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arXiv · 2303.09788

Higher-order quantum transformations of Hamiltonian dynamics

Tatsuki Odake·Hlér Kristjánsson·Akihito Soeda·Mio Murao
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Abstract

We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our algorithm efficiently simulates linear transformations of any seed Hamiltonian with a bounded energy range consisting of a polynomial number of terms in system size, making use of only controlled-Pauli gates and time-correlated randomness. This algorithm is an instance of quantum functional programming, where the desired function is specified as a concatenation of higher-order quantum transformations. By way of example, we demonstrate the simulation of negative time-evolution and time-reversal, and perform a Hamiltonian learning task.

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Tatsuki Odake, Hlér Kristjánsson, Akihito Soeda, Mio Murao. 2023-03-17. Higher-order quantum transformations of Hamiltonian dynamics. https://doi.org/10.1103/physrevresearch.6.l012063

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