Berlin 2024 – scientific programme

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QI: Fachverband Quanteninformation

QI 22: Quantum Simulation I

QI 22.6: Talk

Thursday, March 21, 2024, 11:15–11:30, HFT-FT 101

Quantum computing Floquet energy spectra — •Benedikt Fauseweh^1,2 and Jian-Xin Zhu³ — ¹TU Dortmund University, Germany — ²German Aerospace Center (DLR), Germany — ³Los Alamos National Laboratory, USA

The classical computational framework for describing Floquet systems is challenging. The prevalent method involves simple time evolution for a set of initial states, providing limited insights. The Floquet formalism, which offers information about the entire eigenvalue spectrum, is of theoretical interest. However, its computational complexity is even greater than that of simple time evolution methods.

To address this, we present two quantum algorithms tailored for NISQ devices. Utilizing parameterized quantum circuits, these algorithms are designed to variationally approximate Floquet eigenstates in both time and frequency domains. The accuracy of the first algorithm is dependent on the depth of the quantum circuit, whereas the second focuses on frequency truncation and the width of the parameterized quantum circuit. Notably, as the system size increases, the algorithms exhibit complementary requirements in terms of qubit count and circuit depth.

Additionally, our work underscores a connection between the ability of variational methods to approximate ground states of quantum critical systems and Floquet modes. This observation suggests potential avenues for further research in the behavior and characteristics of driven quantum systems.

Reference: B. Fauseweh and J.-X. Zhu, Quantum 7, 1063 (2023)

Keywords: NISQ; Variational Quantum Algorithms; VQE; Floquet; Digital Quantum Simulation