Suppose someone gives you a fully working quantum computer — what processes or programs are you going to run on it? I work on developing quantum algorithms to simulate quantum physics, which can’t be modeled using a classical computer. I look at what kinds of physical systems you can simulate, and how quantum algorithms can be used to compute certain quantities in condensed matter systems. One formal aspect that I study involves Markovian quantum processes, which are memoryless in the same sense as a random walk: the next step never depends on the prior trajectory. Because of this property, these processes make good thermal noise models for quantum mechanical systems, which is important for quantum computing because we want to be able to design memories that are robust to noise and protected from decoherence. If you put a quantum state into the system, you want it to be stable for a long time. These quantum Markovian processes can be used to describe noisy evolution on that system to some extent. Whether you’re interested in developing algorithms or in trying to design these memories that can withstand noise, one central question is how long it will take for a process to converge, and I have been developing a general framework to estimate that convergence time. Since arriving at IQIM, I have also started to look more in a topological direction at particular models for memory, which is interesting from a condensed matter point of view as well.