Copy-scarce learning of ground states
Abstract
Probing multiple properties of ground states is central to understanding quantum matter, yet conventional readout can be prohibitively costly because it consumes many independently prepared copies. Here, in copy-scarce regimes, we establish optimal trade-offs between the number of initial ground-state copies and elapsed Hamiltonian-evolution time required for estimating multiple observables or reconstructing a full classical description of a unique gapped ground state. We derive a unifying inequality that quantifies how well ground states can be distinguished using initial copies and controlled dynamics, even when all copies may be consumed. It yields worst-case lower bounds on elapsed Hamiltonian time that any protocol must incur to perform either task. We construct parallel catalytic readouts that return all initial copies nearly unchanged while attaining these bounds up to poly-logarithmic factors. Our protocols require no coherent preparation circuit or its inverse, and their elapsed Hamiltonian time depends only logarithmically on the inverse of the desired return error. Thus, optimal copy--dynamics trade-offs can be attained together with catalytic return. Numerical benchmarks further show substantial reductions in end-to-end elapsed Hamiltonian time relative to a task-specialized copy-consuming protocol, even under an optimistic preparation-cost model. Our results reveal a copy--dynamics resource landscape connecting copy-scarce learning to copy-only endpoints realized by known protocols for shadow tomography and pure-state tomography.
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BibTeX
@misc{wada2026copyscarce,
title = {{Copy-scarce learning of ground states}},
author = {Kaito Wada and Nobuyuki Yoshioka},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38513},
eprint = {2609.38513},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38513},
}
RIS
TY - UNPB
TI - Copy-scarce learning of ground states
AU - Kaito Wada
AU - Nobuyuki Yoshioka
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38513
UR - https://arxiv.org/abs/2609.38513
AB - Probing multiple properties of ground states is central to understanding quantum matter, yet conventional readout can be prohibitively costly because it consumes many independently prepared copies. Here, in copy-scarce regimes, we establish optimal trade-offs between the number of initial ground-state copies and elapsed Hamiltonian-evolution time required for estimating multiple observables or reconstructing a full classical description of a unique gapped ground state. We derive a unifying inequality that quantifies how well ground states can be distinguished using initial copies and controlled dynamics, even when all copies may be consumed. It yields worst-case lower bounds on elapsed Hamiltonian time that any protocol must incur to perform either task. We construct parallel catalytic readouts that return all initial copies nearly unchanged while attaining these bounds up to poly-logarithmic factors. Our protocols require no coherent preparation circuit or its inverse, and their elapsed Hamiltonian time depends only logarithmically on the inverse of the desired return error. Thus, optimal copy--dynamics trade-offs can be attained together with catalytic return. Numerical benchmarks further show substantial reductions in end-to-end elapsed Hamiltonian time relative to a task-specialized copy-consuming protocol, even under an optimistic preparation-cost model. Our results reveal a copy--dynamics resource landscape connecting copy-scarce learning to copy-only endpoints realized by known protocols for shadow tomography and pure-state tomography.
ER -