Adaptive variational preparation of the Fermi-Hubbard eigenstates

TL;DR

This paper introduces an adaptive variational quantum eigensolver (ADAPT-VQE) that efficiently prepares accurate ground and excited states of the Fermi-Hubbard model, demonstrating advantages in parameter count, depth, and scalability for NISQ devices.

Contribution

The paper presents a novel adaptive variational algorithm that constructs system-specific ansatzes for the Fermi-Hubbard model, outperforming non-adaptive methods in efficiency and scalability.

Findings

Outperforms non-adaptive VQE in fewer parameters and shorter gate depth.

Achieves asymptotic improvement in fidelity and energy with ansatz depth.

Demonstrates effective preparation of excited states and Green functions.

Abstract

Approximating the ground states of strongly interacting electron systems in quantum chemistry and condensed matter physics is expected to be one of the earliest applications of quantum computers. In this paper, we prepare highly accurate ground states of the Fermi-Hubbard model for small grids up to 6 sites (12 qubits) by using an interpretable, adaptive variational quantum eigensolver(VQE) called ADAPT-VQE. In contrast with non-adaptive VQE, this algorithm builds a system-specific ansatz by adding an optimal gate built from one-body or two-body fermionic operators at each step. We show this adaptive method outperforms the non-adaptive counterpart in terms of fewer variational parameters, short gate depth, and scaling with the system size. The fidelity and energy of the prepared state appear to improve asymptotically with ansatz depth. We also demonstrate the application of adaptive variational methods by preparing excited states and Green functions using a proposed ADAPT-SSVQE algorithm. Lower depth, asymptotic convergence, noise tolerance of a variational approach, and a highly controllable, system-specific ansatz make the adaptive variational methods particularly well-suited for NISQ devices.