Demonstration of low-overhead quantum error correction codes

TL;DR

This paper demonstrates low-overhead quantum error correction codes on a superconducting processor, showing promising results for scalable fault-tolerant quantum computing with efficient syndrome extraction and reduced resource overhead.

Contribution

The authors experimentally implement two low-overhead quantum LDPC codes on a superconducting processor, showcasing scalable error correction with long-range couplers and efficient syndrome measurement.

Findings

Achieved logical error rates of ~8.9% and ~7.8% per cycle for two codes.

Demonstrated simultaneous measurement of nonlocal stabilizers.

Validated feasibility of implementing qLDPC codes on superconducting hardware.

Abstract

Quantum computers hold the potential to surpass classical computers in solving complex computational problems. However, the fragility of quantum information and the error-prone nature of quantum operations make building large-scale, fault-tolerant quantum computers a prominent challenge. To combat errors, pioneering experiments have demonstrated a variety of quantum error correction codes. Yet, most of these codes suffer from low encoding efficiency, and their scalability is hindered by prohibitively high resource overheads. Here, we report the demonstration of two low-overhead quantum low-density parity-check (qLDPC) codes, a distance-4 bivariate bicycle code and a distance-3 qLDPC code, on our latest superconducting processor, Kunlun, featuring 32 long-range-coupled transmon qubits. Utilizing a two-dimensional architecture with overlapping long-range couplers, we demonstrate simultaneous measurements of all nonlocal weight-6 stabilizers via the periodic execution of an efficient syndrome extraction circuit. We achieve a logical error rate per logical qubit per cycle of $(8.91 \pm 0.17)\%$ for the distance-4 bivariate bicycle code with four logical qubits and $(7.77 \pm 0.12)\%$ for the distance-3 qLDPC code with six logical qubits. Our results establish the feasibility of implementing various qLDPC codes with long-range coupled superconducting processors, marking a crucial step towards large-scale low-overhead quantum error correction.