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15 October 2024 |
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Article overview
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Adaptive Online Learning of Quantum States | | Xinyi Chen
; Elad Hazan
; Tongyang Li
; Zhou Lu
; Xinzhao Wang
; Rui Yang
; | | Date: |
1 Jun 2022 | | Abstract: | In the fundamental problem of shadow tomography, the goal is to efficiently
learn an unknown $d$-dimensional quantum state using projective measurements.
However, it is rarely the case that the underlying state remains stationary:
changes may occur due to measurements, environmental noise, or an underlying
Hamiltonian state evolution. In this paper we adopt tools from adaptive online
learning to learn a changing state, giving adaptive and dynamic regret bounds
for online shadow tomography that are polynomial in the number of qubits and
sublinear in the number of measurements. Our analysis utilizes tools from
complex matrix analysis to cope with complex numbers, which may be of
independent interest in online learning. In addition, we provide numerical
experiments that corroborate our theoretical results. | | Source: | arXiv, 2206.00220 | | Services: | Forum | Review | PDF | Favorites | |
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