Zeno-Enhanced Probabilistic Error Cancellation with Quantum Error Detection Codes

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 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.