Sequential minimal optimization for quantum-classical hybrid algorithms
Sequential minimal optimization for quantum-classical hybrid algorithms
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DOI：
10.1103/physrevresearch.2.043158
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发表时间：
2020-10-29
影响因子：
4.2
通讯作者：
Todo, Synge
中科院分区：
文献类型：
--
作者：
Nakanishi, Ken M.;Fujii, Keisuke;Todo, Synge
我们提出了一种用于量子经典混合算法的顺序最小优化方法，该方法收敛速度更快，对统计误差具有鲁棒性，并且无超参数。具体来说，通过仅考虑参数的子集，参数化量子电路的优化问题被划分为可解的子问题。事实上，如果我们选择单个参数，成本函数就会变成一条周期为 2 pi 的简单正弦曲线，因此我们可以精确地最小化所选参数。此外，即使在一般情况下，成本函数也是由具有特定周期的三角函数的简单和给出的，因此可以通过使用经典计算机来最小化。通过重复执行此过程，我们可以优化参数化量子电路，使成本函数变得尽可能小。我们进行数值模拟，并将所提出的方法与现有的无梯度和基于梯度的优化算法进行比较。我们发现所提出的方法大大优于现有的优化算法，并且收敛到几乎独立于参数的初始选择的解决方案。这可以轻松加速几乎所有量子经典混合算法，并将成为利用近期量子设备的关键工具。
We propose a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, robust against statistical error, and hyperparameter-free. Specifically, the optimization problem of the parameterized quantum circuits is divided into solvable subproblems by considering only a subset of the parameters. In fact, if we choose a single parameter, the cost function becomes a simple sine curve with period 2 pi, and hence we can exactly minimize with respect to the chosen parameter. Furthermore, even in general cases, the cost function is given by a simple sum of trigonometric functions with certain periods and hence can be minimized by using a classical computer. By repeatedly performing this procedure, we can optimize the parameterized quantum circuits so that the cost function becomes as small as possible. We perform numerical simulations and compare the proposed method with existing gradient-free and gradient-based optimization algorithms. We find that the proposed method substantially outperforms the existing optimization algorithms and converges to a solution almost independent of the initial choice of the parameters. This accelerates almost all quantum-classical hybrid algorithms readily and would be a key tool for harnessing near-term quantum devices.