The physics of frustration (both classical and quantum), often a signature of strongly correlated systems, has been receiving a lot of attention recently. It is expected that competition between various “conventional” orders favored by different interactions can, at low enough temperatures, lead to new phases of matter with very unconventional properties. One fascinating possibility is so-called fractionalized phases. As the name suggests, the excitations in such phases carry fractions of “normal” particles' charge and spin. In two spatial dimensions, these excitations can also have fractional exchange (or braiding) statistics which makes them very attractive candidates for fault-tolerant quantum computation and, in particular, topological quantum computation. My interests are focused on studying topological order in solids with the special emphasis on Topological Quantum Computation. The two main directions of my research are:
Despite the great potential promise of topological quantum computation, many of the basic practical questions, which have been addressed at least partially in the case of more conventional qubit schemes, remain open. They must be resolved in order for this idea to become a reality, and they touch upon fundamental issues in physics. The first question is whether these non-Abelian topological phases actually exist in nature and specifically, in Quantum Hall systems. The second concern is the possibility of creating and manipulating quasiparticles in these systems, and in particular, whether their braiding can be performed in a practical way. And lastly, the state of the anyonic system should be susceptible to certain experimental probes – despite the fact that it cannot be measured easily by the environment. These questions are at the core of my current research efforts.
The broader impacts of this research go well beyond the usual promise associated with quantum computing such as formidable, often exponential speed-up of important computational tasks with implications ranging from cryptography to quantum chemistry. The conceptual idea of topological quantum computation already has had a large impact due to the deep connections it establishes between topology, condensed matter physics and quantum computation. Some of the best experimental groups in the United States and abroad are currently racing to verify the striking predictions stemming from the recent research in this field, including my own.