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

研究需要：有用的量子计算机（QC）的可行性关键取决于量子纠错码（QECC）的性能。目前的QECC理论依赖于被控系统中过于简单的误差算子模型。与这种简化相关的错误会破坏QECC的群理论结构，并大大降低其实际性能。对于嵌入的、连接的代码结构，由于错误在连接编码的不同层之间传播，这个问题进一步放大。提出的研究目标是建立适用于一系列现有被动和主动QECC的退相干过程的统一描述，并使用结果为几个QC实现开发高度优化的异构串联代码。建议的研究工作：建议的研究将由一个跨学科团队进行，PI在多体量子物理方面具有强大的背景，而co-PI在编码理论方面具有丰富的经验。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该系统的连续测量。几个固态QC实现中的退相干过程将分析编码量子系统，在计算周期期间或结束时间歇性地进行投影综合征测量。二阶和更高阶误差算子的影响将在主方程的近似中得到解决，并精确地处理连续变化的控制场。本研究将解决误差之间的时间和空间相关性，并将特别针对基于形状脉冲编码动态重耦合、无退相干子空间、量子芝诺效应和基于稳定器的QECC的方案。随后，量子编码将应用于基态保护量子比特和连续测量的方案。结果将被表述为不同类型的误差和控制方案的标度定律，并将使使用经典编码理论方法的新量子技术成为可能。pi计划构建有效的串联一致的控制方案，结合不同方法的优点。新的数学方法将被开发出来，产生保护大量量子比特的编码工具和相应的控制序列，而不需要解决它们的集体量子动力学。重点将放在误码率随测量间隔的减小而减小的代码上。拟议的项目整合了加州大学河滨分校研究生和本科生的参与。特别地，创新的以数学为基础的课程寻求积极促进本科生参与研究，并可能为物理，化学和电气工程专业的学生建立另一种教授量子力学的方式。

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.