Randomized Dynamical Decoupling Techniques for Quantum Information Processing

量子力学通过利用没有经典类比的现象，为处理信息提供了新的范例。量子信息的物理实现尤其有望极大地提高我们解决复杂计算问题和模拟复杂系统的能力。然而，量子信息比经典信息更容易受到环境噪声和操作错误的影响。虽然基于容错量子纠错的方法已经被开发出来以应对对抗量子噪声的挑战，但由于涉及到巨大的开销和设计复杂性，这些结果的实际应用仍然受到严重限制。动态解耦技术最近成为量子信息处理中相干动态控制和误差抑制的一种越来越有吸引力的策略。受核磁共振谱学中自旋回波现象和相干平均技术的启发，解耦方法具有避免辅助存储资源和测量能力的显著优点，同时仍然适用于一大类物理相关的设备和误差过程。本研究的中心主题是通过研究一种新的随机设置来进一步推动动态解耦方法的理论和实践意义，该方法克服了现有确定性方法的重要局限性。重点将放在：(I)探索与设备无关的控制理论框架内的随机化解耦方案，特别是确定合并纯确定性和随机协议的优点的最佳方法，并获得预期性能的分析误差界；(Ii)对与拟议的量子信息处理技术直接相关的量子比特设备中的随机化控制方案的实际性能进行基准测试，重点是基于固态自旋的量子比特实现。

Quantum mechanics provides novel paradigms for processing information by harnessing phenomena that have no classical analog. Physical realizations of quantum information promise, in particular, great improvements in our abilities to solve hard computational problems and simulate complex systems. However, quantum information is incredibly more vulnerable than its classical counterpart to the effects of both environmental noise and operational errors. Although powerful approaches based on fault-tolerant quantum error correction have been developed to cope with the challenge of counteracting quantum noise, practical exploitation of these results remains severely constrained due to the large overheads and design complexity involved.Dynamical decoupling techniques have recently emerged as an increasingly attractivestrategy for coherent dynamical control and error suppression in quantum information pro-cessing. Broadly inspired by spin-echo phenomena and coherent averaging techniques innuclear magnetic resonance spectroscopy, decoupling methods offer the compelling advan-tage of avoiding auxiliary memory resources and measurement capabilities, while remainingapplicable to a large class of physically relevant devices and error processes.The central theme of the proposed research is to further push the theoretical and practical significance of dynamical decoupling methods, by investigating a novel randomized setting which overcomes important limitations of existing deterministic schemes. The focus will be on both (i) exploring randomized decoupling schemes within a device-independent control-theoretic framework, by identifying in particular optimal ways for merging advantageous features of purely deterministic and random protocols and by obtaining analytical error bounds on expected performance; (ii) benchmarking the actual performance of randomized control schemes in qubit devices of direct relevance to proposed quantum information processing technologies, with emphasis on solid-state spin-based qubit implementations.