Discovery of energy landscapes towards optimized quantum transport: Environmental effects and long-range tunneling

Carrier transport in quantum networks is governed by a variety of factors, including network dimensionality and connectivity, on-site energies, couplings between sites and whether they are short- or long-range, and environmental effects. In this work, we identify classes of quasi-one-dimensional chains with energy profiles that optimize carrier transport under such influences. Specifically, we optimize on-site energies using Optax's optimistic gradient descent and AdaMax algorithms, enabled by the JAX automatic differentiation framework. Focusing on steady-state transport, we study the system's behavior under combined unitary and nonunitary (dephasing and dissipative) effects using the Lindblad quantum master equation. After validating our optimization scheme on short chains, we extend the study to larger systems where we identify systematic patterns in energy profiles. Our analysis reveals that different types of energy landscape enhance transport, depending on whether inter-site tunneling couplings in the chain are short- or long-range, the existence of environmental interactions, and the temperature of the environment. Our classification and insights of optimal energy landscapes offer guidance for designing efficient transport systems for electronic, photovoltaic and quantum communication applications.