Classical Shadows with Selective GHZ Measurements
Abstract
Classical shadows allow the prediction of many quantum-state properties from measurement data, but their efficiency strongly depends on the underlying measurement ensemble. We introduce selective GHZ measurement (SGM) shadows, which perform Greenberger-Horne-Zeilinger (GHZ)-basis measurements on randomly selected subsets of qubits and computational-basis measurements on their complement. The corresponding quantum circuits are practically feasible, with their number of CNOT gates scaling linearly with the number of qubits. This is in stark contrast to global Clifford circuits, which are generally difficult to implement. Varying the subset distribution allows tuning the SGM shadow protocol for different classes of observables with prescribed X/Y support, allowing us to outperform local Pauli as well as global Clifford shadows in certain scenarios. We determine the exact shadow channel and its inverse for arbitrary subset distributions and prove an explicit bound on the shadow norm using methods from discrete Fourier analysis and Markov semigroup theory. For natural choices of subset distributions, this gives a polynomial scaling for observables with fixed X/Y-locality. Numerical simulations of up to 50 qubits support the predicted improvements for nonlocal observables and long-range systems, and demonstrate the practical benefits of our protocol's generality by showing how the subset distributions can be tailored to settings such as fermionic modes under the Jordan-Wigner transformation.
Related
BibTeX
@misc{faroß2026classical,
title = {{Classical Shadows with Selective GHZ Measurements}},
author = {Nicolas Faroß and Marc Wanner and Pingal Pratyush Nath and Akshay Gaikwad and Anton Frisk Kockum and Devdatt Dubhashi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40095},
eprint = {2609.40095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40095},
}
RIS
TY - UNPB
TI - Classical Shadows with Selective GHZ Measurements
AU - Nicolas Faroß
AU - Marc Wanner
AU - Pingal Pratyush Nath
AU - Akshay Gaikwad
AU - Anton Frisk Kockum
AU - Devdatt Dubhashi
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40095
UR - https://arxiv.org/abs/2609.40095
AB - Classical shadows allow the prediction of many quantum-state properties from measurement data, but their efficiency strongly depends on the underlying measurement ensemble. We introduce selective GHZ measurement (SGM) shadows, which perform Greenberger-Horne-Zeilinger (GHZ)-basis measurements on randomly selected subsets of qubits and computational-basis measurements on their complement. The corresponding quantum circuits are practically feasible, with their number of CNOT gates scaling linearly with the number of qubits. This is in stark contrast to global Clifford circuits, which are generally difficult to implement. Varying the subset distribution allows tuning the SGM shadow protocol for different classes of observables with prescribed X/Y support, allowing us to outperform local Pauli as well as global Clifford shadows in certain scenarios. We determine the exact shadow channel and its inverse for arbitrary subset distributions and prove an explicit bound on the shadow norm using methods from discrete Fourier analysis and Markov semigroup theory. For natural choices of subset distributions, this gives a polynomial scaling for observables with fixed X/Y-locality. Numerical simulations of up to 50 qubits support the predicted improvements for nonlocal observables and long-range systems, and demonstrate the practical benefits of our protocol's generality by showing how the subset distributions can be tailored to settings such as fermionic modes under the Jordan-Wigner transformation.
ER -