Benchmarking Adaptive Variational Quantum Eigensolvers

The variational quantum eigensolver (VQE) is one of the cornerstones of simulations of quantum systems in noisy intermediate-scale quantum devices. Formulations based on established many-body methods tend to map onto unattainable circuit depths, often alleviated by somewhat arbitrary approximations, while amenable implementations typically lose the intuitive connection to their many-body formalism. Novel adaptive variants of VQE are worthy prospect avenues, with potentially shallower circuits, yet at the expense of more measurements. In this work we provide a comprehensive benchmark of the adaptive derivative-assembled pseudo-Trotter (ADAPT) VQE algorithm for the H₂, NaH, and KH molecules, assessing the aptness of the prepared state and its corresponding energy compared to exact diagonalization, which are accompanied by the respective measurement and circuit depth estimates. There is much to be understood about these algorithms and these noiseless simulations pave the way to a better understanding of how they work and constitute the reference figures for future studies in noisy settings and hardware deployment.