  Quantum state transfer (QST) through spin chains has been extensively
investigated. Two schemes, the coupling set for perfect state transfer (PST) or
adding a leakage elimination operator (LEO) Hamiltonian have been proposed to
boost the transmission fidelity. However, these ideal schemes are only suitable
for closed systems and will lose their effectiveness in open ones. In this
work, we invoke a well explored optimization algorithm, Adam, to expand the
applicable range of PST couplings and LEO to the open systems. Our results show
that although the transmission fidelity decreases with increasing system-bath
coupling strength, Markovianity and temperature for both ideal and optimized
cases, the fidelities obtained by the optimized schemes always outweigh the
ideal cases. The enhancement becomes more bigger for a stronger bath,
indicating a stronger bath provides more space for the Adam to optimize. This
method will be useful for the realization of high-fidelity information transfer
in the presence of environment.
