Learning, Optimizing, and Simulating Fermions with Quantum Computers

TL;DR

This paper explores how quantum information tools can improve the simulation, learning, and optimization of fermionic systems, addressing key challenges in quantum simulation and state tomography.

Contribution

It introduces novel protocols for partial quantum state tomography of fermions and refines the understanding of quantum state learning specific to fermionic particles.

Findings

Developed fast partial tomography methods for fermions

Enhanced understanding of quantum state learning for fermions

Addressed bottlenecks in quantum simulation algorithms

Abstract

Fermions are fundamental particles which obey seemingly bizarre quantum-mechanical principles, yet constitute all the ordinary matter that we inhabit. As such, their study is heavily motivated from both fundamental and practical incentives. In this dissertation, we will explore how the tools of quantum information and computation can assist us on both of these fronts. We primarily do so through the task of partial state learning: tomographic protocols for acquiring a reduced, but sufficient, classical description of a quantum system. Developing fast methods for partial tomography addresses a critical bottleneck in quantum simulation algorithms, which is a particularly pressing issue for currently available, imperfect quantum machines. At the same time, in the search for such protocols, we also refine our notion of what it means to learn quantum states. One important example is the ability to articulate, from a computational perspective, how the learning of fermions contrasts with other types of particles.