论文标题
量化贫瘠的高原现象的非结构化变异ansätze模型
Quantifying the barren plateau phenomenon for a model of unstructured variational ansätze
论文作者
论文摘要
量化与非结构化参数化量子电路相关的客观功能景观的平坦度对于理解使用“硬件有效的Ansatz”的变异算法的性能很重要，尤其是对于确保了一个令人难以置信的平坦景观 - 一种所谓的“敞篷高原” - 可以避免。对于这样的Ansätze模型，我们将典型的景观平坦度与某个随机步行家族联系起来，从而使我们能够得出一种蒙特卡洛算法，以有效地估算任何建筑的景观平坦度。统计图还使我们能够在贫瘠的高原现象上证明新的分析界限，并且通常提供了对现象对ANSATZ深度，建筑，Qudit维度以及汉密尔顿组合和空间区域的依赖的新见解。我们的分析利用了Dalzell等人最初开发的技术。研究随机电路中的抗浓缩。
Quantifying the flatness of the objective-function landscape associated with unstructured parameterized quantum circuits is important for understanding the performance of variational algorithms utilizing a "hardware-efficient ansatz", particularly for ensuring that a prohibitively flat landscape -- a so-called "barren plateau" -- is avoided. For a model of such ansätze, we relate the typical landscape flatness to a certain family of random walks, enabling us to derive a Monte Carlo algorithm for efficiently, classically estimating the landscape flatness for any architecture. The statistical picture additionally allows us to prove new analytic bounds on the barren plateau phenomenon, and more generally provides novel insights into the phenomenon's dependence on the ansatz depth, architecture, qudit dimension, and Hamiltonian combinatorial and spatial locality. Our analysis utilizes techniques originally developed by Dalzell et al. to study anti-concentration in random circuits.
