Taming coherent noise with teleportation

TL;DR

This paper shows that teleportation can convert complex coherent errors into simpler Pauli errors, enabling efficient classical simulation and analytical threshold proofs for quantum error correction.

Contribution

It demonstrates that teleportation effectively converts coherent errors into Pauli errors, simplifying analysis and simulation of quantum error correction under such noise.

Findings

Teleportation decoheres errors, with infidelity growing linearly.

Pure Z-coherent errors become equivalent to Pauli errors after teleportation.

Teleportation-based error correction has an analytically provable threshold.

Abstract

Compared to the more widely studied Pauli errors, coherent errors present several new challenges in quantum computing and quantum error correction (QEC). For example, coherent errors may interfere constructively over a long circuit and significantly increase the overall failure rate compared to Pauli noise. Additionally, there is so far no analytical proof for a topological code threshold under coherent errors. Moreover, it is hard to even numerically estimate the performance of QEC under coherent errors as their effect in a Clifford circuit cannot be efficiently classically simulated. In this work, we demonstrate that teleportation effectively tailors coherent errors into Pauli errors, for which analytical and numerical results are abundant. We first show that repeated teleportation of a single qubit decoheres errors, and the average infidelity grows at worst linearly with the number of teleportations, similar to Pauli errors. We then analyze a physically motivated pure $Z$-coherent error model for teleported CSS codes in which over-rotation errors accompany every gate, and find that such an error model is equivalent to a Pauli error model. Our result implies that the performance of a CSS code implemented via teleportation-based error correction or measurement-based error correction with such coherent noise can be efficiently simulated on a classical computer and has an analytically provable threshold. The intrinsic noise-tailoring property of teleportation may ultimately remove the need for randomized compiling in teleportation-based quantum computing schemes.