Variational Quantum-Neural Hybrid Eigensolver.

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum physics

Background:

• The variational quantum eigensolver (VQE) is a key quantum algorithm for the noisy intermediate-scale quantum (NISQ) era, aiming for quantum advantage in simulations.
• Current NISQ hardware limitations, such as short coherence times and limited resources, restrict VQE's capacity and expressiveness.

Purpose of the Study:

• Introduce the variational quantum-neural hybrid eigensolver (VQNHE) to overcome VQE limitations.
• Enhance shallow-circuit quantum Ansatz performance using classical neural network post-processing.

Main Methods:

• Developed the variational quantum-neural hybrid eigensolver (VQNHE).
• Integrated neural networks for classical post-processing of quantum Ansatz outputs.
• Applied VQNHE to simulate ground-state energies of quantum spins and molecules.

Main Results:

• VQNHE consistently and significantly outperforms VQE in accuracy for ground-state energy simulations.
• Demonstrated that VQNHE achieves this improvement with the same quantum resource allocation.
• Showcased VQNHE's scalability with only a polynomial overhead for arbitrary neural post-processing functions.

Conclusions:

• VQNHE represents a scalable advancement over VQE for NISQ-era quantum simulations.
• The hybrid approach offers efficient acceleration of VQE using nonunitary post-processing implementable on current quantum hardware.