Finite-depth scaling of translationally invariant variational quantum circuits

Variational quantum eigensolver (VQE) has emerged as a promising algorithm for quantum computing devices owing to its relative simplicity. However, its utility for large scale condensed matter models is still under question.

In this work, we focus on a particularly simple translation invariant ansatz for VQE, and investigate how the energy error scales with the depth of the circuit. Based on an intuitive physical picture, as well as extensive numerical simulations on Ising models, we argue that energy error scales differently before and after a phase transition, enabling us to identify its location from translation invariant VQE.