Collaborative Research: A Unified Approach to Quantum Tomography, Open Systems Control and Quantum Simulation

信息技术一直是经济增长的引擎，这主要是由于摩尔定律的趋势，即计算机芯片的组件密度和计算能力大约每两年翻一番。在不久的将来，这些电路的构建模块将达到原子尺度，量子物理定律将取代我们熟悉的支配我们日常世界的经典物理定律。令人惊讶的是，理论研究表明，如果我们能够像现在操纵和控制经典设备一样操纵和控制量子设备，那么根据量子力学处理信息的全新途径将会打开。因此，量子计算机原则上能够以指数级的速度比经典计算机更快地解决一些重要的计算问题。人们还认为，一种更简单的设备，通常被称为模拟量子模拟器，可能为化学和材料科学中目前难以解决的重要问题提供近似的解决方案。虽然功能性量子计算机仍然是一个遥远的目标，但量子计算和模拟的变革思想有望从根本上扩展计算机和信息技术的能力，并维持其未来的增长。该奖项建立在科学和工程领域的主要研究人员之前的成就之上，即量子控制，研究如何在量子力学的控制下，即使在不可避免的设备缺陷和外部干扰存在的情况下，也能高精度地操纵和控制物理设备。该奖项的第一个目标是开发新的技术，从而可以评估和验证量子器件的操作。这将通过使用被称为量子断层扫描的协议来完成，该协议通过一系列精心选择的测量来确定量子设备的状态和行为。挑战将是使这些协议更有效，即最大限度地减少所需的测量次数，也更健壮，例如，在存在缺陷的情况下可靠。该奖项的第二个目标是实现基于单个原子的模拟量子模拟器。这种单原子装置将用于模拟一个模型系统，其行为已知是混沌的，即对缺陷和外部干扰超敏感。通过在已知缺陷的情况下量化模拟器的准确性，本研究将解决一些重要但迄今尚未解决的问题：在这种具有挑战性但常见的情况下，人们能在多大程度上相信模拟量子模拟器的预测？它的准确性和可靠性能否通过最先进的量子控制技术得到提高？这些问题的答案与美国顶级研究机构在模拟量子模拟方面的大型联邦资助研究项目有关。在一些物理平台上，最先进的量子控制正在接近容错操作的阈值，并且在许多其他物理平台上正在稳步改进。因此，研究人员现在正在追求基本数字量子计算和模拟量子模拟（AQS）的架构。为了继续沿着这条通往有用的量子信息处理（QIP）的道路前进，迫切需要在量子控制和量子断层扫描领域找到更复杂的工具，特别是对于能够抵抗现实世界错误和缺陷的协议。此外，量子信息界在假设误差不像数字量子计算机那么严重的情况下，大量投资于AQS。这使得研究AQS对误差的容忍度，即使在没有退相干的情况下，以及在量子混沌等复杂动力学背景下鲁棒控制的前景变得势在必行。该奖项将重点关注量子控制和测量，以及它们在量子层析成像和模拟量子模拟中的应用。这项工作将建立在最优控制和测量理论的基础上，将这些理论应用于一个独特的实验测试平台：处于电子基态的冷133c原子的电子-核自旋。该系统提供了较长的相干时间，可以用射频，微波和光场进行操作，可以通过斯特恩-格拉赫分析进行测量，并且具有16维希尔伯特空间，足够大，可以探索QIP的重要任务。凭借其经过验证的应用高保真单一映射和执行高保真正交测量的能力，该测试平台为日益复杂的QIP提供了所需的构建块。计划的研究是理论和实验的结合，并将讨论量子测量和断层扫描的主题。此外，模拟量子模拟，研究自旋15/2量子踢顶（QKT）的量子模拟，并利用QKT范式探索混沌存在下的鲁棒量子模拟。由于鲁棒控制和断层扫描的方法独立于任何特定平台，因此该奖项的结果将作为可以实现的基准，并为其他实验室使用不同物理系统的类似进展提供模板。这将有助于促进QIP更广泛领域的进展。

Information technology has been an engine for economic growth largely due to the trend known as Moore's law, whereby the component density and computational power of computer chips doubles approximately every two years. In the not too distant future the building blocks of these circuits is set to reach atomic scale, where the laws of quantum physics will replace the familiar laws of classical physics that govern our everyday world. Surprisingly, theoretical studies have shown that if we can manipulate and control quantum devices as well as we now manipulate and control classical devices, entirely new avenues will open up to process information according to quantum mechanics. As a result, quantum computers will in principle be able to solve some important computational problems exponentially faster than classical computers. It is also thought that a simpler class of devices, commonly referred to as analog quantum simulators, may provide approximate solutions to important problems in chemistry and materials science that are currently intractable. Though a functional quantum computer remains a distant goal, the transformative ideas of quantum computation and simulation hold promise to radically expand the capabilities of computer and information technology and sustain its future growth.This award builds on previous accomplishments by the Principal Investigators in the science and engineering field known as quantum control, which studies how physical devices governed by quantum mechanics can be manipulated and controlled with high precision, even in the presence of inevitable device imperfections and outside disturbances. The first objective of this award is to develop new techniques whereby one can evaluate and verify the operation of quantum devices. This will be done through the use of protocols known as quantum tomography, which determine the state and behavior of a quantum device through