Optimal Hamiltonian simulation for time-periodic systems

Author:

Mizuta Kaoru1,Fujii Keisuke2314

Affiliation:

1. RIKEN Center for Quantum Computing (RQC), Hirosawa 2-1, Wako, Saitama 351-0198, Japan

2. Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan.

3. Center for Quantum Information and Quantum Biology, Osaka University, Japan.

4. Fujitsu Quantum Computing Joint Research Division at QIQB, Osaka University, 1-2 Machikaneyama, Toyonaka 560-0043, Japan

Abstract

The implementation of time-evolution operators U(t), called Hamiltonian simulation, is one of the most promising usage of quantum computers. For time-independent Hamiltonians, qubitization has recently established efficient realization of time-evolution U(t)=e−iHt, with achieving the optimal computational resource both in time t and an allowable error ε. In contrast, those for time-dependent systems require larger cost due to the difficulty of handling time-dependency. In this paper, we establish optimal/nearly-optimal Hamiltonian simulation for generic time-dependent systems with time-periodicity, known as Floquet systems. By using a so-called Floquet-Hilbert space equipped with auxiliary states labeling Fourier indices, we develop a way to certainly obtain the target time-evolved state without relying on either time-ordered product or Dyson-series expansion. Consequently, the query complexity, which measures the cost for implementing the time-evolution, has optimal and nearly-optimal dependency respectively in time t and inverse error ε, and becomes sufficiently close to that of qubitization. Thus, our protocol tells us that, among generic time-dependent systems, time-periodic systems provides a class accessible as efficiently as time-independent systems despite the existence of time-dependency. As we also provide applications to simulation of nonequilibrium phenomena and adiabatic state preparation, our results will shed light on nonequilibrium phenomena in condensed matter physics and quantum chemistry, and quantum tasks yielding time-dependency in quantum computation.

Funder

MEXT Quantum Leap Flagship Program

JST COI-NEXT program

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Subject

Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics

Reference81 articles.

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3. Adam Smith, M S Kim, Frank Pollmann, and Johannes Knolle. ``Simulating quantum many-body dynamics on a current digital quantum computer''. npj Quantum Information 5, 1–13 (2019).

4. Frank Arute et al. ``Observation of separated dynamics of charge and spin in the Fermi-Hubbard model'' (2020). arXiv:2010.07965.

5. A. Yu. Kitaev. ``Quantum measurements and the Abelian Stabilizer Problem'' (1995). arXiv:quant-ph/9511026.

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