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.

翻译：费米子是遵循看似奇异的量子力学原理的基本粒子，却构成了我们日常所见的所有普通物质。因此，从基础研究与应用需求的双重角度出发，对其进行深入研究具有重大意义。本论文将探讨量子信息与计算工具如何助力这两方面的探索。我们主要通过部分状态学习这一任务展开研究：即开发断层扫描协议，以获取量子系统的简化但充分的经典描述。发展部分断层扫描的快速方法，可解决量子模拟算法中的关键瓶颈——这对当前存在缺陷的量子机器而言尤为紧迫。与此同时，在探索此类协议的过程中，我们也在重新定义"学习量子态"这一概念的内涵。一个重要的例证是，从计算视角阐明费米子的学习过程如何区别于其他类型粒子。