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

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