Zeno-Enhanced Probabilistic Error Cancellation with Quantum Error Detection Codes
Yi Yuan, Yuanchen Zhao, Dong E. Liu

TL;DR
This paper introduces a novel quantum error correction scheme combining quantum error-detecting codes with probabilistic error cancellation, significantly reducing sampling overhead for logical state preparation under noise.
Contribution
It develops a feedback-free QED+PEC method that maps physical noise to a weaker logical channel, enabling efficient error mitigation without real-time decoding.
Findings
First-order QED+PEC reduces overhead by 3-4 orders of magnitude for large qubit systems.
The scheme maintains high fidelity (~0.956) in GHZ-state preparation with 200 qubits.
Global stabilizer extraction can negate the advantage of the proposed method under certain noise conditions.
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…
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