Geometric quantum information processing in open systems

开放系统中的几何量子信息处理

基本信息

  • 批准号:
    0803304
  • 负责人:
  • 金额:
    $ 15万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2008
  • 资助国家:
    美国
  • 起止时间:
    2008-09-01 至 2012-08-31
  • 项目状态:
    已结题

项目摘要

The theoretical promise of quantum information processing (QIP) is widely regarded as one of the most exciting developments in computer science in many years. This is because QIP appears to be able to efficiently solve problems which are classicaly intractable (such factoring, Shors algorithm), and is provably capable of providing significant computational speedups in problems of wide interest (such as database search, Grover's algorithm). As a result QIP has spawned an avalance of activity across many disciplines, including also physics, electrical engineering, chemistry, and materials science. However,how to best implement QIP is still a wide open question. In particular, not only is it still unclear which physical system is best suited for QIP, it is also unresolved whether QIP should be implemented by means of dynamical or geometriclogic gates. This proposal is concerned with the geometric approach.Although the most widely studied version of QIP is based on dynamical evolution of quantum states, other approaches could very well turn out to be easier to implement and/or more robust against unwanted interactions and imperfections. In this proposal, the investigators intend to explore an alternative and promising version of QIP called holonomic quantum computation (HQC, introduced by the PI) that has garnered increasing interest. In HQC a quantum system that has a set of degenerate lowest energy (?ground?) states is driven slowly (adiabatically) around a loop in its control parameter space. In the process the system acquires a so-called geometric phase, meaning that its state changes in accordance with the geometrical properties of this loop. These state changes can then be combined in order to execute a complete quantum algorithm.The resulting geometrical transformations are not only of fundamental interest, but have the advantage over the standard dynamical ones that they are rather robust to certain errors. The reason is that the geometric phase depends only on the area the loop encloses in parameter space, but not on its shape, or on the speed the loop is traversed, provided it is slow. HQC has already attracted the attention of various groups attempting to build quantum computers, especially using trapped ions, because of the aforementioned robustness and because it is a more natural approach to the implementation of quantum logic gates than is the dynamical model.The potential of HQC is exciting, but there are crucial missing elements in HQC theory. Most importantly, the theory of HQC error correction is still primitive, even though error correction will undoubtedly be indispensable for a working holonomic quantum computer. It is essential to develop this general theory as well as detailed insight into specific physical systems that could be used to realize fault tolerant HQC. At the same time, it is vital to investigate HQC?s potential for new algorithms and new insight into physical processes. This proposal presents strategies for addressing these fundamentalopen problems.The success of HQC depends on the ability to keep the quantum system in its ground energy subspace, which in turn depends on maintaining an energy gap between the ground and next lowest energy states.Opening the HQC to interactions with its environment leads to processes that either shrink this gap or cause transitions across it, thus ruining the computation (a process known as decoherence). Equipped with a formulation of geometric phases for open systems recently introduced by the co-PI, the researchers intend to achieve a deep understanding of the effects of decoherence on HQC. The open system geometric phase provides a tool that can quantitatively capture the relationship between error correction and the gap.To thoroughly explore error correction in HQC, the authors plan to leverage their experience in circuit QC with decoherence-free subspaces, dynamical decoupling, and error correcting codes. They intend to use open system adiabatic theory (introduced by the co-PI) to provide thorough analysis of the validity and utility of their proposed error correcting techniques.
量子信息处理(QIP)的理论前景被广泛认为是多年来计算机科学中最令人兴奋的发展之一。这是因为QIP似乎能够有效地解决经典的棘手问题(如因子分解,Shors算法),并且可以证明能够在广泛关注的问题(如数据库搜索,Grover算法)中提供显着的计算加速。因此,QIP在许多学科中产生了大量的活动,包括物理学,电气工程,化学和材料科学。然而,如何最好地实施QIP仍然是一个悬而未决的问题。特别是,它不仅仍然是不清楚的物理系统是最适合的QIP,它也是未解决的QIP是否应该实现通过动态或geometriclogic门。这个建议是关于几何方法的,虽然QIP的最广泛研究的版本是基于量子态的动态演化,其他方法很可能更容易实现和/或更强大的反对不必要的相互作用和缺陷。在这项提案中,研究人员打算探索一种替代的、有前途的QIP版本,称为完整量子计算(HQC,由PI引入),它已经引起了越来越多的兴趣。在HQC中,具有一组简并最低能量(?地面?)状态在其控制参数空间中围绕循环缓慢地(自动地)驱动。在这个过程中,系统获得了所谓的几何相位,这意味着它的状态根据这个环路的几何特性而变化。这些状态的变化可以结合在一起,以执行一个完整的量子算法。由此产生的几何变换不仅是基本的利益,但有比标准的动力学的优势,他们是相当强大的某些错误。原因是几何相位仅取决于回路在参数空间中包围的面积,而不取决于其形状,或者取决于回路的速度,只要它是慢的。HQC已经吸引了试图构建量子计算机的各个团体的注意,特别是使用捕获离子,因为上述鲁棒性,因为它是一种比动力学模型更自然的实现量子逻辑门的方法。HQC的潜力令人兴奋,但在HQC理论中有关键的缺失元素。最重要的是,HQC误差校正的理论仍然是原始的,即使误差校正对于一个工作的完整量子计算机来说无疑是必不可少的。这是必不可少的,以发展这一一般理论,以及具体的物理系统,可用于实现容错HQC的深入了解。与此同时,对HQC的研究也至关重要。的潜力,新的算法和新的洞察物理过程。这个提议提出了解决这些基本问题的策略。HQC的成功取决于将量子系统保持在其基态能量子空间的能力,而这反过来又取决于维持基态和下一个最低能量状态之间的能隙。将HQC开放给与其环境的相互作用会导致缩小这个能隙或引起跨越它的跃迁的过程,从而破坏计算(一个称为去相干的过程)。配备了最近由co-PI引入的开放系统的几何相位公式,研究人员打算深入了解退相干对HQC的影响。开放系统的几何相位提供了一种定量描述误差校正与差距之间关系的工具,为了深入研究HQC中的误差校正,作者计划利用他们在电路质量控制中的经验,包括消相干子空间、动态解耦和误差校正码。他们打算使用开放系统绝热理论(由co-PI引入)来彻底分析他们提出的纠错技术的有效性和实用性。

