在量子计算机上建模随机化学动力学
Modeling Stochastic Chemical Kinetics on Quantum Computers
AI总结：
针对化学主方程求解随物种数指数增长的难题，研究以Schlögl模型为例，结合VQD、QPE与VQSVD等量子算法实现随机化学动力学建模，量子模拟结果与经典计算误差在百分之几内，为相关指数复杂度问题提供量子求解可行路径。
摘要：
化学主方程（Chemical Master Equation，CME）可对随机化学反应网络及其动力学提供高精度描述，但由于可能的状态数随反应物种数量呈指数级增长，其计算资源消耗极高。在本研究中，我们以三分子反应网络的Schlögl模型（施勒格尔模型）为例，展示了如何利用量子算法与硬件对CME描述的随机化学动力学进行建模。为了为量子算法的性能研究提供基准，我们首先在经典计算机上确定了在模型的单稳态和双稳态区域构建随机Schlögl算符的适用参数范围，随后讨论了这些参数选择在量子计算机上建模近似动力学的适用性。接着，我们应用变分量子收缩（Variational Quantum Deflation，VQD）算法计算了描述单稳态与双稳态系统跃迁速率的最小模本征值$\lambda_0$和$\lambda_1$，并结合量子相位估计（Quantum Phase Estimation，QPE）算法与变分量子奇异值分解（Variational Quantum Singular Value Decomposition，VQSVD）算法估计了双稳态情形的零模（基态）。我们在含噪与无噪量子模拟中得到的量子计算结果，与经典计算得到的本征值和零模相比，误差在百分之几以内。总体而言，本研究为指数复杂度的随机化学动力学问题及其他相关随机微分方程的量子求解勾勒出了一条可行路径。
英文摘要：
The Chemical Master Equation (CME) provides a highly accurate, yet extremely resource-intensive representation of a stochastic chemical reaction network and its kinetics due to the exponential scaling of its possible states with the number of reacting species. In this work, we demonstrate how quantum algorithms and hardware can be employed to model stochastic chemical kinetics as described by the CME using the Schlögl Model of a trimolecular reaction network as an illustrative example. To ground our study of the performance of our quantum algorithms, we first determine a range of suitable parameters for constructing the stochastic Schlögl operator in the mono- and bistable regimes of the model using a classical computer and then discuss the appropriateness of our parameter choices for modeling approximate kinetics on a quantum computer. We then apply the Variational Quantum Deflation (VQD) algorithm to evaluate the smallest-magnitude eigenvalues, $λ_0$ and $λ_1$, which describe the transition rates of both the mono- and bi-stable systems, and the Quantum Phase Estimation (QPE) algorithm combined with the Variational Quantum Singular Value Decomposition (VQSVD) algorithm to estimate the zeromode (ground state) of the bistable case. Our quantum computed results from both noisy and noiseless quantum simulations agree within a few percent with the classically computed eigenvalues and zeromode. Altogether, our work outlines a practical path toward the quantum solution of exponentially complex stochastic chemical kinetics problems and other related stochastic differential equations.
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