Solving Efficiently Variational Quantum Circuits with Flat Landscapes*

Variational quantum algorithms represent a promising approach to utilize currently available quantum computing infrastructures. The framework is based on a parameterized quantum circuit that is optimized in a closed loop via a classical algorithm. This tandem approach reduces the load on the quantum computing unit but comes at the cost of a classical optimization that can feature a flat energy landscape. Existing techniques including either imaginary time-propagation, natural gradient or momentum-based approaches have shown limited success, depending on the requirements on the quantum computing unit and the complexity of the problem at hand. In this work, we propose a novel optimizer that aims to distill the best aspects of the existing approaches. By employing the Broyden approach to approximate updates in the Fisher-information and combining it with a momentum-based algorithm, the optimizer reduces quantum-resource requirements while performing superior than more resource-demanding predecessors. Benchmarks for barren plateau, LiH and maxcut demonstrate an overall stable performance with a clear improvement over existing techniques in case of flat landscapes. The optimizer introduces a new development strategy for gradient-based VQAs with a plethora of possible improvements.