Consistent Histories and Quantum Computation

这项用于探索研究的小额赠款由CCR的TOC计划、PHY的理论物理计划和DARPA的信息技术办公室资助，探索将量子力学的一致历史公式应用于新的量子计算领域的一些核心问题。这些应用包括改进量子计算的算法(1)通过在迭代时间进行测量，以及(2)通过错误检测和纠正。量子计算最近引起了很多关注，因为Peter Shor证明了某些任务，包括大数的因式分解，可以在量子计算机上在多项式时间内完成，而目前还没有在“经典”计算机上进行因式分解的多项式时间算法。显然，如果能够建造这样一台计算机，它将在计算科学的许多领域有许多重要的应用，包括在通信和信息处理方面。实际上，建造这样一台量子计算机是一项艰巨的任务，因为存在严重的技术困难。这个SGER项目的目标之一是在卡内基梅隆大学的计算机科学家、理论物理学家和实验物理学家之间发起一项合作努力，以探索一致历史框架在确定这种量子计算设备的可行性方面的应用。一致历史方法使我们有可能用更现实的术语(原子、光子等随着时间的推移实际上在做一些事情)来思考计算过程，而不是通常的“教科书”方法，这种方法将量子系统视为一条“大烟龙”，直到做出最终测量的时间点，系统的波函数“崩溃”成物理上可以理解的东西。*

This Small Grant for Exploratory Research (SGER), funded by the Theory of Computing (TOC) Program, CCR, by the Theoretical Physics Program, PHY and by the Informations Technologies Office, DARPA, explores the application of the consistent history formulation of quantum mechanics to some central problems in the new field of quantum computation. These applications include improving algorithms for quantum computation (1) by carrying out measurements at itermediate times, and (2) by error detection and correction. Quantum computation has recently attracted a lot of attention, because Peter Shor showed that certain tasks, including factoring large numbers, could be carried out in polynomial time on a quantum computer, whereas no polynomial-time algorithm for factoring on a ``classical'' computer is presently known. Clearly, if it could be built, such a computer would have many important applications in many areas of computational science, including in communications and information processing. Actually constructing such a quantum computer represents a daunting task, because of severe technical difficulties. One of the goals of this SGER project is to initiate a collaborative effort between computer scientists, theoretical physicists, and experimental physicists at Carnegie Mellon University, in order to explore the applications of the consistent histories framework to determining the feasibility of such a quantum computing device. The consistent histories approach make it possible to think about the computational process in more realistic terms (where atoms, photons, etc. are actually doing something over time) than is possible in the usual ``textbook'' approach, that views the quantum system as a ``great smokey dragon'' up until the point in time at which a final measurement is made, and the wave function of the system ``collapses'' into something which is physically understandable.***