DMS- MSPA-Interdisciplinary: Optimum Quantum Error Recovery

在标准量子纠错中，噪声系统的输入被嵌入到编码子空间中，并且错误恢复是通过设计来完美地纠正特定错误的操作来执行的，所述特定错误可能是极有可能的物理噪声分量。国际刑警组织建议重新审查恢复行动的选择。对于给定的噪声模型，拟议的研究将寻求最大化恢复状态与输入的纠缠保真度，而不是完美地纠正错误过程的子集。这种优化可以通过半定规划(SDP)来计算，半定规划(SDP)是凸优化的一种良好形式，具有有效的求解算法。该项目的研究目标是：开发和分析噪声量子信道的最优恢复操作，将最优恢复分析扩展到高维量子系统，研究特定于信道的编码和恢复方案的设计，并确定最优恢复操作对容错量子计算的影响。通过结合量子理论、信息论、编码理论和最优化的原理，这项研究将促进数学、物理、计算机科学和工程之间的跨学科努力。广泛的影响这项研究的结果可以影响整个量子计算领域的努力。有效的误差缓解实践可以促进各种活动的发展，从寻找可行的量子计算设备的物理实验到量子计算应用的理论研究。

0625966ShorIn standard Quantum Error Correction, the input to a noisy system is embedded in a coded subspace, and error recovery is performed via an operation designed to perfectly correct specific errors, presumably a highly probable physical noise component. The PI's propose to reexamine the choice of recovery operation. Rather than perfectly correcting a subset of the error process, the proposed research will seek to maximize the entanglement fidelity of the recovered state to the input for a given noise model. This optimization may be calculated via a semidefinite program (SDP), a well-established form of convex optimization with efficient algorithms for its solution. ResearchThe project's research objectives are to:develop and analyze optimum recovery operations from noisy quantum channels,extend the analysis of optimum recoveries to high dimensional quantum systems,investigate the design of channel-specific encoding and recovery schemes, anddetermine the impact of optimum recovery operations for fault-tolerant quantum computation.Intellectual MeritThe proposed research will yield a novel approach to error correction in the challenging and emerging field of quantum information systems. By incorporating principles of quantum theory, information theory, coding theory, and optimization, the research will promote cross-discipline efforts between mathematics, physics, computer science, and engineering.Broader ImpactsThe results of this research can influence efforts throughout the field of quantum computation. Efficient error mitigation practices can prompt developments across the spectrum of activity, from physical experiments seeking feasible quantum computing devices to theoretical research on quantum computing applications.