Collaborative Research: Statistical Mechanics of Non-local Disordered Models Associated with Quantum LDPC Codes

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The main challenge for building a quantum computer is that quantum components are prone to error. Error correction can be used to overcome this challenge but it places stringent requirements on future quantum computer hardware. One promising method of quantum error correction is the so-called Quantum Low-Density-Parity-Check (LDPC) codes. If successful, using these codes a large quantum computer could in principle be built. Compared to other existing schemes, it would be much more efficient, requiring fewer redundant quantum bits, called qubits. Studying these codes will improve our understanding of the quantum theoretical problems related to quantum computation. This project will provide excellent opportunities for graduate students. The award supports theoretical research on physics of non-local discrete and continuous statistical-mechanical models associated with quantum error correcting codes. An important feature of such codes is the existence of the decoding threshold, where a sufficiently large code can deal effectively with any noise level below the threshold, but not above it. Disordered spin models associated with decoding transition (these models have exact Wegner's self-duality), related models with large gauge groups associated with fault-tolerant decoding, as well as models with extensive ground state entropy, including U(1) gauge theories which generalize Wen's mutual Chern-Simons theory describing the ground state of Kitaev's toric code will be constructed and studied. Models associated with quantum LDPC codes are expected to be particularly interesting since their interaction terms involve a limited number of participating particles. The low-energy sectors of these models are expected to be dominated by non-trivial extended defects that generalize the notion of topological defects like domain walls, vortices, etc. New physics includes a phase transition driven by an extensive entropy of defect classes, coming from the exponentially large number of dimensions describing the original quantum code. Results will be relevant to several established fields of physics traditionally dealing with similar models: statistical mechanics of spin glasses, phase transition theory, etc., with potential applications extending to many other fields.