论文标题
量子相识别的精确量子算法：重新归一化组和误差校正
Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
论文作者
论文摘要
我们通过构建量子算法探索重新归一化组（RG）流量和误差校正之间的关系，该量子算法准确地识别受到有限内部Abelian对称性保护的1D对称性保护拓扑（SPT）阶段。对于每个SPT阶段，我们的算法都运行一个模拟RG流的量子电路：该阶段中的任意输入基态波函数将映射到独特的微小输入参考状态，从而允许有效的相位识别。通过将阶段中的通用输入状态视为应用于参考状态的相干“错误”的集合，并工程量子电路有效地检测和纠正此类错误来实现此构建。重要的是，误差校正阈值已被证明与相边界完全一致。我们讨论了结果在凝结物理，机器学习和近期量子算法的背景下的含义。
We explore the relationship between renormalization group (RG) flow and error correction by constructing quantum algorithms that exactly recognize 1D symmetry-protected topological (SPT) phases protected by finite internal Abelian symmetries. For each SPT phase, our algorithm runs a quantum circuit which emulates RG flow: an arbitrary input ground state wavefunction in the phase is mapped to a unique minimally-entangled reference state, thereby allowing for efficient phase identification. This construction is enabled by viewing a generic input state in the phase as a collection of coherent `errors' applied to the reference state, and engineering a quantum circuit to efficiently detect and correct such errors. Importantly, the error correction threshold is proven to coincide exactly with the phase boundary. We discuss the implications of our results in the context of condensed matter physics, machine learning, and near-term quantum algorithms.
