Low-overhead error detection with spacetime codes

TL;DR

This paper presents a low-overhead error detection method for Clifford circuits using spacetime codes, demonstrating significant fidelity improvements on near-term quantum hardware with efficient algorithms for check generation.

Contribution

The authors introduce a novel spacetime code framework for error detection that requires fewer resources than traditional error correction, with practical algorithms and experimental validation.

Findings

Error detection on 50-qubit circuits with 2450 CZ gates.

Fidelity gains up to 236 times over physical qubits.

Efficient check-finding algorithms for Clifford circuits.

Abstract

We introduce a low-overhead approach for detecting errors in arbitrary Clifford circuits on arbitrary qubit connectivities. Our method is based on the framework of spacetime codes, and is particularly suited to near-term hardware since it has a much milder overhead in qubits and gates compared to error correction, while achieving a better sampling overhead than existing error mitigation methods. We present efficient algorithms for finding valid checks that are simultaneously low weight, satisfy connectivity constraints, and cover large detecting regions within the circuit. Using this approach, we experimentally demonstrate error detection on circuits of up to 50 logical qubits containing 2450 CZ gates, and show physical to logical fidelity gains of up to $236\times$. Furthermore, we show our algorithm can efficiently find checks in universal circuits, but the space of valid checks diminishes exponentially with the non-Cliffordness of the circuit. These theoretical and experimental results suggest that Clifford-dominated circuits are promising candidates for near-term quantum advantage.