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

拟议研究的必要性：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。当前的QECC理论依赖于被控系统中误差算子的过于简单的模型。与这种简化相关的错误可能会破坏QECC的群论结构，并大大降低其实际性能。由于级联编码不同层之间的错误传播，该问题在嵌入式级联码构造中被进一步放大。拟议研究的目标是建立适用于一系列现有无源和有源QECC的去相干过程的统一描述，并使用结果为多种QC实现开发高度优化的级联异构码。拟议的研究工作：拟议的研究将由一个跨学科的团队进行，PI在多体量子物理学方面具有很强的背景，而co-PI在编码理论方面具有丰富的经验。该研究涉及两个基本问题：驱动开放系统的量子动力学和连续测量。在几个固态QC实现的退相干过程将被分析的编码量子系统，与投影综合征测量期间，或在计算周期结束时间歇地进行。误差算子中二阶和高阶的影响将在主方程的近似中得到解决，连续变化的控制场被精确地处理。这项研究将解决误差之间的时间和空间相关性，并将专门针对基于成形脉冲编码动态再耦合，无消相干子空间，量子芝诺效应和基于稳定器的QECC的方案。 随后，量子编码将被应用于具有基态保护量子位和连续测量的方案。 结果将被公式化为不同类别的错误和控制方案的标度律特征，并将使新的量子技术，使用经典编码理论的方法。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。将开发新的数学方法，为保护大量量子比特的代码提供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。重点将放在代码的错误率比例缩小测量之间的间隔快于线性。拟议的计划整合了研究生和本科生在加州大学滨江的参与。特别是，创新的Mathematica类旨在积极促进本科生参与研究，并可能建立一种替代方式来教授物理，化学和电气工程专业的学生量子力学。

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.