Shadow bootstrapping: Nearly minimal-setting pure-state tomography with shallow Clifford measurements
Abstract
We present a pure-state tomography algorithm that uses a nearly minimal number of measurement settings while achieving optimal sample complexity with nonadaptive single-copy shallow Clifford measurements. For an arbitrary n-qubit pure state |ψ⟩ ∈ ℂd, where d=2n, the algorithm uses O(d/ε) copies and Õ(1) measurement settings to output a state vector |ψ̂⟩ satisfying 1−|⟨ψ|ψ̂⟩|2≤ε with high probability. Each measurement is implemented by a Clifford circuit of depth O(log n). Reusing each measurement setting allows the data to be stored compactly as per-basis outcome histograms. Given these histograms, classical post-processing runs in Õ(d) time. Our key technique, \textit{shadow bootstrapping}, uses the current estimate to reduce the variance of subsequent residual estimation, enabling progressively more accurate reconstruction with only a constant number of new measurement settings per stage.
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BibTeX
@misc{cho2026shadow,
title = {{Shadow bootstrapping: Nearly minimal-setting pure-state tomography with shallow Clifford measurements}},
author = {Gyungmin Cho and Dohun Kim},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06073},
eprint = {2611.06073},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06073},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Shadow bootstrapping: Nearly minimal-setting pure-state tomography with shallow Clifford measurements
AU - Gyungmin Cho
AU - Dohun Kim
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06073
UR - https://arxiv.org/abs/2611.06073
AB - We present a pure-state tomography algorithm that uses a nearly minimal number of measurement settings while achieving optimal sample complexity with nonadaptive single-copy shallow Clifford measurements. For an arbitrary n-qubit pure state |ψ⟩ ∈ ℂ^d, where d=2^n, the algorithm uses O(d/ε) copies and Õ(1) measurement settings to output a state vector |ψ̂⟩ satisfying 1−|⟨ψ|ψ̂⟩|^2≤ε with high probability. Each measurement is implemented by a Clifford circuit of depth O(log n). Reusing each measurement setting allows the data to be stored compactly as per-basis outcome histograms. Given these histograms, classical post-processing runs in Õ(d) time. Our key technique, \textit{shadow bootstrapping}, uses the current estimate to reduce the variance of subsequent residual estimation, enabling progressively more accurate reconstruction with only a constant number of new measurement settings per stage.
ER -