Optimal number of stabilizer measurement rounds in an idling surface code patch

TL;DR

This paper numerically optimizes the frequency of stabilizer measurements in surface code quantum error correction, considering realistic noise models, to improve logical qubit fidelity.

Contribution

It introduces a numerical method to determine the optimal stabilizer measurement rate for surface codes under realistic noise conditions.

Findings

Optimal measurement rounds decrease with better qubits.

Optimal rounds increase with better gates or larger code sizes.

Results inform architecture-specific error correction strategies.

Abstract

Logical qubits can be protected against environmental noise by encoding them into a highly entangled state of many physical qubits and actively intervening in the dynamics with stabilizer measurements. In this work, we numerically optimize the rate of these interventions: the number of stabilizer measurement rounds for a logical qubit encoded in a surface code patch and idling for a given time. We model the environmental noise on the circuit level, including gate errors, readout errors, amplitude and phase damping. We find, qualitatively, that the optimal number of stabilizer measurement rounds is getting smaller for better qubits and getting larger for better gates or larger code sizes. We discuss the implications of our results to some of the leading architectures, superconducting qubits, and neutral atoms.