缓解线性化后的挑战以在量子计算机上求解非线性系统
Alleviating Post-Linearization Challenges for Solving Nonlinear Systems on a Quantum Computer
AI总结：
本文提出利用Sigma基分解和单位化完成方法，在量子计算机上高效求解非线性系统。
摘要：
量子力学中的线性性限制了当前量子硬件直接求解由非线性微分方程支配的非线性系统的能力。可以采用线性化框架，如Carleman线性化，将其转换为一个高维无限线性系统，作为利用当前量子计算机间接求解非线性系统的方法。我们提供了一个高效的数据访问模型，用于在量子计算机上加载非线性系统的无限线性表示，直至截断阶$N$，通过将哈密顿量分解为非幺正算符的加权和，即Sigma基。我们已证明，Sigma基相较于传统分解方法（通常以Pauli算符的线性组合形式进行）提供了指数级的分解项减少。一旦哈密顿量被分解，我们便利用单位化完成的概念来构建每个加权张量积组件$\mathcal{H}_{j}$的实现电路。
英文摘要：
The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which provides a high dimensional infinite linear system corresponding to a finite nonlinear system, as an indirect way of solving nonlinear systems using current quantum computers. We provide an efficient data access model to load this infinite linear representation of the nonlinear system, upto truncation order $N$, on a quantum computer by decomposing the Hamiltonian into the weighted sum of non-unitary operators, namely the Sigma basis. We have shown that the Sigma basis provides an exponential reduction in the number of decomposition terms compared to the traditional decomposition, which is usually done in a linear combination of Pauli operators. Once the Hamiltonian is decomposed, we then use the concept of unitary completion to construct the circuit for the implementation of each weighted tensor product component $\mathcal{H}_{j}$ of the decomposition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
