Determining ground-state phase diagrams on quantum computers via a generalized application of adiabatic state preparation

TL;DR

This paper introduces a method using local adiabatic ramps to compute ground-state phase diagrams on quantum computers, demonstrated on small systems with IBM quantum hardware, overcoming challenges of accuracy and near degeneracy.

Contribution

It presents a novel application of adiabatic state preparation with local ramps for directly determining ground-state phase diagrams on quantum computers.

Findings

Successfully computed phase diagrams for 2- and 3-site XY models.

Demonstrated feasibility on IBM quantum hardware.

Achieved accurate results despite near degeneracies.

Abstract

Quantum phase transitions materialize as level crossings in the ground-state energy when the parameters of the Hamiltonian are varied. The resulting ground-state phase diagrams are straightforward to determine by exact diagonalization on classical computers, but are challenging on quantum computers because of the accuracy needed and the near degeneracy of competing states close to the level crossings. In this work, we use a local adiabatic ramp for state preparation to allow us to directly compute ground-state phase diagrams on a quantum computer via time evolution. This methodology is illustrated by examining the ground states of the XY model with a magnetic field in the z-direction in one dimension. We are able to calculate an accurate phase diagram on both two and three site systems using IBM quantum machines.