Identifying the Sign of Coherent Over-Rotations with Logarithmically Many Pauli Settings
Abstract
Calibrating a quantum processor means estimating gate-error parameters from data, and a hard-to-estimate parameter is usually assumed to leave a weak signature more repetitions will resolve. Coherent over-rotations break that premise. For commuting single- and two-qubit transverse over-rotations with known support on a computational-basis input, the passive histogram is exactly invariant under a sign group acting on the coherent angles, of order 2n+1 for the complete family with n≥2, so no estimator resolves the signs uniformly at any sample size. A calibration correction applied with the wrong sign doubles the rotation error it should remove. At zero angle the obstruction turns continuous, with a Fisher information singular along every coherent direction and an infinite Cramér-Rao bound. At generic angles the continuous defect clears for 5≤ n≤8, the range we compute, while the sign degeneracy persists. Covering the support removes both, and a design resolves the signed angles uniformly exactly when it covers. On |ηR|<π/2, 0≤ pR<1/2 coverage is constructive, returning each angle in closed form from a ratio of two measured expectations without knowing the rates. A twirl-free code of ⌈log2(n+1)⌉ added product-Pauli settings covers, and for the complete family none uses fewer. Conditioning then sets the Cramér-Rao cost, and we give its floor explicitly. Exact computation matches the theory, the passive fit stays at chance on the signs at every budget while the closed-form inverse recovers them, and angle magnitudes on two IBM Heron processors follow the conditioning ordering.
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BibTeX
@misc{pan2026identifying,
title = {{Identifying the Sign of Coherent Over-Rotations with Logarithmically Many Pauli Settings}},
author = {Yi Pan and Meng Hsiu Tsai and Weihang You and Hanqi Jiang and Junhao Chen and Wei Zhang and Isaac Lyngaas and Yingfeng Wang and Tianming Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.21663},
eprint = {2607.21663},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.21663},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Identifying the Sign of Coherent Over-Rotations with Logarithmically Many Pauli Settings
AU - Yi Pan
AU - Meng Hsiu Tsai
AU - Weihang You
AU - Hanqi Jiang
AU - Junhao Chen
AU - Wei Zhang
AU - Isaac Lyngaas
AU - Yingfeng Wang
AU - Tianming Liu
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2607.21663
UR - https://arxiv.org/abs/2607.21663
AB - Calibrating a quantum processor means estimating gate-error parameters from data, and a hard-to-estimate parameter is usually assumed to leave a weak signature more repetitions will resolve. Coherent over-rotations break that premise. For commuting single- and two-qubit transverse over-rotations with known support on a computational-basis input, the passive histogram is exactly invariant under a sign group acting on the coherent angles, of order 2^n+1 for the complete family with n≥2, so no estimator resolves the signs uniformly at any sample size. A calibration correction applied with the wrong sign doubles the rotation error it should remove. At zero angle the obstruction turns continuous, with a Fisher information singular along every coherent direction and an infinite Cramér-Rao bound. At generic angles the continuous defect clears for 5≤ n≤8, the range we compute, while the sign degeneracy persists. Covering the support removes both, and a design resolves the signed angles uniformly exactly when it covers. On |η_R|<π/2, 0≤ p_R<1/2 coverage is constructive, returning each angle in closed form from a ratio of two measured expectations without knowing the rates. A twirl-free code of ⌈log_2(n+1)⌉ added product-Pauli settings covers, and for the complete family none uses fewer. Conditioning then sets the Cramér-Rao cost, and we give its floor explicitly. Exact computation matches the theory, the passive fit stays at chance on the signs at every budget while the closed-form inverse recovers them, and angle magnitudes on two IBM Heron processors follow the conditioning ordering.
ER -