Quantum: Dynamics of an open quantum system: decoherence processes and encoded control

量子：开放量子系统的动力学：退相干过程和编码控制

• 批准号: 0622242
• 负责人: Leonid Pryadko
• 金额: --
• 依托单位: University of California-Riverside
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0622242&HistoricalAwards=false
• 关键词: Quantum; Dynamics; open; quantum; system

Need for the proposed research: Feasibility of a useful quantum computer (QC) crucially depends upon the performance of quantum error correcting codes (QECC). Current theory of QECC relies upon overly simplistic models of error operators in controlled systems. Errors associated with such simplification can ruin the group-theoretical structure of QECC and substantially degrade their practical performance. The problem is further amplified for embedded, concatenated code constructions, due to the error propagation between different layers of concatenated encoding.The goal of the proposed research is to build a unified description of the decoherence processes applicable for a range of existing passive and active QECC, and use the results to develop highly-optimized heterogeneous concatenated codes for several QC implementations. Research effort proposed: The proposed research will be conducted by an interdisciplinary team, the PI with a strong background in many-body quantum physics, and the co-PI with an extensive experience in coding theory. The proposed research concerns two fundamental problems: quantum kinetics of a driven open system and continuous measurement for such a system. Decoherence processes in several solid-state QC implementations will be analyzed for encoded quantum systems, with projective syndrome measurements done either intermittently during, or at the end of the computation cycle. The effects of second and higher orders in error operators will be addressed in the approximation of the master equation, with the continuously-varying control fields treated exactly. This study will address temporal and spatial correlations between errors and will specifically target schemes based upon shaped-pulse encoded dynamical recoupling, decoherence-free subspaces, quantum Zeno effect, and stabilizer-based QECC. Subsequently, quantum coding will be applied to schemes with ground-state protected qubits and the continuous measurement. The results will be formulated as scaling laws characteristic of different classes of errors and control schemes, and will enable new quantum techniques that use methods of classical coding theory. The PIs plan to construct efficient concatenated coherent control schemes combining the benefits of different approaches. New mathematical methods will be developed that yield the encoding tools and corresponding control sequences for codes protecting large numbers of qubits, without the need of solving for their collective quantum dynamics. The focus will be on codes whose error rates scale down with the interval between measurements faster than linear. The proposed program integrates both graduate and undergraduate participation at UC, Riverside. In particular, the innovative Mathematica-based class seeks to actively boost the undergraduate participation in research and may establish an alternative way to teach quantum mechanics to students majoring in Physics, Chemistry, and Electrical Engineering.

建议研究的必要性：实用的量子计算机(QC)的可行性关键取决于量子纠错码(QECC)的性能。当前的QECC理论依赖于受控系统中错误操作符的过于简单的模型。与这种简化相关的错误可能会破坏量子纠错码的群论结构，并显著降低其实际性能。由于级联编码不同层间的错误传播，这一问题在嵌入式级联码结构中被进一步放大。本研究的目标是建立适用于一系列现有的无源和有源QECC的去相干过程的统一描述，并利用该结果来开发用于多个QC实现的高度优化的异构级联码。建议的研究工作：建议的研究将由一个跨学科团队进行，PI具有强大的多体量子物理背景，共同PI具有丰富的编码理论经验。所提出的研究涉及两个基本问题：驱动开放系统的量子动力学和此类系统的连续测量。将对编码量子系统的几种固态QC实现中的退相干过程进行分析，在计算周期中或在计算周期结束时间歇性地进行投射伴随式测量。误差算符中二阶和高阶的影响将在主方程的近似中处理，而连续变化的控制场将被精确地处理。这项研究将解决误差之间的时间和空间相关性，并将特别针对基于成形脉冲编码的动态重新耦合、无相干子空间、量子Zeno效应和基于稳定器的QECC的方案。随后，量子编码将被应用于具有基态保护量子比特和连续测量的方案。结果将被表述为具有不同类别误差和控制方案特征的标度律，并将使使用经典编码理论方法的新量子技术成为可能。PI计划构建有效的级联相干控制方案，结合不同方法的优点。新的数学方法将被开发出来，为保护大量量子比特的代码产生编码工具和相应的控制序列，而不需要求解它们的集体量子动力学。重点将放在误码率随着测量之间的间隔比线性更快地减小的代码上。拟议的课程整合了加州大学河滨分校研究生和本科生的参与。特别是，基于数学的创新课程旨在积极促进本科生参与研究，并可能建立一种替代方法，向物理、化学和电气工程专业的学生教授量子力学。