Closed-form analytic expressions for shadow estimation with brickwork circuits

Journal
Quantum Information and Computation
Volume
23
Issue
11-12
Start Page
961
End Page
993
Citation
Quantum Information and Computation 23 (11-12): 961-993 (2023-09)
Publisher DOI
10.26421/QIC23.11-12-5
Scopus ID
2-s2.0-85172346708
ArXiv ID
2211.09835v1
Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables. We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.
Subjects
Quantum Physics
Quantum Physics