Scalable Tomography of Coherent Noise via Stabilizer-Code Polarization

Abstract

Coherent errors accumulate linearly rather than diffusively, making them invisible to Pauli-twirl-based characterization. This poses a central challenge for quantum error correction, yet its characterization typically requires multi-qubit process tomography whose cost grows exponentially with system size. We show that measurement-free error correction projects arbitrary few-qubit coherent noise onto a fixed single-logical-qubit effective channel, enabling tomography at constant cost. Exploiting the polarization effects of bit-flip and phase-flip codes, we construct a concatenated effective-channel fingerprint and prove, by a parity-based contradiction argument, that the observation map is globally injective over a prescribed coherent-noise family; hence the underlying noise parameters are uniquely recovered without any sparsity or low-rank assumptions. We further corroborate the theoretical guarantee by a synthetic numerical test: over 500 randomly sampled points in the compact parameter domain, the $64\times 11$ Jacobian of the concatenated fingerprint maintains full column rank with a strictly positive smallest singular value in every case, confirming that all 11 parameter directions remain first-order identifiable throughout the region. The recovered coherent noise model can be fed into decoding algorithms; relative to independent noise priors, we expect this to reduce the logical error rate for surface-code decoders. The protocol offers a scalable route to coherent-noise identification whenever the noise admits a moderate-dimensional parameterization.

arXiv comment5 pages, 2 figure