Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits $n$ if the depth of the ansatz grows linearly with $n$. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

翻译：变分量子算法（VQAs）可能是噪声中等规模量子（NISQ）计算机上实现量子优势的途径。一个自然的问题是：NISQ器件中的噪声是否对VQA性能构成根本性限制？我们严格证明了噪声对VQA存在严重局限性，即噪声会导致训练景观出现贫瘠高原（即梯度消失）。具体而言，对于所考虑的局域泡利噪声，我们证明如果拟设深度随量子比特数$n$线性增长，梯度会以指数形式随$n$消失。这些噪声引起的贫瘠高原（NIBPs）在概念上区别于与随机参数初始化相关的无噪声贫瘠高原。我们的结论适用于通用拟设，其特殊情况包括量子交替算子拟设和幺正耦合簇拟设等。针对前者，我们的数值启发式方法在现实硬件噪声模型下展示了NIBP现象。