Variational Quantum-Neural Hybrid Eigensolver

Abstract

The variational quantum eigensolver (VQE) is one of the most representative quantum algorithms in the noisy intermediate-size quantum (NISQ) era, and is generally speculated to deliver one of the first quantum advantages for the ground-state simulations of some non-trivial Hamiltonians. However, short quantum coherence time and limited availability of quantum hardware resources in the NISQ hardware strongly restrain the capacity and expressiveness of VQEs. In this Letter, we introduce the variational quantum-neural hybrid eigensolver (VQNHE) in which the shallow-circuit quantum ansatz can be further enhanced by classical post-processing with neural networks. We show that VQNHE consistently and significantly outperforms VQE in simulating ground-state energies of quantum spins and molecules given the same amount of quantum resources. More importantly, we demonstrate that for arbitrary post-processing neural functions, VQNHE only incurs an polynomial overhead of processing time and represents the first scalable method to exponentially accelerate VQE with non-unitary post-processing that can be efficiently implemented in the NISQ era.

4.6 pages, 3 figures, with supplemental materials

References in corpus (24)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Variational Quantum Algorithms
• Quantum computational advantage using photons
• Noisy intermediate-scale quantum (NISQ) algorithms
• Hybrid quantum-classical algorithms and quantum error mitigation
• Real- and imaginary-time evolution with compressed quantum circuits
• Differentiable Quantum Architecture Search
• Hardware-efficient variational quantum algorithms for time evolution
• Qubit-excitation-based adaptive variational quantum eigensolver
• Neural Predictor based Quantum Architecture Search
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Static and dynamical correlation in diradical molecules by Quantum Monte Carlo using the Jastrow Antisymmetrized Geminal Power ansatz
• Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm
• Adaptive pruning-based optimization of parameterized quantum circuits
• Markovian Quantum Neuroevolution for Machine Learning
• Variational inference with a quantum computer
• Benchmarking adaptive variational quantum eigensolvers
• MoG-VQE: Multiobjective genetic variational quantum eigensolver
• Non-unitary operations for ground-state calculations in near term quantum computers
• Hybrid convolutional neural network and PEPS wave functions for quantum many-particle states
• Quantum Architecture Search via Deep Reinforcement Learning
• A Neural-Network Variational Quantum Algorithm for Many-Body Dynamics
• Assessing the Accuracy of the Jastrow Antisymmetrized Geminal Power in the H4 Model System
• VSQL: Variational Shadow Quantum Learning for Classification

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