Matching and maximum likelihood decoding of a multi-round subsystem quantum error correction experiment

TL;DR

This paper demonstrates quantum error correction on superconducting qubits with real-time feedback, comparing decoding methods, and achieving low logical error rates, marking progress toward fault-tolerant quantum computing.

Contribution

It introduces a multi-round quantum error correction experiment with dynamic circuits and real-time decoding, comparing matching and maximum likelihood decoders on a superconducting qubit lattice.

Findings

Logical error rate as low as 0.04 with matching decoder

Logical error rate as low as 0.03 with maximum likelihood decoder

Decoders' performance improvements are promising for fault-tolerant quantum computing

Abstract

Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with improvements in control electronics, are enabling increasingly advanced demonstrations of the necessary operations for applying quantum error correction. Here, we perform quantum error correction on superconducting qubits connected in a heavy-hexagon lattice. The full processor can encode a logical qubit with distance three and perform several rounds of fault-tolerant syndrome measurements that allow the correction of any single fault in the circuitry. Furthermore, by using dynamic circuits and classical computation as part of our syndrome extraction protocols, we can exploit real-time feedback to reduce the impact of energy relaxation error in the syndrome and flag qubits. We show that the logical error varies depending on the use of a perfect matching decoder compared to a maximum likelihood decoder. We observe a logical error per syndrome measurement round as low as $\sim0.04$ for the matching decoder and as low as $\sim0.03$ for the maximum likelihood decoder. Our results suggest that more significant improvements to decoders are likely on the horizon as quantum hardware has reached a new stage of development towards fully fault-tolerant operations.