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  • Letter
  • Open Access

Higher-order quantum transformations of Hamiltonian dynamics

Tatsuki Odake1,*, Hlér Kristjánsson1,†, Akihito Soeda2,1,3, and Mio Murao1,4,‡

  • 1Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
  • 2National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8430, Japan
  • 3Department of Informatics, School of Multidisciplinary Sciences, SOKENDAI (The Graduate University for Advanced Studies), 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
  • 4Trans-Scale Quantum Science Institute, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan

  • *tatsuki.odake@phys.s.u-tokyo.ac.jp
  • †Present address: Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5, Canada, and Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada.
  • ‡murao@phys.s.u-tokyo.ac.jp
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Phys. Rev. Research 6, L012063 – Published 22 March, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L012063

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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Phys. Rev. Research 6, L012063– Published 22 March, 2024
  • Received 21 May 2023
  • Accepted 6 December 2023
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