Theoretical approaches to quantum computing frequently model the state of a quantum system as something that changes discretely in time. However, an unmeasured quantum system fundamentally evolves continuously in time as described by Schroedinger's equation. Even the quantum measurement process can be described by a continuous-time stochastic differential equation. This research explores quantum computation in its complete continuous-time formulation, with the goal of uncovering new paradigms for processing quantum information.
The research focuses on three key areas: continuous-time quantum computing architectures, continuous-time quantum error correction, and continuous-time quantum algorithms. These areas were selected because examples highlighting the differences between continuous-time and discrete-time quantum computing formulations are already known in each of them. For example, continuous-time quantum walk architectures require no external dynamical controls, continuous-time quantum feedback can mediate quantum error correction, and continuous-time quantum scattering can calculate Boolean formulas with fewer queries than any classical algorithm can. A major objective of this research is to expand upon these directions and develop new ones. The strategy will be to focus on problems that are sufficiently well-defined and tractable that progress can be made.
This project not only supports graduate student training in quantum information science but also supports education and outreach activities through the Southwest Quantum Information and Technology (SQuInT) Network. The PI will seek out exceptional students outside his home institution, especially encouraging those in underrepresented groups, and sponsor their attendance at SQuInT meetings to further enrich this growing field.
