The quantum-statistical model proposed earlier by Skourtis and Nitzan to describe a charge (hole) propagation in a fragment of artificial DNA molecule has been generalized and further investigated. A numerical simulation of a charge transport was carried out taking into account two different dissipative processes, including the capture of the charged carrier by the environment and the decoherence of its quantum wave properties due to the influence of stochastic fields of the environment. The interaction of the carrier with the environment is regulated by a small set of phenomenological parameters whose values vary in the process of simulation. Within this model, the propagation of a hole carrier in DNA is described by solving the quantum Franke-Kossakovski–Lindblad–Glauber–Sudarshan equation (hereinafter referred to as the Lindblad equation) for the carrier density matrix using the Lindblad MPO Solver program. Results of numerical analysis of the model are in a good agreement with experimental observations and demonstrate two different types of the charged carrier motion, presumably tunneling and incoherent hopping. The model is put in more general context and non-unitary dynamics of the hole carrier is treated within the framework of a theory of continuous quantum measurements by the environment in an open quantum system. The main concepts of the theory of decoherence and superselection for open quantum systems and the prospects for their application for further study of various mechanisms of motion of a charged carrier in DNA are briefly discussed.
The quantum-statistical model proposed earlier by Skourtis and Nitzan to describe a charge (hole) propagation in a fragment of artificial DNA molecule has been generalized and further investigated. A numerical simulation of a charge transport was carried out taking into account two different dissipative processes, including the capture of the charged carrier by the environment and the decoherence of its quantum wave properties due to the influence of stochastic fields of the environment. The interaction of the carrier with the environment is regulated by a small set of phenomenological parameters whose values vary in the process of simulation. Within this model, the propagation of a hole carrier in DNA is described by solving the quantum Franke-Kossakovski–Lindblad–Glauber–Sudarshan equation (hereinafter referred to as the Lindblad equation) for the carrier density matrix using the Lindblad MPO Solver program. Results of numerical analysis of the model are in a good agreement with experimental observations and demonstrate two different types of the charged carrier motion, presumably tunneling and incoherent hopping. The model is put in more general context and non-unitary dynamics of the hole carrier is treated within the framework of a theory of continuous quantum measurements by the environment in an open quantum system. The main concepts of the theory of decoherence and superselection for open quantum systems and the prospects for their application for further study of various mechanisms of motion of a charged carrier in DNA are briefly discussed.
The quantum-mechanical model proposed earlier by Skourtis and Nitzan (J. of Chem. Phys. 119, (2003) 6271) to describe a charge transfer in a fragment of artificial DNA molecule has been numerically investigated. The current rationale for the model is carried out and values of its parameters are indicated. Within this model, the description of the transport of a hole carrier in DNA is based on solutions to the time-dependent Schrödinger equation including damping effects. The non-unitary dynamics of the hole carrier is treated by us within the framework of a theory of continuous quantum measurements by the environment in an open quantum system. Results of numerical analysis of the model are in a good agreement with experimental observations and demonstrate two different types of the charged carrier motion, presumably tunneling and incoherent hopping. The main concepts of the theory of decoherence and superselection for open quantum systems and the prospects for their application for further study of various mechanisms of motion of a charged carrier in DNA are briefly discussed.
The influence of quantum tunnelling on double hydrogen transfers within DNA base pairs is investigated by solving the time-dependent Schrodinger equation (TDSE) for a one-dimensional double well potential, whilst accounting for environment coupling. The energies of the canonical (standard, amino-keto) and tautomeric (non-standard, imino-enol) charge-neutral forms of the adenine-thymine base pair (A-T and A*-T*, respectively) are calculated using density functional theory. These compare favourably to results in existing literature. The reaction pathway is also calculated using a transition state search to provide the barrier height and shape, and these are combined to create the potential using a polynomial fit. It is found that tunnelling is very unlikely to be a significant mechanism for the creation of adenine-thymine tautomers within DNA, with the anti-Zeno effect from environment coupling only being able to boost the tunnelling probability at any given time to ~2 x 10-9. This is barely increased when varying several parameters, such as barrier height, potential asymmetry, and mass (kinetic isotope effect). In addition, the general effect on a quantum system by its surrounding environment is explored. A novel comparison between two distinct methods of environment coupling - dissipation (via the addition of a Lindblad term to the master equation) and von Neumann measurements - is performed. This is done using a simpler model of benzoic acid dimer, where it is shown that the two methods describe the same physical process of decoherence and can be thought of as equivalent until the link between them breaks down at high temperatures and measurement frequencies.
