EAGER-QAC-QCH: NSF-BSF: Quantum Computation as a Non-Equilibrium Dynamical Many-Body System

非技术总结本奖项是根据通过量子算法挑战赛邀请的一项热切的建议而颁发的，亲爱的同事们。它支持研究和教育，学习如何准备和操纵量子力学状态以执行计算的新概念，其中包括使用量子计算机解决问题所需的协议或算法。在过去的几年里，量子计算硬件有了显著的进步。谷歌和IBM最近都展示了拥有约50个完全可控的超导量子比特的设备，这些比特具有高保真和长相干时间。量子比特的数量可能会进一步增加，但独立的外部控制的数量是扩大现代量子计算体系结构的关键瓶颈。这意味着，近期的量子计算机将不会像经典处理器那样运行。PI的目标是开发特定的操作协议，这将允许现有的量子设备执行特定的优化任务，而这些任务对于传统的经典算法来说是非常困难的。后者苦于在极长的时间内陷入次优解。量子隧道允许同时探索多个潜在的最佳配置，并最终能够找到真正唯一的最佳配置。这个项目的目的是调查这些量子算法效率的理论极限。实际的演示方案将被概念化，并可能在现有的原型量子设备上实施。NSF基金将为一名研究生研究助理和(部分)博士后研究员提供培训。两人都将接受构建量子计算算法的理论设备方面的培训。该项目的成果将被纳入明尼苏达大学的研究生班以及通过精细理论物理研究所共同组织的定期暑期学校。该项目的一部分将与魏兹曼研究所的尤瓦尔·格芬教授密切合作，后者将由BSF单独提供资金。BSF部分将为另一名博士后研究员提供培训。技术总结本奖项是根据通过量子算法挑战赛邀请的一项热切的建议而颁发的，亲爱的同事们。它支持研究和教育，学习如何准备和操纵量子力学状态以执行计算的新概念，其中包括使用量子计算机解决问题所需的协议或算法。PI将考虑量子近似优化算法(QAOA)和量子图像识别方案。两者都基于信息处理引擎的思想，该引擎重复执行特定的周期。这个循环涉及到主动量子系统的耦合和去耦合，该系统可以用带有信息浴的谢林顿-柯克帕特里克自旋玻璃来建模，该自旋玻璃编码了所需的优化问题。我们将探索Sachdev-Ye-Kitaev(SYK)模型的量子比特实现，作为信息浴的模型。SYK系统是一个黑洞的全息对偶系统，它具有有限的熵，直到指数级的小温度。这允许在自旋玻璃的多个局部极小值之间进行量子隧穿。在每个周期结束时执行的量子测量操作提供了一组逐渐改进的候选最佳自旋构型。该项目的一个目标是评估在这样的集合中找到真正最优的可能性。另一个目标是优化周期，以确定信息引擎效率的理论界限。该项目的NSF-BSF部分将根据工作物质的折合密度矩阵进行理论描述。我们希望找到一个类似于Lindblad的演化方程。它将允许使用现有强大的领域理论和计算技术对计算方案进行有效分析。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Non-technical Summary This award is made on an EAGER proposal invited through the Quantum Algorithm Challenge Dear Colleague Letter. It supports research and education to study new concepts for how quantum mechanical states can be prepared and manipulated to perform computation which includes protocols or algorithms required to use a quantum computer to solve a problem. Quantum computing hardware has significantly advanced over the past few years. Both Google and IBM have recently demonstrated devices with about 50 fully controlled superconducting qubits with high fidelity and long coherence times. The number of qubits may be expected to increase even further, but the number of independent external controls presents a crucial bottleneck in scaling up the modern quantum computing architecture. This means that near-term quantum computers are not going to operate the way classical processors do. The PI aims to develop specific operating protocols, which will allow already existing quantum devices to perform particular optimization tasks, which are exponentially hard for conventional classical algorithms. The latter suffer from being trapped into sub-optimal solutions for extremely long times. Quantum tunneling allows for simultaneous exploration of multiple potentially optimal configurations, and ultimately enables finding the true unique optimum. This project is aimed to investigate theoretical limits for efficiency of these quantum algorithms. Practical demonstration schemes will be conceptualized and possibly implemented on existing prototypical quantum devices. NSF funds will provide training for a graduate student research assistant and (partially) a postdoctoral fellow. Both will be trained in the theoretical apparatus underlying construction of algorithms for quantum computation. The results of the project will be incorporated in graduate classes at the University of Minnesota as well as at regular summer schools, which the PI co-organizes through the Fine Theoretical Physics Institute. Part of the project will be conducted in close cooperation with Prof. Yuval Gefen of the Weizmann Institute, who will be funded separately by BSF. The BSF part will provide training for another postdoctoral fellow. Technical Summary This award is made on an EAGER proposal invited through the Quantum Algorithm Challenge Dear Colleague Letter. It supports research and education to study new concepts for how quantum mechanical states can be prepared and manipulated to perform computation which includes protocols or algorithms required to use a quantum computer to solve a problem. The PI will consider quantum approximate optimization algorithms (QAOA) and quantum image recognition schemes. Both are based on the idea of an information processing engine, which repeatedly performs a particular cycle. The cycle involves coupling and decoupling of the active quantum system, which can be modeled by a Sherrington-Kirkpatrick spin glass encoded with a desired optimization problem, with the information bath. A qubit realization of the Sachdev-Ye-Kitaev (SYK) model will be explored as a model for the information bath. The SYK system, being a holographic dual of a black hole, possesses a finite entropy down to the exponentially small temperature. This allows quantum tunneling among multiple local minima of the spin glass. The quantum measurement operation, performed in the end of each cycle, provides a progressively improving set of candidate optimal spin configurations. A goal of the project is to evaluate the probability of finding the true optimum within such a set. Another goal is to optimize the cycle to determine theoretical bounds for efficiency of the information engine. The NSF-BSF part of the project will deal with a theoretical description in terms of the reduced density matrix of the working substance. We expect to find a Lindblad-like evolution equation. It will allow for an efficient analysis of computation schemes using existing powerful field-theoretical and computational techniques.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.