Shot- and Noise-Aware Pauli Correlation Encoding for Max-Cut Experiments on IBM Heron Quantum Processor
Abstract
Pauli correlation encoding (PCE) encodes m binary variables in the signs of k-body Pauli correlators of n=O(m1/k) qubits, and trains a parameterized circuit on a relaxed loss of sharpness α. The strongest published schedules sharpen this loss aggressively and are benchmarked with exact expectation values, whereas a quantum computer estimates correlators from a finite number of shots. We show that the sharpness is a hidden shot budget. Since the expected sign of a correlator estimated from S shots, erf(c√(S/2)), agrees with tanh(0.851√S c) to within $0.019$, the edge term of the relaxed loss at α=0.851√S approximately equals, up to a constant, minus twice the cut expected from decoding S shots. This explains why schedules tuned with exact expectation values lose their advantage at realistic budgets, and yields a shot-aware schedule whose final sharpness is set by the shot budget. On five G-set graphs with $800$ variables on $13$ qubits, this schedule outperforms every published schedule at its target budget in all $150$ paired comparisons of the decoded circuit output, owing to the sharpness at 1.6×104 shots and mostly to switching off the regularization at 103; after a classical bit-swap search, it remains the best on average at 1.6×104 shots. Device noise damps the correlators by a factor s, which amounts to a smaller shot budget s2S. On the IBM Heron processor ibm_fez, an all-to-all ansatz of the type used for the best published G-set results compiles to $835$ CZ gates and decodes to a random cut, while our $96$-CZ hardware-native circuit, trained in simulation and sharpened to α≃0.65 s√S, retains up to $0.919$ of the best-known cut. For new circuits, a damping and an offset calibrated on other circuits of the same graph predicted the decoded cuts at 103 shots to within $0.002$.
Related
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BibTeX
@misc{boussahi2026shot,
title = {{Shot- and Noise-Aware Pauli Correlation Encoding for Max-Cut Experiments on IBM Heron Quantum Processor}},
author = {Achraf Boussahi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19544},
eprint = {2610.19544},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19544},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Shot- and Noise-Aware Pauli Correlation Encoding for Max-Cut Experiments on IBM Heron Quantum Processor
AU - Achraf Boussahi
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19544
UR - https://arxiv.org/abs/2610.19544
AB - Pauli correlation encoding (PCE) encodes m binary variables in the signs of k-body Pauli correlators of n=O(m^1/k) qubits, and trains a parameterized circuit on a relaxed loss of sharpness α. The strongest published schedules sharpen this loss aggressively and are benchmarked with exact expectation values, whereas a quantum computer estimates correlators from a finite number of shots. We show that the sharpness is a hidden shot budget. Since the expected sign of a correlator estimated from S shots, erf(c√(S/2)), agrees with tanh(0.851√S c) to within $0.019$, the edge term of the relaxed loss at α=0.851√S approximately equals, up to a constant, minus twice the cut expected from decoding S shots. This explains why schedules tuned with exact expectation values lose their advantage at realistic budgets, and yields a shot-aware schedule whose final sharpness is set by the shot budget. On five G-set graphs with $800$ variables on $13$ qubits, this schedule outperforms every published schedule at its target budget in all $150$ paired comparisons of the decoded circuit output, owing to the sharpness at 1.6×10^4 shots and mostly to switching off the regularization at 10^3; after a classical bit-swap search, it remains the best on average at 1.6×10^4 shots. Device noise damps the correlators by a factor s, which amounts to a smaller shot budget s^2S. On the IBM Heron processor ibm_fez, an all-to-all ansatz of the type used for the best published G-set results compiles to $835$ CZ gates and decodes to a random cut, while our $96$-CZ hardware-native circuit, trained in simulation and sharpened to α≃0.65 s√S, retains up to $0.919$ of the best-known cut. For new circuits, a damping and an offset calibrated on other circuits of the same graph predicted the decoded cuts at 10^3 shots to within $0.002$.
ER -