EMT/QIS: Continuous-time quantum computation

量子计算的理论方法经常将量子系统的状态建模为随时间离散变化的东西。 然而，一个不可测的量子系统从根本上说是在时间上连续演化的，正如薛定谔方程所描述的那样。 即使是量子测量过程也可以用连续时间随机微分方程来描述，本研究以完整的连续时间公式来探索量子计算，旨在揭示处理量子信息的新范式，研究重点集中在三个关键领域：连续时间量子计算体系结构、连续时间量子纠错和连续时间量子算法. 之所以选择这些领域，是因为每个领域都有突出连续时间和离散时间量子计算公式之间差异的例子。 例如，连续时间量子行走架构不需要外部动态控制，连续时间量子反馈可以调解量子纠错，连续时间量子散射可以计算布尔公式，查询次数比任何经典算法都少。 本研究的一个主要目标是扩展这些方向并开发新的方向。 该战略将集中在明确定义和易于处理的问题上，以便取得进展。该项目不仅支持量子信息科学的研究生培训，而且还通过西南量子信息和技术（SQuInT）网络支持教育和推广活动。PI将在他的家乡机构之外寻找优秀的学生，特别是鼓励那些代表性不足的群体，并赞助他们出席SQuInT会议，以进一步丰富这一不断发展的领域。

Theoretical approaches to quantum computing frequently model the state of aquantum system as something that changes discretely in time. However, anunmeasured quantum system fundamentally evolves continuously in time asdescribed by Schroedinger's equation. Even the quantum measurement processcan be described by a continuous-time stochastic differential equation.This research explores quantum computation in its complete continuous-timeformulation, with the goal of uncovering new paradigms for processingquantum information.The research focuses on three key areas: continuous-time quantum computingarchitectures, continuous-time quantum error correction, and continuous-timequantum algorithms. These areas were selected because examples highlightingthe differences between continuous-time and discrete-time quantum computingformulations are already known in each of them. For example,continuous-time quantum walk architectures require no external dynamicalcontrols, continuous-time quantum feedback can mediate quantum errorcorrection, and continuous-time quantum scattering can calculate Booleanformulas with fewer queries than any classical algorithm can. A majorobjective of this research is to expand upon these directions and developnew ones. The strategy will be to focus on problems that are sufficientlywell-defined and tractable that progress can be made.This project not only supports graduate student training in quantuminformation science but also supports education and outreach activitiesthrough the Southwest Quantum Information and Technology (SQuInT) Network.The PI will seek out exceptional students outside his home institution,especially encouraging those in underrepresented groups, and sponsor theirattendance at SQuInT meetings to further enrich this growing field.