Provably Efficient Self-Calibrating Quantum Fault Tolerance

Quantum error correction requires all physical operations to stay below the fault-tolerance threshold, which is undermined by drift in analog control parameters. Since future fault-tolerant computations may run for days or months, halting for recalibration is impractical. This paper establishes a theory of self-calibrating quantum fault tolerance, building on the idea of repurposing syndrome measurements as calibration signals. The authors prove that, for a broad class of control-induced errors, the detection rate forms a locally strongly convex surrogate objective with high probability, enabling efficient online optimization using only syndrome data collected during error correction. They prove convergence to an epsilon detection rate within O(1/epsilon^2) epochs for time-independent drifts, with additional guarantees for time-dependent drifts, and show that convergence is independent of code distance for quantum LDPC codes. Pulse-level simulations of neutral-atom arrays and large-scale circuit-level Clifford simulations confirm the predictions. This work establishes self-calibrating fault tolerance as a provably efficient paradigm, where the same syndrome measurements both protect logical information and stabilize hardware.