Quantum Computational Advantage via Contextual Measurements

信息处理设备，如计算机，在我们的现代生活中已经无处不在，不可或缺。一种新的有前途的范式，称为量子信息科学（QIS），利用微观量子态，例如电子的自旋，来编码信息。反直觉的量子效应，如被称为纠缠的叠加和量子相关，使我们能够在传统的非黑即白（所谓的0或1）逻辑之外处理灰色阴影的信息，并获得比传统设备的巨大改进。量子信息系统的进步也使我们能够开始操纵量子多体系统，并利用人工合成的量子系统进行量子计算和模拟。虽然几个量子比特寄存器的量子控制在几种物理体系结构中是可行的，但仍然存在巨大的挑战，包括如何建立具有良好可扩展性控制的宏观纠缠，以及如何实现超越经典模拟的复杂量子系统的量子模拟。近年来人们发现，表现出一定对称性和拓扑现象的强受挫量子自旋系统具有作为量子计算机的内在能力。通过这个具体的例子，该项目寻求宏观量子顺序和量子优势在计算和模拟之间的深层联系，通过利用中间电路测量，这是作为噪声中等规模量子（NISQ）原型计算机的新能力出现的。在一般意义上，这项研究将有助于促进科学的进步，主要是量子信息科学的知识库，并培养未来的科学家在这个高度跨学科的领域。量子量子系统的核心是纠缠和测量之间的基本相互作用。虽然纠缠的复杂性代表了一种独特的量子资源，但其特有的非经典特征只有通过测量才能显现出来。从贝尔关于非定域性的定理（或更一般的上下文性）到最近对玻色子采样问题的量子模拟，量子信息系统的大多数里程碑式成果都依赖于平衡这两种不同成分的创新方法，以取得巨大的实际效果。基于测量的量子计算（MBQC）框架便于在计算和模拟中研究这种相互作用和量子加速的起源。一方面，对称保护的拓扑秩序（SPTO），如具有几何挫折相互作用的量子自旋系统的基态，表现出量子自旋液体的奇异磁性，不仅实现了感兴趣的多体纠缠，而且是最近量子模拟的目标。另一方面，中路测量作为NISQ计算机的新能力而出现。虽然众所周知，基于测量结果的中路测量和调整对于量子纠错至关重要，但人们对测量如何增强量子计算的理解较少，特别是在NISQ时代量子资源有限的情况下。该项目加深了对量子计算优势场景的理解，通过SPTO扩展了一类多体纠缠，测量的上下文可观测值，以及测量之间的因果关系。从广义上讲，该项目进一步交叉了QIS和量子多体物理两个研究领域，及时地在量子模拟时代到来之际，量子多体物理提出了许多问题，量子计算机应该比传统计算机更有效地解决这些问题。该项目由物理系的QIS计划和促进竞争研究的既定计划（EPSCoR）共同资助。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。

Information processing devices, like computers, have become ubiquitous and indispensable in our modern life. A new promising paradigm, called quantum information science (QIS), takes advantage of microscopic quantum states, for instance spins of electrons, to encode information. Counterintuitive quantum effects, such as superposition and quantum correlation called entanglement, enable us to process information with shades of gray beyond the conventional black-or-white (so-called 0-or-1) logic, and to attain drastic improvements over conventional devices. The progress of QIS also enables us to start manipulating quantum many-body systems and utilizing artificially synthetic quantum systems for quantum computation and simulation. While quantum control of the register of several qubits is feasible in several physical architectures, there remain formidable challenges, including how to build macroscopic entanglement robustly with well-scalable control, and how to achieve quantum simulation of complex quantum systems beyond possible classical simulation. It has been recently discovered that strongly frustrated quantum spin systems which manifest certain symmetries and topological phenomena possess intrinsic capability as a quantum computer. Through this concrete example, the project seeks a deep connection between macroscopic quantum orders and quantum advantage in computation and simulation, by utilizing mid-circuit measurements which emerge as new capacity of noisy intermediate-scale quantum (NISQ) prototype computers. In a general sense, the research will contribute to promote the progress of science, primarily the knowledge base of quantum information science, and to train future scientists in this highly interdisciplinary field. A fundamental interplay between entanglement and measurement lies at the heart of QIS. While the complexity of entanglement represents a uniquely quantum resource, its characteristic nonclassical features only reveal themselves through measurement. From Bell’s theorem on nonlocality (or more generally contextuality) to recent quantum simulations of the boson-sampling problem, most landmark results of QIS have relied upon innovative means of balancing these two contrasting ingredients to great practical effect. The framework of measurement-based quantum computation (MBQC) is convenient to study such an interplay and the origin of quantum speed-up in computation and simulation. On one hand, a symmetry-protected topological order (SPTO), such as the ground states of quantum spin systems with geometrically frustrated interactions which exhibit exotic magnetism of quantum spin liquid, not only realizes many-body entanglement of interest but also has been a recent target of quantum simulation. On the other hand, mid-circuit measurements emerge as new capacity of NISQ computers. While it is widely known that mid-circuit measurements and adaptations based on measurement outcomes are crucial for quantum error correction, it is less understood how measurements can empower quantum computation, particularly when quantum resources are limited as in the NISQ era. The project deepens understanding of the scenarios for quantum computational advantage, by extending a class of many-body entanglement through SPTO, contextual observables of measurements, and causal relations among measurements. Broadly, the project cross-fertilizes further two research fields, QIS and quantum many-body physics, timely at the coming age of quantum simulation when quantum many-body physics suggests many problems which quantum computers should be more efficient to solve than conventional computers.This project is jointly funded by the QIS program in the Division of Physics and the Established Program to Stimulate Competitive Research (EPSCoR).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.