Bu, K., Koh, D. E., Garcia, R. J., & Jaffe, A. (2024). Classical shadows with Pauli-invariant unitary ensembles. Npj Quantum Information, 10(1). https://doi.org/10.1038/s41534-023-00801-w
Abstract:
Classical shadows provide a noise-resilient and sample-efficient method for learning quantum system properties, relying on a user-specified unitary ensemble. What is the weakest assumption on this ensemble that can still yield meaningful results? To address this, we focus on Pauli-invariant unitary ensembles—those invariant under multiplication by Pauli operators. For these ensembles, we present explicit formulas for the reconstruction map and sample complexity bounds and extend our results to the case when noise impacts the protocol implementation. Two applications are explored: one for locally scrambled unitary ensembles, where we present formulas for the reconstruction map and sample complexity bounds that circumvent the need to solve an exponential-sized linear system, and another for the classical shadows of quantum channels. Our results establish a unified framework for classical shadows with Pauli-invariant unitary ensembles, applicable to both noisy and noiseless scenarios for states and channels and primed for implementation on near-term quantum devices.
License type:
Attribution 4.0 International (CC BY 4.0)
Funding Info:
This research / project is supported by the Agency for Science, Technology and Research - Central Research Fund
Grant Reference no. : NA
This research / project is supported by the Agency for Science, Technology and Research - Quantum Engineering Programme
Grant Reference no. : NRF2021-QEP2-02-P03
This research / project is supported by the Agency for Science, Technology and Research - Career Development Fund
Grant Reference no. : C230917003