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 nonperturbative 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 through numerical simulations, as well as simulations on Rigetti and IonQ quantum computers

Variational Adiabatic Gauge Transformation on Real Quantum Hardware for Effective Low-Energy Hamiltonians and Accurate Diagonalization / Gentini Laura; Cuccoli Alessandro; Banchi Leonardo. - In: PHYSICAL REVIEW APPLIED. - ISSN 2331-7019. - ELETTRONICO. - 18:(2022), pp. 034025.0-034025.0. [10.1103/PhysRevApplied.18.034025]

Variational Adiabatic Gauge Transformation on Real Quantum Hardware for Effective Low-Energy Hamiltonians and Accurate Diagonalization

Gentini Laura;Cuccoli Alessandro;Banchi Leonardo
2022

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 nonperturbative 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 through numerical simulations, as well as simulations on Rigetti and IonQ quantum computers
2022
18
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0
Gentini Laura; Cuccoli Alessandro; Banchi Leonardo
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1286842
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