Abstract 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 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.
Energy and charge transfer processes, which are central to photosynthesis, catalysis, and molecular electronics, are governed by quantum dynamics in contact with complex environments. Interactions with surrounding degrees of freedom give rise to dissipation, decoherence, and energy exchange, shaping the mechanisms that determine chemical reactivity and transport phenomena. In Part IV of the QFlux tutorial series, we extend our study of quantum dynamics to open quantum systems, where time evolution is intrinsically non-unitary. Using the Lindblad master equation as a unifying and practical framework, we show how environmental effects can be modeled, simulated, and visualized with QFlux , an open-source platform that bridges classical and quantum computation. The tutorial presents the theoretical foundations of open-system dynamics, constructs the Lindblad propagator, and implements representative simulations ranging from spin models to chemically relevant double-well potentials. Special attention is given to dilation methods, which embed non-unitary dynamics within an enlarged unitary space through ancillary qubits, enabling open-system simulations on quantum hardware. This installment provides both conceptual insight and computational methodology for exploring dissipative quantum dynamics, laying the groundwork for subsequent parts addressing variational, non-Markovian approaches.
Abstract Chapter 22 investigates the dynamics of open quantum systems that interact with their environment. We discuss the time-evolution of the joint system in terms of a time-ordered exponential of an integral over the Hamiltonian and determine a similar formulation for a Liouvillian super-operator. Based on these ideas we develop the notion of dynamical maps and apply the Born-Markov approximation to arrive at a dynamical semi-group and general Markovian master equations. We then turn to a specific example of such an equation of motion for the density operator: the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation which captures both dissipative dynamics and decoherence using Lindblad operators. We employ the GKLS equation to model the absorption, and spontaneous as well as stimulated emission of radiation by a two-level atom. We then discuss the Jaynes-Cummings model that describes the interaction of such an atom with a single mode of the electromagnetic field in a cavity
Accurate control of a quantum system is complicated to achieve partly due to the system being coupled to its surrounding environment. The coupling induces dissipation and decoherence not only destroying the coherent quantum state but making the application of control unpredictable. When the control results from manipulation of external fields, it is usually referred to as driving and its joint effect with decoherence constitutes an active field of study in reduced-density-operator theory. Recently, this field has been pushed forward by its necessity in simulating Cooper pair pumping where the geometric nature of quantum evolution allows for controlled transport of charge carriers in superconducting circuits. Such circuits themselves are under constant investigation as they grant access to fundamental quantum phenomena and facilitate promising applications such as those in quantum information processing.\nIn this dissertation, driven quantum systems under decoherence are investigated. Extensions and improvements to a recent master equation for nearly adiabatic driving are presented and analyzed. The emergent properties in quantum evolution are studied both analytically and numerically. Related to the findings, a general conservation law of operator current is derived and used to explain observed nonconservation in previous theoretical studies. The derived theory is applied to Cooper-pair pumping and shown to lead to important properties such as superadiabatic ground-state pumping. A recent pumping experiment is simulated and the breakdown point for ideal pumping is found with feasible physical parameters. A study of charge transport in the presence of flux noise is presented leading to detectable dissipative currents and the typical description of the device used for pumping is extended to include a nonvanishing loop inductance.\nA novel approach to implement control of quantum systems is proposed based on constructing a tunable coupling to an artificial environment using either a coplanar waveguide cavity or coupled quantum LC resonators. Tunability allowing for both efficient initialization and protected evolution is theoretically demonstrated. Finally, a general framework for quantum driving is constructed without the typical assumption of a classical driving force leading to peculiar results.\nThis dissertation presents original research on both modeling the control of open quantum systems as well as the realization of such control. The work simulates physical phenomena in superconducting circuits and makes predictions for future experiments. In addition, it introduces novel theoretical tools and approaches that advance the state of the art.