低量子比特区域变分本征解的最优量子抽样回归算法
An optimal quantum sampling regression algorithm for variational eigensolving in the low qubit number regime
摘要：
鉴于我们目前访问量子处理器的方式（即通过云），VQE算法运行起来非常昂贵。为了缓解这个问题，我们引入了量子采样回归（QSR），这是一种替代的混合量子经典算法，并基于低量子比特数制度下的时间复杂度分析了它的一些用例。为了换取一些额外的经典资源，这种新的策略被证明是最佳的，它需要从量子处理器的样本数量。我们开发了一个简单的分析模型来评估这种算法何时比VQE更有效，并且从相同的理论考虑出发，建立了一个阈值，在该阈值之上可以发生量子优势。最后，我们证明了我们的算法的基准问题的有效性。
英文摘要：
The VQE algorithm has turned out to be quite expensive to run given the way we currently access quantum processors (i.e. over the cloud). In order to alleviate this issue, we introduce Quantum Sampling Regression (QSR), an alternative hybrid quantum-classical algorithm, and analyze some of its use cases based on time complexity in the low qubit number regime. In exchange for some extra classical resources, this novel strategy is proved to be optimal in terms of the number of samples it requires from the quantum processor. We develop a simple analytical model to evaluate when this algorithm is more efficient than VQE, and, from the same theoretical considerations, establish a threshold above which quantum advantage can occur. Finally, we demonstrate the efficacy of our algorithm for a benchmark problem.
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