Quantum Error Correction with High Rate Codes

Quantum low-density parity-check (qLDPC) codes have emerged as a compelling route to scalable, fault-tolerant quantum computation and communication with dramatically reduced overheads compared to surface-code architectures. In this talk, I will present a unified perspective on recent advances in high-rate qLDPC coding and their implications for large-scale quantum computation. First, we show how high-rate qLDPC codes can be implemented on realistic hardware platforms such as reconfigurable neutral atom arrays [1, 5]. We then explore universal operations enabled by high-rate, high-distance qLDPC codes [3, 4]. In particular, finite-block-length "tricycle" codes support constant-depth logical CCZ gates across three code blocks, enabling direct magic-state generation and single-shot error correction with logical error rates on the order of 10^(-10). This achieves full universality without the large overheads of conventional magic-state distillation. We further introduce new neural decoders for qLDPC codes [6]. Applied to bivariate bicycle codes, these decoders reach the highest logical accuracies reported to date, exhibiting no observed error floors down to very low logical error rates - addressing a long-standing limitation of machine-learning-based decoders. Finally, we extend qLDPC techniques to distributed quantum computing [2] and conclude with a discussion of the challenges and opportunities for realizing practical high-rate qLDPC quantum architectures.