Quantum low-density parity-check codes for erasure-biased atomic quantum processors

TL;DR

This paper demonstrates that quantum LDPC codes, specifically Clifford-deformed La-cross and Bivariate Bicycle codes, outperform surface codes in erasure-biased quantum processors by achieving lower logical error rates and high thresholds, suitable for near-term experiments.

Contribution

It shows that quantum LDPC codes are highly effective for erasure-biased quantum computing architectures, providing high thresholds and low logical errors in regimes accessible to current experiments.

Findings

Quantum LDPC codes outperform surface codes in erasure-biased settings.

Large-scale simulations confirm lower logical error probabilities for LDPC codes.

Different QEC codes benefit variably from high erasure fractions.

Abstract

Identifying the best families of quantum error correction (QEC) codes for near-term experiments is key to enabling fault-tolerant quantum computing. Ideally, such codes should have low overhead in qubit number, high physical error thresholds, and moderate requirements on qubit connectivity to simplify experiments, while allowing for high logical error suppression. Quantum Low-Density Parity-Check (LDPC) codes have been recently shown to provide a path towards QEC with low qubit overhead and small logical error probabilities. Here, we demonstrate that when the dominant errors are erasures -- as can be engineered in different quantum computing architectures -- quantum LDPC codes additionally provide high thresholds and even stronger logical error suppression in parameter regimes that are accessible to current experiments. Using large-scale QEC numerical simulations, we benchmark the performance of two families of high-rate quantum LDPC codes, namely Clifford-deformed La-cross codes and Bivariate Bicycle codes, under a noise model strongly biased towards erasure errors. Both codes outperform the surface code by offering up to orders of magnitude lower logical error probabilities. Interestingly, we find that this decrease in the logical error probability may not be accompanied by an increase in the code threshold, as different QEC codes benefit differently from large erasure fractions. While here we focus on neutral atom qubits, the results also hold for other quantum platforms, such as trapped ions and superconducting qubits, for which erasure conversion has been demonstrated.