# Provably Efficient Self-Calibrating Quantum Fault Tolerance

arXiv: https://arxiv.org/abs/2608.05686 · HTML: https://mlsanity.com/paper/2608.05686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 75 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Meta-Harness: End-to-End Optimization of Model Harnesses](https://mlsanity.com/paper/2603.28052/) (2026)
- [A Convergence Theory for Over-parameterized Variational Quantum Eigensolvers](https://mlsanity.com/paper/2205.12481/) (2022)
- [Quantum Probe Tomography](https://mlsanity.com/paper/2510.08499/) (2025)
- [Quantum Control Landscapes Are Almost Always Trap Free](https://mlsanity.com/paper/1608.06198/) (2016)
- [Agentic AI for Scientific Reasoning in Autonomous Quantum Sensing Experiments](https://mlsanity.com/paper/2607.25145/) (2026)

## Abstract (arXiv)

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 such 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 a simple and efficient online optimization algorithm using only syndrome measurements collected during normal error correction. We prove convergence to an varepsilon detection rate within O(1/varepsilon2) 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.