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 64×11 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.
Related
- Fault-tolerant quantum error correction for constant-excitation stabilizer codes under coherent noise
- A note on tomography of states with low stabilizer rank
- Hierarchy of Rényi Coherent Information in Stabilizer Codes
- Stabilizer Learning under Global Depolarizing Noise with Polynomial Copies and 2t Time
- Noise redistribution by stabilizer codes: an organizing view of concatenated three-qubit codes
BibTeX
@misc{huang2026scalable,
title = {{Scalable Tomography of Coherent Noise via Stabilizer-Code Polarization}},
author = {Long Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19779},
eprint = {2610.19779},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19779},
}
RIS
TY - UNPB
TI - Scalable Tomography of Coherent Noise via Stabilizer-Code Polarization
AU - Long Huang
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.19779
UR - https://arxiv.org/abs/2610.19779
AB - 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 64×11 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.
ER -