Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes

Journal article, 2024

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 momentumbased algorithm, qBang reduces quantumresource requirements while performing better than more resource -demanding alternatives. Benchmarks for the barren plateau, quantum chemistry, and the maxcut 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.