Quantum Computing and Quantum Simulation for Complex Systems

Junxu Li, Purdue University

Abstract

The blooming of quantum computer hardware provokes enormous enthusiasm seeking for applications in various fields. Particularly, it is always of great interest to study the chemical or physical systems with quantum enhanced learning process or quantum simulation in the NISQ era. Here we will present our recent research on chemical or physical systems based on quantum computing. One main focus of this dissertation is the quantum classification algorithms development, especially for the entanglement classification. As a quantum mechanical property describing the correlation between quantum mechanical systems, entanglement has no classical analog. In the past 100 years, entanglement has been attracting enormous attentions in both the theoretical and experimental research. We investigate the entanglement classification in chemical reactions, generalizing the typical CHSH inequality from discrete measurement results into the continuous measurement results. Furthermore, we develop a quantum classification algorithm based on the typical instance-based learning algorithms, which in turn is applied into the entanglement classification problems. Additionally, the proposed quantum algorithm has a variety of applications, such as the prediction of phase transition. Quantum-enhanced classification algorithm is never the only practicable application of quantum computer. Moreover, we propose a universal quantum circuit implementation to estimate a given one-dimensional functions with a finite Fourier expansion. We demonstrate the circuit implementation with the application on square wave function. Additionally, we present a quantum circuit for the typical time-independent perturbation theory. Perturbation theory is always one of the most powerful tools for physicists and chemists dealing with the eigenenergy problems in quantum mechanics. Though PT is quite popular today, it seems that the techniques for PT does not take a ride in the era of quantum computing. In this dissertation, we present a a universal quantum circuit implementation for the time-independent PT method, which is often termed as Rayleigh–Schr"odinger PT. In order to demonstrate the implementation of the proposed quantum circuit, the extended Fermi Hubbard Model is introduced as an example. In particular, the proposed quantum circuit shows considerable speedup comparing with the typical PT methods.

Degree

Ph.D.

Advisors

Kais, Purdue University.

Subject Area

Energy|Atomic physics|Electromagnetics|Physics

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