As our demand for computational power grows, we encounter the question: "What are the physical limits to computation?" An answer is necessarily incomplete unless it can incorporate physics at the smallest scales, where we expect our near-term high-performance computing to occur. Microscopic physics -- namely, quantum mechanics -- behaves counterintuitively to our everyday experience, however. Quantum matter can occupy superpositions of states and build stronger correlations than are possible classically. This affects how quantum computers and quantum thermodynamic engines will behave.
Though these properties may seem to overwhelmingly defeat our attempts to build a quantum computer at-first-glance, what is remarkable is that they can also be immensely helpful to computation. Quantum mechanics hinders and helps computation, and the nuanced details of how we perform computations are important. In this dissertation, we examine the transition between these two behaviors and connect it to a well-studied behavior in condensed matter physics, known as the many-body-localization transition.
Our idea utilizes the fact that quantum many-body systems have an intrinsic fastest speed at which signals can travel. When this speed is maximal, we expect arbitrary universal quantum computation to be achievable, since strong quantum correlations, or entanglement, can be built quickly. When it is limited, however, the difficulty of the computation is classically simulatable. We demonstrate a similar transition in the amount of thermodynamic work that can be performed by a quantum system when entanglement is present.
We first consider computations consisting of the evolution of a single particle or many noninteracting particles. When the number of such noninteracting particles is comparable to the total size of the system, we do not know of any way to simulate such computations classically. However, we find that we can still determine the fastest signal speed in such systems. We extend our result to interacting particles, which are universal for quantum computation, and observe a many-body-localization transition in a simple computational model using our algorithm. Finally, we apply ideas from quantum information to simulate the thermodynamic performance of a simple quantum system, showing that quantum effects can enable it to outperform its classical counterpart.
Level of Degree
Physics & Astronomy
First Committee Member (Chair)
Second Committee Member
Carlton M Caves
Third Committee Member
Ivan H Deutsch
Fourth Committee Member
Steven T Flammia
quantum information, quantum thermodynamics, matchgates, many-body localization
Chapman, Adrian Kristian. "Localization and Scrambling of Quantum Information with Applications to Quantum Computation and Thermodynamics." (2018). https://digitalrepository.unm.edu/phyc_etds/202