The vast majority of electronic structure simulations for materials are performed using density functional theory (DFT) and first order many-body perturbation theory (GW). While these methods can accurately describe the electronic properties of a wide array of materials, they are fundamentally ill-suited to quantitatively study the entangled physics that is fundamental to most materials proposed for use in "quantum technologies." Classic examples of such materials include Mott insulators, quantum magnets, and superconductors.
On the other hand, many-body methods such as quantum Monte Carlo and tensor networks can describe entangled physics, but generally struggle to include all chemically realistic detail of any specific material. I am interested in bridging this gap between chemically realistic and entangled simulations by making methodological advances in (i) many-body solvers, and (ii) the representation of the many-body electronic structure problem.
A critical ingredient in many proposed and developing quantum technologies is coherence over long timescales. Experimentally, this manifests as the need to keep a quantum system in a specific, experimentally controlled state for a long period of time by preventing that state from interacting with other physical processes present in the experiment. Designing effective (nano)materials for coherent quantum devices requires us to identify the precise interactions that limit coherence time.
In a real (nano)material, there are a very large number of interacting physical processes. I am interested in developing new methods for simulating quantum dynamics that allow us to account for these interactions between (i) the state of interest and other degrees of freedom, as well as (ii) the weak interactions between environment degrees of freedom that will become meaningful at the long timescales relevant to decoherence. In more technical terms, I am interested in simulating open quantum system dynamics which must be described by an interacting environment to make useful contact with experiments.
Tensor networks are the primary theoretical and numerical tool that I like to use to understand the above-mentioned interacting many-body quantum systems. The associated algorithms and numerical methods used to manipulate tensor networks are still developing, and much progress remains to be made in this area. I am interested in various fundamental algorithmic problems related to the contraction and approximation of two- and three-dimensional tensor networks (PEPS).
In the worst cases, neither electronic structure nor quantum dynamics problems can be solved accurately and efficiently using classical computers. This fact, among others, has caused these problems to become some of the most widely discussed potential "useful" applications of a quantum computer. On the other hand, a quantum computer itself is just a specific example of an interacting quantum many-body system. I am interested in questions at the (theoretical) interface of these two facts. For example, (i) can we develop classical algorithms to better understand and optimize the performance of real quantum computers? (ii) can we identify specific static or dynamical problems of physical or chemical importance that are convincingly beyond the capability of classical algorithms but are efficiently solvable with quantum algorithms?