Steane [[7,1,3]] Code | 7-Qubit CSS Color Code
Quick Technical Answer:
The Steane [[7,1,3]] code is a Calderbank-Shor-Steane (CSS) quantum error-correcting code that encodes 1 logical qubit into 7 physical qubits. It corrects any arbitrary single-qubit error and permits transversal implementation of all Clifford gates (H, S, CNOT).
Formula / Unitary:
[[n, k, d]] = [[7, 1, 3]], \quad H_{\text{CSS}} = \begin{pmatrix} 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ 0 & 1 & 1 & 0 & 0 & 1 & 1 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 \end{pmatrix}
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Frequently Asked Questions
What is the key advantage of the Steane code over surface codes?
The Steane code allows both the Hadamard (H) and Phase (S) gates to be executed transversally (applying single-qubit gates bitwise across all 7 physical qubits), avoiding complex lattice surgery.