Quantum Computational Advantage via Contextual Measurements

像计算机这样的信息处理设备在我们的现代生活中已经变得无处不在和不可或缺。一个新的有前途的范例，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。违反直觉的量子效应，如叠加和量子相关（称为纠缠），使我们能够处理超出传统的黑或白色（所谓的0或1）逻辑的灰色信息，并获得比传统设备大幅度的改进。QIS的进展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。虽然量子控制寄存器的几个量子比特是可行的，在几个物理体系结构，仍然存在巨大的挑战，包括如何建立宏观纠缠鲁棒性良好的可扩展控制，以及如何实现量子模拟的复杂量子系统超越可能的经典模拟。近年来，人们发现，表现出一定对称性和拓扑现象的强阻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秩序与计算和模拟中的量子优势之间的深层联系，通过利用中间电路测量，这些测量作为噪声中间尺度量子（NISQ）原型计算机的新能力而出现。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基础，并在这个高度跨学科的领域培养未来的科学家。 量子信息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能通过测量来揭示。从贝尔的非定域性定理（或更一般的上下文）到最近的玻色子采样问题的量子模拟，QIS的大多数里程碑式的结果都依赖于平衡这两个对比成分的创新手段，以获得巨大的实际效果。基于测量的量子计算（MBQC）框架便于研究这种相互作用以及计算和模拟中量子加速的起源。一方面，具有几何阻挫相互作用的量子自旋系统的基态具有量子自旋液体的奇异磁性，这种具有保序性的拓扑序不仅可以实现感兴趣的多体纠缠，而且也是量子模拟的一个新目标。另一方面，中间电路测量作为NISQ计算机的新能力而出现。虽然众所周知，基于测量结果的中间电路测量和自适应对于量子纠错至关重要，但人们对测量如何增强量子计算能力的了解较少，特别是当量子资源有限时，如NISQ时代。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量以及测量之间的因果关系。从广义上讲，该项目进一步交叉施肥两个研究领域，QIS和量子多体物理学，该项目由物理系QIS计划和刺激竞争性研究既定计划（EPSCoR）联合资助，该奖项反映了NSF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.