Increasing the distance of topological codes with time vortex defects

TL;DR

This paper introduces space-time defects called 'time vortices' into topological quantum codes, significantly reducing qubit requirements for a given error rate by optimizing code embedding and vortex placement.

Contribution

It proposes a novel method of incorporating time vortices into topological codes, demonstrating asymptotic qubit savings and improved performance through simulations.

Findings

Vortexed codes require less than half the qubits of vortex-free codes for the same distance.

Smallest vortexed code with 30 qubits outperforms vortex-free code with 42 qubits.

Monte Carlo simulations confirm enhanced performance of vortexed Floquet color codes.

Abstract

We propose modifying topological quantum error correcting codes by incorporating space-time defects, termed ``time vortices,'' to reduce the number of physical qubits required to achieve a desired logical error rate. A time vortex is inserted by adding a spatially varying delay to the periodic measurement sequence defining the code such that the delay accumulated on a homologically non-trivial cycle is an integer multiple of the period. We analyze this construction within the framework of the Floquet color code and optimize the embedding of the code on a torus along with the choice of the number of time vortices inserted in each direction. Asymptotically, the vortexed code requires less than half the number of qubits as the vortex-free code to reach a given code distance. We benchmark the performance of the vortexed Floquet color code by Monte Carlo simulations with a circuit-level noise model and demonstrate that the smallest vortexed code (with $30$ qubits) outperforms the vortex-free code with $42$ qubits.