Provably Efficient Self-Calibrating Quantum Fault Tolerance

2026-08-06

AI Summary

This work addresses the challenge of control parameter drift induced by environmental noise in quantum computing, which undermines fault-tolerant conditions and renders conventional calibration impractical during long-duration computations. The paper establishes the first theoretical framework for self-calibrating fault-tolerant quantum computation by seamlessly integrating calibration into the error correction cycle. It leverages syndrome measurement outcomes to construct an online optimization mechanism, proving that the detection rate serves as a strongly convex proxy objective. This enables efficient convergence independent of code distance, with theoretical guarantees of achieving an $\varepsilon$ detection rate within $O(1/\varepsilon^2)$ rounds. The approach is validated through simulations at both pulse and Clifford circuit levels using quantum LDPC codes, demonstrating effectiveness on neutral-atom arrays and large-scale circuits.

Abstract

Quantum error correction protects logical information only when every physical operation remains below the fault-tolerance threshold, a condition that must be maintained continuously rather than only at the initial calibration. In practice, however, analog control parameters inevitably drift because of environmental fluctuations. As future fault-tolerant quantum computations are expected to run for days or even months, interrupting computation for repeated recalibration becomes fundamentally impractical. A promising alternative is to integrate calibration directly into computation by repurposing syndrome measurements as a calibration signal (Sivak et al, Nature 2026), but whether such self-calibration can be achieved with provable efficiency remains an open question. Here we establish a theoretical framework for self-calibrating quantum fault tolerance. We prove that, for a broad class of control-induced errors, the detection rate defines a locally strongly convex surrogate objective for analog calibration with high probability. This geometric property enables efficient online optimization using only syndrome measurements collected during normal error correction. We prove convergence to an $\varepsilon$ detection rate within $O(1/\varepsilon^2)$ epochs for time-independent drifts and also establish guarantees for time-dependent drifts. We further show that the convergence rate is independent of the code distance for quantum low-density parity-check (LDPC) codes. Pulse-level simulations of neutral-atom arrays and large-scale circuit-level Clifford simulations confirm these theoretical predictions. Our results establish self-calibrating fault tolerance as a provably efficient paradigm in which the same syndrome measurements simultaneously protect logical information and stabilize the underlying hardware.

Problem

• quantum fault tolerance
• self-calibration
• parameter drift
• syndrome measurements
• quantum error correction

Innovation

• self-calibrating quantum fault tolerance
• syndrome-based calibration
• strongly convex surrogate objective
• online optimization
• quantum LDPC codes