Benchmarking the ability of a controller to execute quantum error corrected non-Clifford circuits

Abstract

Reaching fault-tolerant quantum computation relies on the successful implementation of non-Clifford circuits with quantum error correction (QEC). In QEC, quantum gates and measurements encode quantum information into an error-protected Hilbert space, while classical processing decodes the measurements into logical errors. QEC non-Clifford gates pose the greatest computation challenge from the classical controller perspective, as they require mid-circuit decoding-dependent feed-forward, modifying the physical gate sequence based on the decoding outcome of previous measurements within the same circuit. In this work, we introduce the first benchmarks to holistically evaluate the capability of a combined controller-decoder system to run non-Clifford QEC circuits. We show that executing an error-corrected non-Clifford circuit, comprised of numerous non-Clifford gates, strictly hinges upon the classical controller-decoder system. Particularly, its ability to perform decoding-based feed-forward with low-latency, defined as the time between the last measurement required for decoding and the dependent mid-circuit quantum operation. We analyze how the system latency dictates the circuit operational regime: latency divergence, classical-controller-limited runtime, or quantum-operation-limited runtime. Based on this understanding, we introduce latency-based benchmarks to set a standard for developing QEC control systems as an essential components of fault-tolerant quantum computation.