Spacetime mitigation of logical errors
Abstract
Error detection can suppress noise at a lower sampling cost than probabilistic error cancellation (PEC), but leaves residual logical errors. We combine the two approaches to mitigate these errors while lowering the cost of PEC. We introduce a spacetime Pauli-Lindblad representation and use it to construct the post-selected logical noise perturbatively from physical noise and syndrome information. Individually undetected faults contribute at first order, while detected faults with canceling syndromes generate higher-order terms coupling distinct spacetime locations. To reconcile the nonlinearity of post-selection with the linearity of PEC, we formulate the combined protocol in terms of unnormalized post-selected maps, with normalization performed only after averaging. On the ibm_aachen superconducting quantum processor, Clifford experiments validate the post-selected noise model and its perturbative scaling. We then demonstrate error detection with first-order PEC for transverse-field Ising dynamics using 22 data and 27 check qubits. The combined protocol recovers the mean magnetization within statistical uncertainty through six Trotter steps and reduces the inferred sampling overhead by up to a factor of 63 relative to PEC without post-selection.
Related
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BibTeX
@misc{fischer2026spacetime,
title = {{Spacetime mitigation of logical errors}},
author = {Laurin E. Fischer and Ali Javadi-Abhari and Simon Martiel and Alireza Seif},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13108},
eprint = {2609.13108},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13108},
}
RIS
TY - UNPB
TI - Spacetime mitigation of logical errors
AU - Laurin E. Fischer
AU - Ali Javadi-Abhari
AU - Simon Martiel
AU - Alireza Seif
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13108
UR - https://arxiv.org/abs/2609.13108
AB - Error detection can suppress noise at a lower sampling cost than probabilistic error cancellation (PEC), but leaves residual logical errors. We combine the two approaches to mitigate these errors while lowering the cost of PEC. We introduce a spacetime Pauli-Lindblad representation and use it to construct the post-selected logical noise perturbatively from physical noise and syndrome information. Individually undetected faults contribute at first order, while detected faults with canceling syndromes generate higher-order terms coupling distinct spacetime locations. To reconcile the nonlinearity of post-selection with the linearity of PEC, we formulate the combined protocol in terms of unnormalized post-selected maps, with normalization performed only after averaging. On the ibm_aachen superconducting quantum processor, Clifford experiments validate the post-selected noise model and its perturbative scaling. We then demonstrate error detection with first-order PEC for transverse-field Ising dynamics using 22 data and 27 check qubits. The combined protocol recovers the mean magnetization within statistical uncertainty through six Trotter steps and reduces the inferred sampling overhead by up to a factor of 63 relative to PEC without post-selection.
ER -