Statistical Mechanics of Non-Local Disordered Models Associated with Quantum LDPC codes

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Large-scale quantum computation is impossible without coherence. Quantum error correction (QEC) is therefore an important technique to protect coherence. QEC codes can enable quantum computers to tolerate occasional faults. Topological QEC codes like Kitaev's surface code provide quantum error corrections with give relatively high fault-tolerant thresholds for scalable quantum computation. However, they require a large overhead in the number of ancilla qubits. The research in this project aims to develop more general quantum low-density parity-check (LDPC) QEC codes which may work with smaller overhead. This project will also explore statistical mechanics of classical and quantum spin models that are related to LDPC codes. Understanding the stability of various phases and phase transitions in such physical models, both with and without disorder, will lead to better coherence protection techniques. Another benefit will be improved understanding of the properties of quantum and classical models in curved spaces, e.g., due to background gravity.In more technical terms, the PI will continue his studies of disordered spin models associated with decoding transition, related gauge models associated with fault-tolerant decoding, and quantum models with extensive ground state entropy, including U(1) gauge models. The focus of the research will be on the relations between differently defined transitions: the decoding transition, transitions defined in terms of a divergent specific heat, correlation length, domain wall tension, spin susceptibilities, area/perimeter law, etc, as well as transitions defined in terms of entanglement entropy, topological entropy, fidelity, and related information-theoretic quantities. These results will be incorporated in a practical decoding algorithm for quantum LDPC codes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.