Neural network encoded variational quantum algorithms

Abstract

We introduce a general framework called neural network (NN) encoded variational quantum algorithms (VQAs), or NN-VQA for short, to address the challenges of implementing VQAs on noisy intermediate-scale quantum (NISQ) computers. Specifically, NN-VQA feeds input (such as parameters of a Hamiltonian) from a given problem to a neural network and uses its outputs to parameterize an ansatz circuit for the standard VQA. Combining the strengths of NN and parameterized quantum circuits, NN-VQA can dramatically accelerate the training process of VQAs and handle a broad family of related problems with varying input parameters with the pre-trained NN. To concretely illustrate the merits of NN-VQA, we present results on NN-variational quantum eigensolver (VQE) for solving the ground state of parameterized XXZ spin models. Our results demonstrate that NN-VQE is able to estimate the ground-state energies of parameterized Hamiltonians with high precision without fine-tuning, and significantly reduce the overall training cost to estimate ground-state properties across the phases of XXZ Hamiltonian. We also employ an active-learning strategy to further increase the training efficiency while maintaining prediction accuracy. These encouraging results demonstrate that NN-VQAs offer a new hybrid quantum-classical paradigm to utilize NISQ resources for solving more realistic and challenging computational problems.

4.4 pages, 5 figures, with supplemental materials

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• Limitations of Noisy Quantum Devices in Computational and Entangling Power
• Pitfalls when tackling the exponential concentration of parameterized quantum models
• Variational post-selection for ground states and thermal states simulation
• Dual-VQE: A quantum algorithm to lower bound the ground-state energy
• Generative flow-based warm start of the variational quantum eigensolver
• The Dual Role of Low-Weight Pauli Propagation: A Flawed Simulator but a Powerful Initializer for Variational Quantum Algorithms
• Superior resilience to poisoning and amenability to unlearning in quantum machine learning