Dimensional Jump in Quantum Error Correction

TL;DR

This paper demonstrates how gauge fixing enables switching between different spatial dimensions in topological stabilizer codes, facilitating efficient fault-tolerant quantum computation with local operations and single-shot error correction.

Contribution

It introduces a method to switch spatial dimensions in topological codes via gauge fixing, enabling constant-overhead fault-tolerant quantum computation.

Findings

Dimension switching via gauge fixing is feasible.

Fault-tolerant computation with constant time overhead is achievable.

Single-shot error correction is essential for the method.

Abstract

Topological stabilizer codes with different spatial dimensions have complementary properties. Here I show that the spatial dimension can be switched using gauge fixing. Combining 2D and 3D gauge color codes in a 3D qubit lattice, fault-tolerant quantum computation can be achieved with constant time overhead on the number of logical gates, up to efficient global classical computation, using only local quantum operations. Single-shot error correction plays a crucial role.