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

没有相干性，大规模量子计算是不可能的。因此，量子纠错（QEC）是保护相干性的重要技术。QEC代码可以使量子计算机能够容忍偶尔的故障。 拓扑QEC码，如Kitaev的表面码，提供量子纠错，并为可扩展的量子计算提供相对高的容错阈值。 然而，它们需要大量的辅助量子位的开销。 本计画的研究目的是开发更通用的量子低密度奇偶校验码，以更小的系统开销来实现。 本项目还将探索与LDPC码相关的经典和量子自旋模型的统计力学。 了解这些物理模型中各种相位和相变的稳定性，无论有无无序，都将导致更好的相干性保护技术。 另一个好处将是提高对弯曲空间中量子和经典模型性质的理解，例如，在更专业的术语中，PI将继续研究与解码跃迁相关的无序自旋模型，与容错解码相关的相关规范模型，以及具有广泛基态熵的量子模型，包括U（1）规范模型。研究的重点将是不同定义的过渡之间的关系：解码过渡，过渡定义的发散比热，相关长度，畴壁张力，自旋磁化率，面积/周长定律等，以及过渡定义的纠缠熵，拓扑熵，保真度，和相关的信息理论量。 这些结果将被纳入一个实用的量子LDPC码的解码算法。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.