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

本奖项是根据量子算法挑战Dear Colleague Letter邀请的EAGER提案颁发的。它支持研究和教育，以研究如何准备和操纵量子力学状态来执行计算的新概念，包括使用量子计算机解决问题所需的协议或算法。量子计算硬件在过去几年中取得了重大进展。谷歌和IBM最近都展示了具有大约50个完全控制的超导量子比特的设备，具有高保真度和长相干时间。量子比特的数量可能会进一步增加，但独立外部控制的数量是扩大现代量子计算架构的关键瓶颈。这意味着短期内量子计算机不会像传统处理器那样运行。PI旨在开发特定的操作协议，这将允许已经存在的量子设备执行特定的优化任务，这对于传统的经典算法来说是指数级的困难。后者因为长时间陷入次优解决方案而受苦。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独特的最佳配置。本项目旨在研究这些量子算法效率的理论极限。实际演示方案将概念化并可能在现有的原型量子器件上实现。NSF基金将为一名研究生、研究助理和一名博士后（部分）提供培训。两者都将在量子计算算法的理论设备基础上进行训练。该项目的成果将被纳入明尼苏达大学的研究生课程，以及PI通过精细理论物理研究所共同组织的常规暑期学校。部分项目将与Weizmann研究所的Yuval Gefen教授密切合作进行，他将由BSF单独资助。BSF部分将为另一名博士后提供培训。本奖项是根据量子算法挑战Dear Colleague Letter邀请的EAGER提案颁发的。它支持研究和教育，以研究如何准备和操纵量子力学状态来执行计算的新概念，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，重复执行特定的循环。这个循环涉及到主动量子系统的耦合和解耦，它可以用一个谢林顿-柯克帕特里克自旋玻璃来建模，该玻璃编码了一个期望的优化问题，并带有信息浴。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系统是黑洞的全息对偶体，具有有限的熵，直至指数级小的温度。这允许自旋玻璃的多个局部极小值之间的量子隧穿。在每个周期结束时进行的量子测量操作提供了一组逐步改进的候选最佳自旋配置。该项目的目标是评估在这样一个集合中找到真正最优的概率。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降低密度矩阵进行理论描述。我们期望找到一个林德布莱德式的进化方程。它将允许使用现有的强大的场理论和计算技术对计算方案进行有效的分析。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。

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.