Regensburg 2016 – wissenschaftliches Programm

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MA: Fachverband Magnetismus

MA 21: Transport: Quantum Coherence and Quantum Information Systems - Theory 2
(Joint session of HL, MA and TT organized by TT)

MA 21.2: Vortrag

Dienstag, 8. März 2016, 14:15–14:30, H22

A method to efficiently simulate the thermodynamic properties of the Fermi-Hubbard model on a quantum computer — •Pierre-Luc Dallaire-Demers and Frank K. Wilhelm — Saarland University, Saarbrücken, Germany

Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamic properties can be computed from its grand canonical potential. In general, there is no closed form expression of the grand canonical potential for lattices of more than one spatial dimension, but solutions can be numerically approximated using cluster methods. To model long-range effects such as order parameters, a powerful method to compute the cluster's Green's function consists in finding its self-energy through a variational principle. This allows the possibility of studying various phase transitions at finite temperature in the Fermi-Hubbard model. However, a classical cluster solver quickly hits an exponential wall in the memory (or computation time) required to store the computation variables. Here it is shown theoretically that the cluster solver can be mapped to a subroutine on a quantum computer whose quantum memory usage scales linearly with the number of orbitals in the simulated cluster and the number of measurements scales quadratically. A quantum computer with a few tens of qubits could therefore simulate the thermodynamic properties of complex fermionic lattices inaccessible to classical supercomputers.