Variational hybrid quantum–classical algorithms are powerful tools to maximize the use of noisy intermediate-scale quantum devices. While past studies have developed powerful and expressive ansatze, their near-term applications have been limited by the difficulty of optimizing in the vast parameter space. In this work, we propose a heuristic optimization strategy for such ansatze used in variational quantum algorithms, which we call ‘parameter-efficient circuit training (PECT)’. Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms, in which each iteration of the algorithm activates and optimizes a subset of the total parameter set. To update the parameter subset between iterations, we adapt the Dynamic Sparse Reparameterization scheme which was originally proposed for training deep convolutional neural networks. We demonstrate PECT for the Variational Quantum Eigensolver, in which we benchmark unitary coupled-cluster ansatze including UCCSD and k-UpCCGSD, as well as the Low-Depth Circuit Ansatz (LDCA), to estimate ground state energies of molecular systems. We additionally use a layerwise variant of PECT to optimize a hardware-efficient circuit for the Sycamore processor to estimate the ground state energy densities of the one-dimensional Fermi-Hubbard model. From our numerical data, we find that PECT can enable optimizations of certain ansatze that were previously difficult to converge and more generally can improve the performance of variational algorithms by reducing the optimization runtime and/or the depth of circuits that encode the solution candidate(s).

变分混合量子经典算法是强大的工具，可以最大限度地利用嘈杂的中级量子设备。尽管过去的研究已经开发出功能强大且富有表现力的分析仪，但由于难以在广阔的参数空间中进行优化，因此其近期应用受到了限制。在这项工作中，我们针对变分量子算法中使用的这种拟议提出了启发式优化策略，我们将其称为“参数有效电路训练（PECT）”。PECT不会立即优化所有的ansatz参数，而是启动了一系列变分算法，其中算法的每次迭代都会激活并优化总参数集的子集。为了更新迭代之间的参数子集，我们采用了动态稀疏重新参数化该方案最初是为训练深度卷积神经网络而提出的。我们展示了变分量子本征求解器的PECT，其中我们对包括UCCSD和k-UpCCGSD以及低深度电路Ansatz（LDCA），用于估计分子系统的基态能量。我们还使用PECT的逐层变量来优化Sycamore处理器的硬件效率电路，以估算一维费米-哈伯德模型的基态能量密度。从我们的数值数据中，我们发现PECT可以实现某些以前难以收敛的分析器的优化，并且更普遍地可以通过减少优化运行时间和/或对解决方案候选进行编码的电路深度来提高变分算法的性能。 ）。