Quantum information and computation

物理学对我们计算和处理信息的能力有什么终极限制？我们如何才能最有效地操纵量子态，以最大化它们的计算能力？物质的量子态的信息处理能力是什么？这些基本问题指导着我在量子信息科学方面的研究计划，这是一门交叉学科，使用物理、数学和计算机科学的思想和方法，根据量子力学来研究信息和计算。当量子效应与之相关时，经典的直觉就会崩溃。量子态自然会随着环境的变化而演变，表现为引入误差的噪音。因此，我的研究的一个关键方面旨在了解在通信或计算时纠正这些错误的最佳方法。但量子力学并不一定令人讨厌。利用量子效应进行某些计算也是可能的，比如破解密码系统和模拟物理系统，速度比任何传统计算机都要快得多。因此，我的研究还研究了如何最好地利用量子力学进行计算。这项研究是及时的--基于最近的实验进展的新兴量子计算行业有望在不久的将来推出小型量子计算机。然而，目前还不太清楚何时会出现商业上可行的可伸缩量子计算机。我的研究将在数学上取得重大进展，以加速这一时间尺度，一方面开发更强大的方法来保护量子数据，另一方面开发新的算法和应用程序。目前实现量子计算的方法利用了一系列物理系统，从基于传统半导体的超导量子比特，到本质上是量子力学的物质的奇异相。由于传统的方法不太可能超过数百个量子比特，我的研究旨在更深入地了解具有拓扑秩序的量子物质的奇异相的性质，以便我们更好地准备在未来的量子计算机和其他设备中使用它们。通过向上述三个问题提出具体的研究目标，我们将对量子信息的分布方式有更深入的了解，从而深入了解信息的真实物理本质。深度数学理论的意外应用将提出新的算法，揭示研究领域之间的新联系，并为重要的数学问题提供新的方法。这项研究是一个独特的机会，可以在量子信息科学的这些方面培训来自广泛背景的HQP，使他们拥有必要的工具和知识，为即将到来的量子革命做出贡献。

What are the ultimate limits that physics places on our ability to compute and process information? How can we most efficiently manipulate quantum states in order to maximize their computational power? What are the information-processing abilities of quantum states of matter? These fundamental questions guide my research program in quantum information science, an interdisciplinary subject using ideas and methods from physics, mathematics and computer science to study information and computation in light of quantum mechanics. When quantum effects are relevant, classical intuition breaks down. Quantum states naturally evolve with their environment, manifesting as noise that introduces errors. A key aspect of my research therefore aims to understand the best ways to correct these errors when communicating or computing. But quantum mechanics is not necessarily a nuisance. It is also possible to harness quantum effects to perform certain calculations, such as breaking cryptosystems and simulating physical systems, dramatically faster than any conventional computer. My research therefore also studies how best to take advantage of quantum mechanics to compute. This research is timely - an emerging quantum computing industry based on recent experimental advances is promising small quantum computers in the near future. It is less clear, however, when commercially viable scalable quantum computers will emerge. My research will make significant mathematical advances in order to accelerate this timescale by developing, on the one hand, more powerful methods for protecting quantum data, and on the other hand, new algorithms and applications. Current approaches to realizing quantum computation utilize a range of physical systems, from superconducting qubits based on conventional semiconductors, to exotic phases of matter that are intrinsically quantum mechanical. As the conventional approach is not likely to scale beyond hundreds of qubits, my research aims to gain a deeper understanding of the properties of exotic phases of quantum matter possessing topological order, so that we may be better equipped to use them in future quantum computers and other devices. By advancing specific research objectives towards the above three questions, we will obtain a deeper understanding of the ways that quantum information can be distributed, giving insight into the true physical nature of information. Unforeseen applications of deep mathematical theories will suggest new algorithms, uncovering new connections between research areas and offering new approaches to important mathematical problems. This research represents a unique opportunity to train HQP from a wide range of backgrounds in these aspects of quantum information science, equipping them with the necessary tools and knowledge to contribute to the upcoming quantum revolution.