Heisenberg-limited Hamiltonian learning for interacting bosons

• URL: http://arxiv.org/abs/2307.04690v1
• Date: Mon, 10 Jul 2023 16:44:23 GMT
• Title: Heisenberg-limited Hamiltonian learning for interacting bosons
• Authors: Haoya Li, Yu Tong, Hongkang Ni, Tuvia Gefen, Lexing Ying
• Abstract summary: We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. In the protocol, we only use bosonic coherent states, beam splitters, phase shifters, and homodyne measurements.
• Score: 6.352264764099532
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. For Hamiltonians with an underlying bounded-degree graph structure, we can learn all parameters with root mean squared error $\epsilon$ using $\mathcal{O}(1/\epsilon)$ total evolution time, which is independent of the system size, in a way that is robust against state-preparation and measurement error. In the protocol, we only use bosonic coherent states, beam splitters, phase shifters, and homodyne measurements, which are easy to implement on many experimental platforms. A key technique we develop is to apply random unitaries to enforce symmetry in the effective Hamiltonian, which may be of independent interest.

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