Incoherent Approximation of Leakage in Quantum Error Correction

TL;DR

This paper introduces a computationally efficient approximation method for modeling leakage errors in quantum error correction, enabling more scalable simulations without significant loss of accuracy.

Contribution

The paper presents the Subspace Twirling Approximation (STA), a novel method that simplifies leakage modeling by assuming incoherence, validated through simulations of surface and repetition codes.

Findings

STA accurately predicts error correction performance.

Incoherence naturally emerges during stabilizer measurements.

Method reduces computational overhead significantly.

Abstract

Quantum error correcting codes typically do not account for quantum state transitions - leakage - out of the computational subspace. Since these errors can last for multiple detection rounds they can significantly contribute to logical errors. It is therefore important to understand how to numerically model them efficiently. Fully quantum simulations of leakage require more levels per leaked qubit, which substantially limits the system sizes that may be simulated. To address this, we introduce a Subspace Twirling Approximation (STA) on quantum channels that preserves the incoherence between the computational and leakage subspaces. The assumption of incoherence enables the quantum simulation of leakage at little computational overhead. We motivate the approximation's validity by showing that incoherence is achieved naturally during repeated stabilizer measurements. Additionally, we provide various simulation results which show that the STA yields accurate error correction statistics in the repetition and surface codes with physical error parameters.