Hybrid quantum-classical computing in the noisy intermediate-scale quantum (NISQ) era with variational algorithms can exhibit barren plateau issues, causing difficult convergence of gradient-based optimization techniques. In this paper, we discuss "post-variational strategies", which shift tunable parameters from the quantum computer to the classical computer, opting for ensemble strategies when optimizing quantum models. We discuss various strategies and design principles for constructing individual quantum circuits, where the resulting ensembles can be optimized with convex programming. Further, we discuss architectural designs of post-variational quantum neural networks and analyze the propagation of estimation errors throughout such neural networks. Finally, we show that empirically, post-variational quantum neural networks using our architectural designs can potentially provide better results than variational algorithms and performance comparable to that of two-layer neural networks.

翻译：在含噪中等规模量子（NISQ）时代，采用变分算法的混合量子-经典计算可能出现贫瘠高原问题，导致基于梯度的优化技术难以收敛。本文探讨"后变分策略"，即将可调参数从量子计算机转移到经典计算机，在优化量子模型时采用集成策略。我们讨论了构建单个量子电路的多种策略与设计原则，其形成的集成模型可通过凸规划进行优化。进一步地，我们分析了后变分量子神经网络的架构设计，并研究了此类神经网络中估计误差的传播特性。最后，实证表明，采用本文架构设计的后变分量子神经网络相比变分算法可能获得更优结果，且性能可与两层神经网络相媲美。