QUANTUM COMPUTING AND QUANTUM SIMULATION FOR COMPLEX SYSTEMS

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