Testing quantum fault tolerance on small systems

TL;DR

This paper evaluates a quantum fault tolerance protocol across small quantum systems, demonstrating its effectiveness against control errors but its limitations under decoherence, through detailed simulations.

Contribution

It provides a comprehensive testing of a recent fault tolerance protocol on multiple small quantum systems, highlighting its strengths and limitations.

Findings

Fault-tolerant scheme improves results with control errors

Fails to meet fault tolerance criteria under decoherence

Effective for error types dominated by control and measurement errors

Abstract

We extensively test a recent protocol to demonstrate quantum fault tolerance on three systems: (1) a real-time simulation of five spin qubits coupled to an environment with two-level defects, (2) a real-time simulation of transmon quantum computers, and (3) the 16-qubit processor of the IBM Q Experience. In the simulations, the dynamics of the full system is obtained by numerically solving the time-dependent Schr\"odinger equation. We find that the fault-tolerant scheme provides a systematic way to improve the results when the errors are dominated by the inherent control and measurement errors present in transmon systems. However, the scheme fails to satisfy the criterion for fault tolerance when decoherence effects are dominant.