Wang Samson, Fontana Enrico, Cerezo M, Sharma Kunal, Sone Akira, Cincio Lukasz, Coles Patrick J
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
Imperial College London, London, UK.
Nat Commun. 2021 Nov 29;12(1):6961. doi: 10.1038/s41467-021-27045-6.
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.
变分量子算法（VQAs）可能是在有噪声的中等规模量子（NISQ）计算机上实现量子优势的一条途径。一个自然的问题是，NISQ设备上的噪声是否会对VQA性能造成根本性限制。我们严格证明了有噪声VQAs存在一个严重的限制，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，对于所考虑的局部泡利噪声，我们证明，如果近似电路的深度随量子比特数n线性增长，那么梯度会随n呈指数级消失。这些由噪声引起的贫瘠高原（NIBPs）在概念上与无噪声的贫瘠高原不同，后者与随机参数初始化有关。我们的结果是针对一个通用的近似电路得出的，该近似电路包括量子交替算子近似电路和酉耦合簇近似电路等特殊情况。对于前者，我们的数值启发式方法证明了在实际硬件噪声模型下的NIBP现象。
