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
- Covariant code — Covariant codes for \(n>1\) are block quantum codes.
- Quantum maximum-distance-separable (MDS) code
- Perfect quantum code
- Single-shot code
- Small-distance block quantum code
- Quasi-cyclic quantum code
- Quantum Lego code
- Topological code — Topological codes are block codes because an infinite family of tensor-product Hilbert spaces is required to formally define a phase of matter.
- Dynamically-generated QECC
- Quantum locally testable code (QLTC)
- Quantum low-density parity-check (QLDPC) code
- Modular-qudit code
- Galois-qudit code
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