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Including the effect of the molecular environment in the numerical modeling of time-resolved electronic spectroscopy remains an important challenge in computational spectroscopy. In this contribution, we present a general approach for the simulation of the optical response of multi-chromophore systems in a structured environment and its implementation as a quantum algorithm. A key step of the procedure is the pseudomode embedding of the system-environment problem resulting in a finite set of quantum states evolving according to a Markovian quantum master equation. This formulation is then solved by a collision model integrated into a quantum algorithm designed to simulate linear and nonlinear response functions. The workflow is validated by simulating spectra for the prototypical excitonic dimer interacting with fast (memoryless) and finite-memory environments. The results demonstrate, on the one hand, the potential of the pseudomode embedding for simulating the dynamical features of nonlinear spectroscopy, including lineshape, spectral diffusion, and relaxations along delay times. On the other hand, the explicit synthesis of quantum circuits provides a fully quantum simulation protocol of nonlinear spectroscopy harnessing the efficient quantum simulation of many-body dynamics promised by the future generation of fault-tolerant quantum computers.

Simulating charge and energy transfer in extended molecular networks requires an effective model to include the environment because it significantly affects the quantum dynamics. A prototypical effect known as Environment-Assisted Quantum Transport (ENAQT) consists in the modulation and sometimes enhancement of the transfer efficiency by the interaction with an environment. A simple description of this phenomenon is obtained by a quantum master equation describing a quantum walk over the molecular network in the presence of inter-site decoherence. We consider the problem of simulating the dynamics underlying ENAQT in a digital quantum computer. Two different quantum algorithms are introduced, the first one based on stochastic Hamiltonians and the second one based on a collision scheme. We test both algorithms by simulating ENAQT in a small molecular network on a quantum computer emulator and provide a comparative analysis of the two approaches. Both algorithms 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 increases quadratically. We discuss the algorithmic quantum trajectories generated by the two simulation strategies showing that they realize distinct unravellings of the site-dephasing master equation. In our approach, the non-unitary dynamics of the open system is obtained through effective representations of the environment, paving the way to digital quantum simulations of quantum transport influenced by structured environments.

The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker-Plank-Smoluchowski equation models the time evolution of the probability density of selected degrees of freedom in the diffusive regime and it is therefore a workhorse of physical chemistry. In this paper we report the development and implementation of a Variational Quantum Eigensolver procedure to solve the Fokker-Planck-Smoluchowski eigenvalue problem. We show that such an algorithm, typically adopted to address quantum chemistry problems, can be applied effectively to classical systems paving the way to new applications of quantum computers. We compute the conformational transition rate in a linear chain of rotors experiencing nearest-neighbour interaction. We provide a method to encode on the quantum computer the probability distribution for a given conformation of the chain and assess its scalability in terms of operations. Performance analysis on noisy quantum emulators and quantum devices (IBMQ Santiago) is provided for a small chain showing results in good agreement with the classical benchmark without further addition of any error mitigation technique.