Quantum Simulation of Out-of-Equilibrium Spin Models

在计算机上模拟复杂系统提高了我们对自然现象的理解，并有助于开发新技术。然而，有些系统甚至超过了最先进的超级计算机的模拟能力。量子模拟器可以克服这一挑战，并对量子化学、材料科学、凝聚态物质和高能物理产生重大影响。虽然通用量子计算机有望给计算带来更广泛的革命，但它们仍处于起步阶段，而量子模拟器已经可以处理一些特定任务的问题。这是通过遵循一种不同于基于计算机的模拟器的方法来实现的，即使用一个量子系统直接模拟另一个目标系统的演化。这一策略的弱点在于缺乏灵活性。该项目旨在通过引入可编程的模拟量子模拟器来扩展量子模拟的能力，该模拟器结合了直接模拟系统进化的简便性和通过逻辑门设计模拟器动力学的灵活性。此外，该项目将开发新的度量来评估性能并获得关于模拟系统的最全面的信息。为了实现这些目标，研究人员将使用一种混合方法，将自然哈密顿量下的进化(如在模拟量子模拟器中)与周期控制(集体量子门)相结合来设计近似感兴趣的相互作用模型的Floquet哈密顿量。由于模拟性能应该在经典模拟器无法访问的大型(可扩展)量子系统上进行评估，该项目将通过实验验证量子控制协议，设计能够表征多体动力学的实验可访问度量，如超时有序关联和Loschmidt回波。用作量子模拟器的系统将包括准一维核自旋链、3D晶体中的核自旋和钻石中的自旋杂质。与冷原子和离子等合成物质系统相比，使用自旋系统来解决这些问题有几个优点。首先，该系统直接映射到理论上研究的典型自旋哈密顿量，它可以建立在凝聚态物理磁共振研究的悠久传统上。此外，这些自旋系统允许探索比冷原子和离子更广泛的区域，例如高温条件，以及远远超出可以精确模拟的条件，例如大型3D系统，以及与明确定义的环境相互作用的开放系统。探索这种丰富的自旋系统的非平衡动力学将带来一系列新的物理现象，正如将用几个量子自旋模型的范例来演示的那样。该项目的一个特别重点是调查量子热化或由于局部化或预热化而缺乏量子热化，这是探索将多体系统用于量子应用的关键问题。这一奖项反映了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。

Simulating complex systems on a computer improves our understanding of natural phenomena and helps to develope new technology. Yet, some systems are beyond the simulation capabilities of even the most advanced supercomputers. Quantum simulators could overcome this challenge and greatly impact quantum chemistry, material science, condensed matter, and high-energy physics. While general-purpose quantum computers promise to more broadly revolutionize computing, they are still in their infancy, while quantum simulators can already tackle some task-specific problems. This is achieved by following a different approach than computer-based simulators, by using one quantum system to directly mimic the evolution of another, target system. The weakness in this strategy is that it lacks flexibility. This project aims to expand the capabilities of quantum simulation by introducing programmable analog quantum simulators which combine the ease of directly mimicking a system evolution, with the flexibility of engineering the simulator dynamics via logic gates. In addition, the project will develop novel metrics to evaluate performance and to acquire the most comprehensive information about the simulated system.To achieve these goals, the researchers will employ a hybrid approach, combining evolution under the natural Hamiltonian (as in analog quantum simulators) with periodic control (collective quantum gates) to engineer a Floquet Hamiltonian approximating the interaction models of interest. As the simulation performance should be assessed on large (scalable) quantum systems not accessible to classical simulators, the project will validate the quantum control protocols experimentally, devising experimentally accessible metrics that can characterize the many-body dynamics, such as out-of-time ordered correlations and Loschmidt echoes. The systems used as quantum simulators will include quasi-1D nuclear spin chains, nuclear spins in 3D crystals, and spin impurities in diamond. There are several advantages of using spin systems to address these questions over synthetic matter systems such as cold atoms and ions. First, the system directly maps to typical spin Hamiltonians studied theoretically and it can build upon the long tradition of magnetic resonance investigation of condensed matter physics. In addition, these spin systems allow exploring broader regimes than cold atoms and ions, for example high-temperature conditions, and conditions that are well beyond what can be simulated exactly, such as large, 3D systems, and open systems interacting with a well-defined environment. Exploring the out-of-equilibrium dynamics of such rich spin systems will bring forward a host of new physical phenomena, as it will be demonstrated with a few paradigmatic examples of quantum spin models. A particular focus of the project is on investigating quantum thermalization or its absence due to localization or prethermalization, a key question in the quest to exploit many-body systems for quantum applications.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.