Zeno-Enhanced Probabilistic Error Cancellation with Quantum Error Detection Codes
Abstract
Probabilistic error cancellation (PEC) is unbiased but suffers exponential sampling overhead set by noise-weighted circuit volume, whereas quantum error-detecting codes (QEDCs) remove many physical faults by stabilizer post-selection but leave an undetectable logical residue. We exploit this complementarity by using post-selection to map physical noise to a weaker accepted logical channel, and then applying PEC only to the residual channel. The resulting feedback-free QED+PEC scheme interleaves Clifford logical blocks, stabilizer measurements, post-selection, and probabilistic cancellation on accepted trajectories, without real-time decoding or active recovery. A key complication is that post-selection correlates accepted fault branches through stabilizer-commutation constraints, so the sparse Pauli-Lindblad factorization underlying bare PEC no longer applies directly. We therefore construct the inverse channel perturbatively: for fixed order K, only accepted fault branches up to order K are retained, reducing preprocessing from 2m branches to O(mK) per block. The order-K protocol cancels the normalized post-selected channel through degree K, leaving a per-block error O(WK+1) that accumulates at most linearly. For logical GHZ-state preparation with the $[[n,n-2,2]]$ Iceberg code under circuit-level depolarizing noise and ideal stabilizer measurements, first-order QED+PEC reaches n=200 physical qubits and lowers sampling overhead by three to four orders of magnitude relative to standard PEC while maintaining F≃0.956. Syndrome-noise tests show that readout-only flips mainly increase post-selection cost, whereas noisy GHZ-assisted global stabilizer extraction can remove the advantage. This identifies a discrete-Zeno trade-off: cheap detection reshapes the effective channel PEC must invert, rather than simply adding overhead.
Related
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BibTeX
@misc{yuan2026zenoenhanced,
title = {{Zeno-Enhanced Probabilistic Error Cancellation with Quantum Error Detection Codes}},
author = {Yi Yuan and Yuanchen Zhao and Dong E. Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.12149},
eprint = {2605.12149},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.12149},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Zeno-Enhanced Probabilistic Error Cancellation with Quantum Error Detection Codes
AU - Yi Yuan
AU - Yuanchen Zhao
AU - Dong E. Liu
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2605.12149
UR - https://arxiv.org/abs/2605.12149
AB - Probabilistic error cancellation (PEC) is unbiased but suffers exponential sampling overhead set by noise-weighted circuit volume, whereas quantum error-detecting codes (QEDCs) remove many physical faults by stabilizer post-selection but leave an undetectable logical residue. We exploit this complementarity by using post-selection to map physical noise to a weaker accepted logical channel, and then applying PEC only to the residual channel. The resulting feedback-free QED+PEC scheme interleaves Clifford logical blocks, stabilizer measurements, post-selection, and probabilistic cancellation on accepted trajectories, without real-time decoding or active recovery. A key complication is that post-selection correlates accepted fault branches through stabilizer-commutation constraints, so the sparse Pauli-Lindblad factorization underlying bare PEC no longer applies directly. We therefore construct the inverse channel perturbatively: for fixed order K, only accepted fault branches up to order K are retained, reducing preprocessing from 2^m branches to O(m^K) per block. The order-K protocol cancels the normalized post-selected channel through degree K, leaving a per-block error O(W^K+1) that accumulates at most linearly. For logical GHZ-state preparation with the $[[n,n-2,2]]$ Iceberg code under circuit-level depolarizing noise and ideal stabilizer measurements, first-order QED+PEC reaches n=200 physical qubits and lowers sampling overhead by three to four orders of magnitude relative to standard PEC while maintaining F≃0.956. Syndrome-noise tests show that readout-only flips mainly increase post-selection cost, whereas noisy GHZ-assisted global stabilizer extraction can remove the advantage. This identifies a discrete-Zeno trade-off: cheap detection reshapes the effective channel PEC must invert, rather than simply adding overhead.
ER -