CCF: AF: Small: Quantum Data Structures and Algorithms

量子计算着眼于以量子力学方式处理信息的潜在好处。由于量子物理的叠加原理与干涉现象相结合，量子算法能够比传统的经典计算机更有效地执行某些任务。由于它使用了来自各个领域的想法，量子计算的研究跨越了从实验物理学家到计算机科学再到纯数学的范围。相反，这项研究经常影响到这些不同的领域。首席研究员维姆·范·达姆博士将开发和分析量子算法使用的新数据结构。众所周知，从标准的经典计算理论来看，存储信息的方式在提高处理这些数据的算法的效率方面起着至关重要的作用。虽然量子算法的理论到目前为止已经相当复杂，但对于数据结构在增加量子信息处理的好处方面可能发挥的作用，人们知之甚少。这项建议旨在弥补这种理解的不足。Van Dam将研究量子计算机的特定架构如何影响数据的最佳存储。他还将研究以量子力学方式编码树、图、模拟数据和哈希函数的数据结构的可能性。最后，Van Dam和他的学生将研究量子软件的特性，其中一个将量子变换存储为量子态。作为该项目的一部分，Van Dam将在加州大学圣巴巴拉分校举办量子计算、通信和密码学理论年会。Van Dam还将参加UCSB的研究指导计划，在该计划中，有天赋的高中生将在首席研究员的研究小组中工作。

Quantum computing looks at the potential benefits of processing information in a quantum mechanical manner. Due to the superposition principle of quantum physics in combination with the interference phenomenon, quantum algorithms are capable of performing certain tasks more efficiently than is possible with traditional, classical computers. As it uses ideas from various fields, research in quantum computing spans the spectrum from experimental physicists, through computer science, to pure mathematics. Conversely, this research often affects these various different fields. The principle investigator, Dr Wim van Dam, will develop and analyze new data structures to be used by quantum algorithms. As is well known from standard classical computation theory, the way in which information is stored can play a crucial role in increasing the efficiency of the algorithms that act on this data. While the theory of quantum algorithms is fairly well sophisticated by now, much less is known about the role that data structures might have in increasing the benefits of processing information quantum mechanically. This proposal aims to remedy this lack of understanding. Van Dam will investigate how the specific architecture of a quantum computer affects the optimal storage of data. He will also look at the possibility of data structures to encode trees, graphs, analog data, and hash functions in a quantum mechanical manner. Lastly Van Dam and his students will investigate the properties of quantum software where one stores quantum transformations as quantum states.As part of the project Van Dam will host the Annual Conference on the Theory of Quantum Computation, Communication and Cryptography on the campus of UC Santa Barbara. Van Dam will also participate in UCSB's Research Mentorship Program during which gifted high-school students get to work in the research groups of the principle investigator.