Quantum Computational Advantage via Contextual Measurements

University Of New Mexico, Albuquerque NM

Investigators

Abstract

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.