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

Abstract

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.

arXiv comment33 pages, 15 figures, 4 tables

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Cited by in corpus (7)

• Barren Plateaus in Variational Quantum Computing
• Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques
• Accelerating quantum imaginary-time evolution with random measurements
• Modified Conjugate Quantum Natural Gradient
• Quantum natural gradient with thermal-state initialization
• Generative flow-based warm start of the variational quantum eigensolver
• Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm