableau

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

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Gottesman(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 Gottesman(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 Gottesman(4) instance of this code family

Gottesman(5)

Parity Check Tableau

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

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

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

Shor Syndrome Extraction Circuit

can be generated with QuantumClifford.shor_syndrome_circuit

the Shor syndrome extraction circuit of the Gottesman(5) instance of this code family

Gottesman(6)

Parity Check Tableau

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

Encoding Circuit

can be generated with QuantumClifford.naive_encoding_circuit

the encoding circuit of the Gottesman(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 Gottesman(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 Gottesman(6) instance of this code family

Performance of Specific Decoders

TODO