Variational Adiabatic Gauge Transformation on real quantum hardware for effective low-energy Hamiltonians and accurate diagonalization

TL;DR

This paper introduces VAGT, a non-perturbative hybrid quantum algorithm that uses current quantum computers to efficiently diagonalize Hamiltonians, enabling better low-energy theories for quantum many-particle systems.

Contribution

The paper presents VAGT, a novel variational quantum algorithm for diagonalizing Hamiltonians without perturbation theory, applicable on near-term quantum hardware.

Findings

VAGT successfully diagonalizes Hamiltonians with shallow circuits.

Numerical and hardware simulations demonstrate VAGT's accuracy.

VAGT operates with polynomial complexity in the number of runs.

Abstract

Effective low-energy theories represent powerful theoretical tools to reduce the complexity in modeling interacting quantum many-particle systems. However, common theoretical methods rely on perturbation theory, which limits their applicability to weak interactions. Here we introduce the Variational Adiabatic Gauge Transformation (VAGT), a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit that brings the Hamiltonian to either its block-diagonal or full-diagonal form. If a Hamiltonian can be diagonalized via a shallow quantum circuit, then VAGT can learn the optimal parameters using a polynomial number of runs. The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.