论文标题
通过经典阴影和降低的量子仿真的测量优化
Measurement optimization of variational quantum simulation by classical shadow and derandomization
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
Simulating large quantum systems is the ultimate goal of quantum computing. Variational quantum simulation (VQS) gives us a tool to achieve the goal in near-term devices by distributing the computation load to both classical and quantum computers. However, as the size of the quantum system becomes large, the execution of VQS becomes more and more challenging. One of the most severe challenges is the drastic increase in the number of measurements; for example, the number of measurements tends to increase by the fourth power of the number of qubits in a quantum simulation with a chemical Hamiltonian. This work aims to dramatically decrease the number of measurements in VQS by recently proposed shadow-based strategies such as classical shadow and derandomization. Even though previous literature shows that shadow-based strategies successfully optimize measurements in the variational quantum optimization (VQO), how to apply them to VQS was unclear due to the gap between VQO and VQS in measuring observables. In this paper, we bridge the gap by changing the way of measuring observables in VQS and propose an algorithm to optimize measurements in VQS by shadow-based strategies. Our theoretical analysis not only reveals the advantage of using our algorithm in VQS but theoretically supports using shadow-based strategies in VQO, whose advantage has only been given numerically. Additionally, our numerical experiment shows the validity of using our algorithm with a quantum chemical system.