Zeno-Enhanced Probabilistic Error Cancellation with Quantum Error Detection Codes

• URL: http://arxiv.org/abs/2605.12149v1
• Date: Tue, 12 May 2026 14:06:27 GMT
• Title: Zeno-Enhanced Probabilistic Error Cancellation with Quantum Error Detection Codes
• Abstract summary: We exploit a complementarity between quantum error-detecting codes and probabilistic error cancellation.<n>We map physical noise to a weaker accepted logical channel, and then applying PEC only to the residual channel.<n>The resulting feedback-free QED+PEC scheme interleaves Clifford logical blocks, stabilizer measurements, post-selection, and probabilistic cancellation.
• Score: 2.6031571481535143
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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 $2^m$ 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 $F\simeq0.956$. 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.

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