标题： 用于模拟耦合经典振荡器的实用量子电路实现 显示英文标题

标题： Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators

摘要： 模拟大规模耦合振子系统对经典算法提出了巨大的计算挑战，尤其是在热力学极限下进行第一性原理分析时。 受Babbush等人提出的量子算法框架的启发，我们提出了并实现了用于模拟一维弹簧-质量系统的详细量子电路构造。 我们的方法结合了关键的量子子例程，包括块编码、量子奇异值变换（QSVT）和幅值放大，以实现与模拟经典振子动力学相关的酉时间演化算子。 在均匀弹簧-质量设置中，我们的电路构造需要门复杂度为$\mathcal{O}\bigl(\log_2^2 N\,\log_2(1/\varepsilon)\bigr)$，其中$N$是振子的数量，$\varepsilon$是近似的目标精度。 对于更一般、非均匀的弹簧-质量系统，总门复杂度为$\mathcal{O}\bigl(N\log_2 N\,\log_2(1/\varepsilon)\bigr)$。 两种情况都需要$\mathcal{O}(\log_2 N)$个量子比特。 数值模拟在所有测试配置中都与经典求解器一致，表明这种基于电路的哈密顿量模拟方法可以显著降低计算成本，并可能在未来量子硬件上实现更大规模的多体研究。 显示英文摘要

摘要： Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm framework proposed by Babbush et al., we present and implement a detailed quantum circuit construction for simulating one-dimensional spring-mass systems. Our approach incorporates key quantum subroutines, including block encoding, quantum singular value transformation (QSVT), and amplitude amplification, to realize the unitary time-evolution operator associated with simulating classical oscillators dynamics. In the uniform spring-mass setting, our circuit construction requires a gate complexity of $\mathcal{O}\bigl(\log_2^2 N\,\log_2(1/\varepsilon)\bigr)$, where $N$ is the number of oscillators and $\varepsilon$ is the target accuracy of the approximation. For more general, heterogeneous spring-mass systems, the total gate complexity is $\mathcal{O}\bigl(N\log_2 N\,\log_2(1/\varepsilon)\bigr)$. Both settings require $\mathcal{O}(\log_2 N)$ qubits. Numerical simulations agree with classical solvers across all tested configurations, indicating that this circuit-based Hamiltonian simulation approach can substantially reduce computational costs and potentially enable larger-scale many-body studies on future quantum hardware.