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Published February 2022 | Accepted Version
Book Section - Chapter Open

Exponential Separations Between Learning With and Without Quantum Memory

Abstract

We study the power of quantum memory for learning properties of quantum systems and dynamics, which is of great importance in physics and chemistry. Many state-of-the-art learning algorithms require access to an additional external quantum memory. While such a quantum memory is not required a priori, in many cases, algorithms that do not utilize quantum memory require much more data than those which do. We show that this trade-off is inherent in a wide range of learning problems. Our results include the following: We show that to perform shadow tomography on an n-qubit state ρ with M observables, any algorithm without quantum memory requires Ω̅(min(M,2ⁿ)) samples of ρ in the worst case. Up to log factors, this matches the upper bound of [1], and completely resolves an open question in [2], [3]. We establish exponential separations between algorithms with and without quantum memory for purity testing, distinguishing scrambling and depolarizing evolutions, and uncovering symmetry in physical dynamics. Our separations improve and generalize prior work of [4] by allowing for a broader class of algorithms without quantum memory. We give the first tradeoff between quantum memory and sample complexity. More precisely, we prove that to estimate absolute values of all n -qubit Pauli observables, algorithms with k

Additional Information

© 2021 IEEE. S.C. was supported by NSF Awards 2103300, CCF-1453261, CCF-1565235 and Ankur Moitra's ONR Young Investigator Award. J.C. was supported by a Junior Fellowship from the Harvard Society of Fellows, as well as the Department of Energy under grant DE-SC0007870. H.H. was supported by the J. Yang & Family Foundation and Google PhD Fellowship.

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Created:
August 22, 2023
Modified:
October 23, 2023