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arXiv · 2303.02209

Large-scale simulations of Floquet physics on near-term quantum computers

Timo Eckstein·Refik Mansuroglu·Piotr Czarnik·Jian-Xin Zhu·Michael J. Hartmann·Lukasz Cincio·Andrew T. Sornborger·Zoë Holmes
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Abstract

Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantum frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum's trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency $\omega$ but also a linear advantage in simulation time $t$ compared to~Trotterization.

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Timo Eckstein, Refik Mansuroglu, Piotr Czarnik, Jian-Xin Zhu, Michael J. Hartmann, Lukasz Cincio, Andrew T. Sornborger, Zoë Holmes. 2023-03-03. Large-scale simulations of Floquet physics on near-term quantum computers. https://doi.org/10.1038/s41534-024-00866-1

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