  Variational quantum algorithms (VQAs) represent a promising approach to
utilizing current quantum computing infrastructures. VQAs are based on a
parameterized quantum circuit optimized in a closed loop via a classical
algorithm. This hybrid approach reduces the quantum processing unit load but
comes at the cost of a classical optimization that can feature a flat energy
landscape. Existing optimization techniques, including either imaginary
time-propagation, natural gradient, or momentum-based approaches, are promising
candidates but place either a significant burden on the quantum device or
suffer frequently from slow convergence. In this work, we propose the quantum
Broyden adaptive natural gradient (qBang) approach, a novel optimizer that aims
to distill the best aspects of existing approaches. By employing the Broyden
approach to approximate updates in the Fisher information matrix and combining
it with a momentum-based algorithm, qBang reduces quantum-resource requirements
while performing better than more resource-demanding alternatives. Benchmarks
for the barren plateau, quantum chemistry, and the max-cut problem demonstrate
an overall stable performance with a clear improvement over existing techniques
in the case of flat (but not exponentially flat) optimization landscapes. qBang
introduces a new development strategy for gradient-based VQAs with a plethora
of possible improvements.
