MODELS AND QUANTUM ALGORITHMS FOR OPEN SYSTEM DYNAMICS: THE CASE STUDY OF EXCITON TRANSPORT IN MOLECULAR NETWORKS

As physical systems of chemical interest are rarely isolated, molecular processes should always be intended within the framework of open system dynamics. Notable examples are charge and energy transfer in molecular networks, for which intense theoretical and experimental research has highlighted the central role of the interplay between the system Hamiltonian and decoherences due to the interaction with the environment. At intermediate system-environment interaction strengths, the cooperation between coherent and incoherent dynamics can result in a prototypical effect called environment-assisted quantum transport (ENAQT), which consists of the enhancement of transport efficiency. ENAQT is believed to play a primary part in the high efficiency of natural light-harvesting complexes. A comprehensive understanding and powerful simulation strategies for these dynamical phenomena could help us, for example, in the design of artificial devices, based on the engineering of materials and their environment, for high-performance cells for photovoltaic applications. However, the simulation of open quantum systems poses the theoretical challenge of devising an adequate equation of motion for the dynamics and a computational strategy for its solution, which becomes prohibitively difficult for classical computers when handling large quantum systems. Thanks to the theoretical and experimental scientific advances of the last decades, we are now at the dawn of the so-called second quantum revolution that promises novel technological tools based on harnessing quantum coherence. Quantum computers, i.e., physical systems manipulated at the quantum level with high precision, are concrete examples. In recent years, quantum computers have already demonstrated they can tackle some complex problems considered intractable by classical computers: the so-called quantum advantage. The simulation of quantum systems has always been a strong motivation behind the development of quantum computers, as they are expected to provide advantages in dealing with large systems based on their huge computational space. However, despite its importance, the simulation of open system dynamics has received relatively little attention. One of the reasons is the non-trivial challenge of reproducing the evolution of open quantum systems in the framework of quantum circuits. In this thesis, we approach the study of open system dynamics by drawing two parallel paths. On the one hand, we intend to explore in detail some salient features of quantum transport in molecular networks. To do so, we will critically analyse existing models for open system dynamics, ranging from Markovian to non-Markovian regime, from weak to strong coupling and from infinite to finite temperature. On the other hand, we consider the problem of simulating the dynamics underlying ENAQT with digital quantum computers. An algorithmic package is developed to implement the dynamics in different conditions. The algorithms are designed with two different strategies, the first one based on stochastic Hamiltonians and the second one based on a collision model. We demonstrate the potentiality of our algorithms by simulating ENAQT on a quantum computer emulator and provide a comparative analysis of the two approaches. Both algorithmic strategies can be implemented in a memory-efficient encoding with the number of required qubits scaling logarithmically with the size of the simulated system, while the number of gates scales polynomially depending on the target environmental conditions. We discuss the algorithmic quantum trajectories generated during the execution of the algorithms showing that they realize distinct unravellings of the dynamics of the open system.