## Description

A code constructed in a multi-partite quantum system, i.e., a physical space consisting of a tensor product of \(n > 1\) identical subsystems, e.g., qubits, modular qudits, Galois qudits, or oscillators.

## Protection

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.

Noise models for block codes include stochastic noise, in which every possible error is assigned a probability. In the case of local stochastic noise, the probability decreases rapidly (typically, exponentially) with the number of subsystems that an error acts on. On the other hand, the adversarial noise model consists of errors acting on at most a fixed number of subsystems.

## Transversal Gates

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.

## Parent

## Children

- Oscillator-into-oscillator code
- Covariant code — Covariant codes for \(n>1\) are block quantum codes.
- Dynamically-generated QECC
- Quantum maximum-distance-separable (MDS) code
- Single-shot code
- Small-distance block quantum code
- Quasi-cyclic quantum code
- Holographic 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.
- Quantum locally testable code (QLTC)
- Quantum low-weight check (QLWC) code
- Quantum locally recoverable code (QLRC)
- Modular-qudit code
- Galois-qudit code

## Cousins

- Monolithic quantum code — Block quantum codes for \(n=1\) are monolithic codes.
- Block code

## Page edit log

- Victor V. Albert (2023-02-14) — most recent

## Cite as:

“Block quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/block_quantum