Quantum Mechanics at the Complexity Frontier

University Of Washington, Seattle WA

Investigators

Abstract

The development of quantum information technology promises to revolutionize both fundamental and applied science. For example, on the fundamental side, we expect that quantum devices will efficiently simulate poorly understood quantum mechanical theories, providing insight into their behavior. On the applied side, such simulations would allow for the design of new nanomaterials and biochemical molecules. The first experimental step in developing quantum devices has been to bring single quanta under complete control. This has mostly been accomplished over the last two decades. Laboratories around the world now routinely trap, isolate and probe individual atoms, ions, electrons, spins and photons. These systems form 'qubits', the elementary building blocks of quantum computers. The next step is to put these qubits together to form quantum circuits, simulators, networks and eventually computers. However, as the number of qubits in a device grows, so too does the complexity of describing and controlling the properties of that device. This complexity underlies the potential power of quantum technology but also brings many theoretical and experimental challenges. This project seeks to address two of these challenges. First, what physical mechanisms can stabilize the multi-qubit systems so as to make them usable quantum devices? One possibility is provided by a recently discovered phenomenon called 'many-body localization'. Usually, the unavoidable presence of disorder in experiments leads to difficulties controlling the qubits. Counter-intuitively, it seems that putting in more disorder can actually help by 'localizing' the quantum information, preventing it from escaping into the environment as noise. Many of the fundamental features of localization remain unknown. By a combination of classical computational and analytical studies, the group aims to elucidate the conditions under which the many-body localized phase arises, the near-term experimental consequences and its potential as an intrinsic platform for quantum computing. Second, what kinds of problems can we expect a quantum computer to be able to solve? There are efficient quantum algorithms for particular problems, such as simulating molecular structure and breaking cryptographic codes. However, the most general optimization problems are believed to be hard even for a quantum computer. What distinguishes these hard problems from the tractable ones is an outstanding open question whose answer has profound consequences. The aim is to develop a better understanding of typical quantum optimization problems through a case study of a canonical example: quantum satisfiability. It is expected that insights into this problem will lead to new heuristic quantum algorithms. A similar line of inquiry in classical computation led to important classical optimization algorithms, such as simulated annealing and belief propagation. From a somewhat more technical point of view, these two projects are related by their reliance on the techniques of disordered statistical mechanics and spin glass theory. Their study will rely on both numerical simulations using large scale classical computer clusters and analytic study using the cavity method and its quantum generalizations. This latter method was developed previously for the study of quantum spin glasses. The projects will help train one to two graduate students in the relevant physics and techniques.