Use of optimization methods for Quantum Mechanics problems: transmission of quan- tum states and few-body problems

FERRÓN, ALEJANDRO; SERRA, PABLO; OMAR OSENDA

La Plata

Congreso; X Conference on Quantum Foundations, Ten Irreversible Years of Quantum Foundations In Argentina; 2021

Instituto de Física de La Plata

Using a global optimization algorithmwe obtain spin chains with site-dependentexchange coefficients which allow almostperfect quantum state transfer betweenthe extremes of the chains without anyfurther time-dependent external control.We consider chains with isotropic andanisotropic Heisenberg Hamiltonian withup to 100 spins. The method allow usto choose the arrival of the transferredstate by changing the range available tothe exchange coupling strengths. We con-sider short transferred times, in partic-ular shorter than those achievable withknown time-dependent control schemes.The chains obtained with the optimiza-tion method show some remarkable andinteresting traits as, for instance, the scal-ing of the magnitude of the exchange cou-plings needed to achieve near perfect statetransfer with the length of the chain andthe arrival time. This scaling makes itpossible to decide if the chain with site-dependent coefficients can be implementedin an actual system according to the rangeof interactions allowed in it. We com-pare the robustness of the transmissionprotocol against static disorder on the ex-change coefficients using different figuresof merit, which allow us to conclude thatthe isotropic Heisenberg chain is the bestoption when compared with anisotropicchains. This comparison is relevant sincethe method allow us to start with chainsthat all achieve near perfect quantum statetransfer, regime that was not available previously in these chains without time-dependent external control.