Paper Introduction: Variational Quantum Amplitude Estimation, a new quantum Monte Carlo method.
In this article, I would like to introduce a paper proposing a new quantum Monte Carlo method that came out this year, Variational Quantum Amplitude Estimation (VQAE). This is intended to improve the relationship of computation time to error rate in quantum Monte Carlo methods. Quantum Monte Carlo and classical Monte Carlo are methods to make the right-hand side of a particular function f(x)≈∑jMcjhj closer to the left-hand side. In the usual quantum Monte Carlo method, the computation time is O(1/ε) with respect to the error rate ε. This is the case when the sample size is 2M for M samples. However, the method proposed in this paper gives an accuracy of O(1/ε1+β) for an error rate of M samples, where β is a constant that is 1 for full classical Monte Carlo and 0 for the quantum case. The actual calculation will be somewhere in between. The most time-consuming part of the Monte Carlo method is the multiplication by the Grover operator. The VQAE method uses variational calculations to reduce the number of calculations and increase the accuracy. The flow is shown in Fig. 1. The post-processing part of optimizing θ is done for 5000 points by grid search.
Fig. 1 Flowchart of VQAE as presented in my paper, where Q is the Grover operator.
This method is very similar to the Frame Superposition Cluster (FSC) , which was the subject of my paper, so I felt a sense of familiarity with it. However, there were some parts of the optimization method that were not explained, and depending on that, it might take more time than Quantum Monte Carlo. The method is very good, and I hope that an explanation of it will make the paper better.