项目成果

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Paolo Zanardi其他文献

Mode transformations and entanglement relativity in bipartite Gaussian states
  • DOI:
    10.1016/j.physleta.2006.01.059
  • 发表时间:
    2006-06-05
  • 期刊:
  • 影响因子:
  • 作者:
    Emanuele Ciancio;Paolo Giorda;Paolo Zanardi
  • 通讯作者:
    Paolo Zanardi
Long-time quantum scrambling and generalized tensor product structures
长时间量子置乱和广义张量积结构
  • DOI:
    10.1103/physreva.109.052424
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    2.9
  • 作者:
    Faidon Andreadakis;E. Dallas;Paolo Zanardi
  • 通讯作者:
    Paolo Zanardi
Local Response of Topological Order to an External Perturbation
拓扑序对外部扰动的局部响应
  • DOI:
  • 发表时间:
    2013
  • 期刊:
  • 影响因子:
    8.6
  • 作者:
    Alioscia Hamma;Lukasz Cincio;Siddhartha Santra;Paolo Zanardi;Luigi Amico
  • 通讯作者:
    Luigi Amico
Universal control of quantum subspaces and subsystems
量子子空间和子系统的通用控制
  • DOI:
  • 发表时间:
    2003
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Paolo Zanardi;Paolo Zanardi;Seth Lloyd
  • 通讯作者:
    Seth Lloyd
Virtual quantum subsystems.
  • DOI:
    10.1103/physrevlett.87.077901
  • 发表时间:
    2001-07
  • 期刊:
  • 影响因子:
    8.6
  • 作者:
    Paolo Zanardi
  • 通讯作者:
    Paolo Zanardi

Paolo Zanardi的其他文献

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{{ truncateString('Paolo Zanardi', 18)}}的其他基金

Operational Quantum Mereology: an Information Scrambling Approach
操作量子分体学:一种信息置乱方法
  • 批准号:
    2310227
  • 财政年份:
    2023
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
Coherence Power of Quantum Processes
量子过程的相干力
  • 批准号:
    1819189
  • 财政年份:
    2018
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
Differential Geometric Methods for Quantum Information Processing
量子信息处理的微分几何方法
  • 批准号:
    0969969
  • 财政年份:
    2010
  • 资助金额:
    $ 15万
  • 项目类别:
    Continuing Grant
Information Geometry of Quantum Phase Transitions
量子相变的信息几何
  • 批准号:
    0804914
  • 财政年份:
    2008
  • 资助金额:
    $ 15万
  • 项目类别:
    Continuing Grant

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