The Complexity of Noise: A Philosophical Outlook on Fault-Tolerant Quantum Computation

噪声的复杂性：容错量子计算的哲学观

• 批准号: 0847547
• 负责人: Amit Hagar
• 金额: $ 14.4万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-02-15 至 2010-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0847547&HistoricalAwards=false
• 关键词: Complexity; Noise; Philosophical; Outlook; Fault

This project on quantum computation is supported by NSF's Science, Technology, and Society program. It is also fund by the joint initiative with Mathematical and Physical Sciences Directorate: Research at the Interface of the Mathematical and Physical Sciences and Society. In quantum computation, algorithms exist that can solve problems more efficiently than any known classical algorithms. While the laws of quantum mechanics are error-free, computers (physical objects that are subject to the laws of physics) are subject to imprecision that can cause a mismatch between what they are supposed to do and what they actually do. The elimination of such errors has become a predominant goal.A worldwide quest for the realization of a large scale computationally superior quantum computer that is fault-tolerant is currently taking place. Optimists suppose that under a certain threshold of errors, an arbitrary long fault-tolerant quantum computation can be achieved with only moderate overhead in computational cost. Pessimists object that there are fundamental (as opposed to merely technological) reasons why large scale quantum computers will never be computationally superior to classical ones no matter what innovations are introduced. Since a complete characterization of actual errors is itself an intractable task, arguments for and against the feasibility of such machines invite philosophical scrutiny.This project aims to gain further insights for the debate by reformulating the problem within statistical mechanics. The reformulation is suggested by many similarities that exist between the foundations of statistical mechanics (particularly the debate on the origins of thermodynamic irreversibility) and the foundations of quantum mechanics (and the analogous debate on its universal applicability). On this view, rather than an active attempt to shield the quantum computer from external noise, fault-tolerant quantum computing should be portrayed as a passive attempt to prepare computationally superior quantum states that are noise-resilient. Skepticism about the feasibility of a large scale computationally superior quantum computer could then be vindicated by demonstrating how to connect the putative scarcity of such computational superior noise-resilient states with the computational cost involved in locating them.The pedagogical component of this project aims to expose humanities students to the exciting transition in the meaning of notions such as "computation" and "complexity," which have left their cradle, mathematical logic, and have migrated into physics with the advancement of technology. The goal of this component is achieved by devising a new upper-level undergraduate course in the humanities and a corresponding compendium (that will be placed online) in which the historical and the philosophical foundations of this transition are discussed.

NSF的科学，技术和社会计划支持量子计算的该项目。它还由与数学和物理科学局的联合计划资助：数学和物理科学与社会的界面研究。在量子计算中，存在比任何已知的经典算法更有效地解决问题的算法。虽然量子力学定律是无错误的，但计算机（受物理定律约束的物理对象）可能会导致不精确，这可能会在他们应该做的事情和实际做的事情之间引起不匹配。消除此类错误已成为一个主要的目标。全世界寻求实现当前正在发生的大规模计算上的量子计算机。乐观主义者认为，在一定的错误阈值下，只有中等开销的计算成本，就可以实现任意长的长断层量子计算。悲观主义者反对说，无论引入哪些创新，大规模量子计算机在计算上永远都不会优于经典计算机的基本原因（仅仅是技术）的原因。由于对实际错误的完整表征本身是一项棘手的任务，因此对此类机器的可行性的争论邀请了哲学审查。该项目旨在通过对统计力学中的问题进行重新解决，以进一步了解辩论。重新制定是由统计力学基础（尤其是关于热力学不可逆性起源的辩论）与量子力学基础（以及其普遍适用性的类似辩论）之间存在的许多相似之处。在此视图中，不应将量子计算机免受外部噪声屏蔽量子的主动尝试，而应将易于故障的量子计算描述为一种被动的尝试，以准备降噪的计算上优质量子状态。然后，可以通过演示如何将这种计算性较高噪声状态的假定稀缺性与定位涉及的计算成本联系起来的假定稀缺性来证明有关大规模计算上量子计算机的可行性的怀疑主义。随着技术的发展，已迁移到物理学。该组成部分的目标是通过设计人文学科的新上层本科课程，并讨论了该过渡的历史和哲学基础的相应纲要（将被放置在线）。