Block quantum code
A code constructed in a physical space consisting of a tensor product of \(n\) identical subsystems, e.g., qubits, modular qudits, Galois qudits, or oscillators.
Block codes protect from errors acting on a few of the \(n\) subsystems. A block code with distance \(d\) detects errors acting on up to \(d-1\) subsystems, and corrects erasure errors on up to \(d-1\) subsystems.
Transversal gates are logical gates on block codes that can be realized as tensor products of unitary operations acting on subsets of subsystems whose size is independent of \(n\). When the subsets are of size one and the single-subsystem unitaries are identical, then the gates are sometimes called strongly transversal.
- Oscillator-into-oscillator code
- Quantum low-density parity-check (QLDPC) code
- Quantum maximum-distance-separable (MDS) code
- Perfect quantum code
- Small-distance block quantum code
- Quantum quasi-cyclic code
- Quantum Lego code
- Dynamically-generated QECC
- Quantum locally testable code (QLTC)
- Modular-qudit code
- Galois-qudit code
- Block code
- Covariant code — Covariant codes for \(n>1\) are block quantum codes.
Page edit log
- Victor V. Albert (2023-02-14) — most recent
“Block quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/block_quantum