AI 中文总结
研究针对特定酉算子，提出将量子相位估计电路复杂度从\(\mathcal{O}(n^2)\)降至\(\mathcal{O}(n)\)的算法，在四量子比特光子系统实现，相比以往方案更具确定性且可扩展到高维酉算子。
AI 中文摘要
量子算法能比经典算法更快解决某些计算问题。许多算法如Shor因式分解、Grover无结构搜索及HHL求解线性系统算法，都依赖量子相位估计（QPE）。本文针对一类在基于量子傅里叶变换的协议、循环群表示和周期性演化量子系统中频繁出现的酉算子，提出一种QPE算法，成功将电路复杂度从\(\mathcal{O}(n^2)\)降至\(\mathcal{O}(n)\)，并在四量子比特光子系统上实现。该系统由光子对实现，两个量子比特编码在偏振自由度，另两个编码在路径模式。与以往基于双轨编码和KLM协议的QPE光子实现不同，本方案完全确定，且可扩展到更高维酉算子。
英文摘要
Quantum algorithms solve certain computational problems faster than the best known classical algorithms. Many algorithms, including Shor's for factoring, Grover's for unstructured search, and the HHL for solving linear systems, rely on quantum phase estimation (QPE) as a fundamental subroutine. The QPE protocol proceeds through the initialization of a control register in a uniform superposition, controlled unitary evolution encoding the eigenphase, and a final inverse quantum Fourier transform followed by measurement to extract the phase. Here, we address a special class of unitary operators that frequently appear in quantum Fourier transform-based protocols, cyclic group representations, and periodically evolving quantum systems. We introduce a QPE algorithm that successfully reduces the circuit complexity from $\mathcal{O}(n^2)$ to $\mathcal{O}(n)$ for a special class of unitary operators and implement it on a four-qubit photonic system. The four-qubit system is realised using a photon pair, with two qubits encoded in its polarization degree of freedom and the remaining two in its path modes. In contrast to previous photonic implementations of QPE based on dual-rail encoding and KLM protocol, where controlled operations are inherently probabilistic and thus reduce the overall success probability of phase estimation, our scheme is fully deterministic. Moreover, it is scalable to higher-dimensional unitaries, provided the underlying structure of the unitaries is preserved.
Comments11 pages, 5 figures