a series of carefully chosen measurements. The challenge will be to make these protocols more efficient, i. e., minimizing the number of measurements required, and also more robust, e. g., reliable in the presence of imperfections. The second objective of this award is to realize an analog quantum simulator based on a single atom. This single-atom device will be used to simulate a model system whose behavior is known to be chaotic, i. e., hypersensitive to imperfections and outside disturbances. By quantifying the accuracy of the simulator in the presence of known imperfections, this research will address essential but so far unanswered questions: How far can one trust the predictions of an analog quantum simulator in this challenging but common scenario? And can its accuracy and reliability be improved through state-of-the-art techniques for quantum control? The answer to these questions is relevant for large, federally funded research programs in analog quantum simulation at top research institutions across the US.State-of-the-art quantum control is approaching the thresholds for fault-tolerant operation on a few physical platforms and is steadily improving on many others. As a result, researchers are now pursuing architectures for rudimentary digital quantum computation and analog quantum simulation (AQS). To continue on this path towards useful quantum information processing (QIP), there is an urgent need for more sophisticated tools in the areas of quantum control and quantum tomography, and especially for protocols that are resistant to real-world errors and imperfections. Furthermore, the quantum information community is heavily invested in AQS under the assumption that errors are less critical than in a digital quantum computer. This makes it imperative to study the tolerance of AQS to errors, even in the absence of decoherence, and the prospects of robust control in the context of complex dynamics such as quantum chaos.This award will focus on quantum control and measurement, and their application in quantum tomography and analog quantum simulation. The work will build on well established ideas from optimal control and measurement theory, bringing these to bear on a unique experimental testbed: electron-nuclear spins of cold 133Cs atoms in their electronic ground state. This system provides long coherence times, can be manipulated with radio-frequency, microwave, and optical fields, is accessible to measurement though Stern-Gerlach analysis, and has a 16-dimensional Hilbert space, large enough to explore non-trivial tasks of QIP. With its proven capability to apply high-fidelity unitary maps and perform high-fidelity orthogonal measurements, the testbed provides the building blocks needed for QIP at levels of increasing complexity. The planned research is a mixture of theory and experiment, and will address topics in quantum measurement and tomography. In addition, analog quantum simulation, studying the quantum simulation of a spin-15/2 Quantum Kicked Top (QKT) and the use of the QKT paradigm to explore robust quantum simulation in the presence of chaos will be explored. Because the methodologies of robust control and tomography are independent of any particular platform, results from this award will serve as a benchmark for what can be achieved, and a template for similar advances elsewhere in laboratories working with different physical systems. This will help facilitate progress in the broader field of QIP.