Collaborative Research: Quantum Complexity, Chaos, and Implications for Analog Quantum Simulation

量子技术是推动国家经济引擎的信息革命的下一个前沿领域。利用量子物理的微观定律处理信息的机器可以解决即使是最强大的超级计算机也难以解决的关键问题，比如设计新的高科技材料和药物。通用量子计算机还需要几年的时间，但目前的量子技术已经足够先进，私营公司和政府机构可以开发特殊用途的“量子模拟器”，用于解决特定问题。不幸的是，这种机器的操作对噪音和缺陷非常敏感，这与“蝴蝶效应”非常相似，即即使是最小的干扰（打个比方，蝴蝶扇动翅膀）也会影响天气预报的预测能力。该项目旨在更好地理解量子模拟器解决困难计算问题的能力与受噪声和不完美影响时其预测的极端脆弱性之间的权衡。这样的理解对于量子技术在科学和工程问题上的成功应用至关重要。量子模拟需要接触动力学复杂的高度纠缠多体系统。长期以来，人们一直担心这样的系统会表现出“量子混沌”，这将使任何大规模量子模拟对缺陷都非常敏感。然而，与此同时，有人认为对特殊目的量子模拟的要求不如通用数字量子计算严格。因此，这就是量子模拟核心的紧张：一个人能拥有进入大规模纠缠态所需的复杂动力学，同时又有一个可靠的设备，不会因为超敏而无法操作吗？简而言之：我们能相信一个非平凡量子模拟器的输出吗？拟议的研究将在基于单个铯原子自旋的量子模拟器的实验中对这些问题进行测试。该测试平台提供了最先进的控制和诊断，并提供了驱动和观察几乎无限种类的复杂动力学的能力，包括许多目前在其他地方探索的模拟量子模拟的范例模型。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Quantum technology is the next frontier in the information revolution that powers the nation's economic engine. Machines that process information using the microscopic laws of quantum physics can solve critical problems that are intractable with even the most powerful supercomputers, such as design of new high tech materials and pharmaceuticals. A general purpose quantum computer is still years in the future, but current quantum technology is now sufficiently advanced for private companies and government agencies to pursue the development of special purpose "quantum simulators" that can be applied to select problems. Unfortunately, the operation of such machines can be very sensitive to noise and imperfection, in a manner closely analogous to the "butterfly effect" whereby even the smallest disturbance (metaphorically, the flap of a butterfly's wing) can affect the predictive power of weather forecasts. This project seeks to better understand the tradeoff between a quantum simulator's power to solve hard computational problems, and the extreme fragility of its predictions when subject to noise and imperfections. Such understanding will be essential for the successful application of quantum technology to problems in science and engineering.Quantum simulation requires access to highly entangled many body systems whose dynamics are complex. It has long been a concern that such systems exhibit "quantum chaos" which will make any large scale quantum simulation hypersensitive to imperfections. Yet, at the same time it is argued that requirements for a special purpose quantum simulation are less stringent than for universal digital quantum computing. This, then, is the tension at the heart of quantum simulation: Can one have the complex dynamics needed to access massively entangled states, and at the same time have a reliable device that is not rendered inoperable by hypersensitivity? In short: Can one trust the output of a non-trivial quantum simulator? The proposed research will put those questions to the test in experiments with a quantum simulator based on the spins of individual cesium atoms. This test bed provides access to state-of-the-art control and diagnostics, and offers the ability to drive and observe a nearly unlimited variety of complex dynamics, including many of the paradigmatic models of analog quantum simulation currently explored elsewhere.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.