Measurement induced quantum walks on an IBM Quantum Computer

We study a quantum walk of a single particle that is subject to stroboscopic projective measurements on a graph with two sites. This two-level system is the minimal model of a measurement induced quantum walk. The mean first detected transition and return time are computed on an IBM quantum computer as a function of the hopping matrix element between the sites and the on-site potential. The experimentally monitored quantum walk reveals the theoretically predicted behavior, such as the quantization of the first detected return time and the strong increase of the mean first detected transition time near degenerate points, with high accuracy

Non-Equilibrium Dynamics of a Dissipative Two-Site Hubbard Model Simulated on the IBM Quantum Computer

Many-body physics is one very well suited field for testing quantum algorithms and for finding working heuristics on present quantum computers. We have investigated the non-equilibrium dynamics of one- and two-electron systems, which are coupled to an environment that introduces decoherence and dissipation. In our approach, the electronic system is represented in the framework of a two-site Hubbard model while the environment is modelled by a spin bath. In order to simulate the non-equilibrium population probabilities of the different states on the quantum computer we have encoded the electronic states and environmental degrees of freedom into qubits and ancilla qubits (bath), respectively. The total evolution time was divided into short time intervals, during which the system evolves. After each of these time steps, the system interacts with ancilla qubits representing the bath in thermal equilibrium. We have specifically studied spin baths leading to both, unital and non-unital dynamics of the electronic system and have found that electron correlations clearly enhance the electron transfer rates in the latter case. For short time periods, the simulation on the quantum computer is found to be in good qualitative agreement with the exact results. We also show that slight improvements are already possible with various error mitigation techniques while even significant improvements can be achieved by using the recently implemented single-qubit reset operations. Our method can be well extended to simulate electronic systems in correlated spin baths as well as in bosonic and fermionic baths

Multiple-charge transfer and trapping in DNA dimers

We investigate the charge transfer characteristics of one and two excess charges in a DNA base-pair dimer using a model Hamiltonian approach. The electron part comprises diagonal and off-diagonal Coulomb matrix elements such a correlated hopping and the bond-bond interaction, which were recently calculated by Starikov [E. B. Starikov, Phil. Mag. Lett. {\bf 83}, 699 (2003)] for different DNA dimers. The electronic degrees of freedom are coupled to an ohmic or a super-ohmic bath serving as dissipative environment. We employ the numerical renormalization group method in the nuclear tunneling regime and compare the results to Marcus theory for the thermal activation regime. For realistic parameters, the rate that at least one charge is transferred from the donor to the acceptor in the subspace of two excess electrons significantly exceeds the rate in the single charge sector. Moreover, the dynamics is strongly influenced by the Coulomb matrix elements. We find sequential and pair transfer as well as a regime where both charges remain self-trapped. The transfer rate reaches its maximum when the difference of the on-site and inter-site Coulomb matrix element is equal to the reorganization energy which is the case in a GC-GC dimer. Charge transfer is completely suppressed for two excess electrons in AT-AT in an ohmic bath and replaced by damped coherent electron-pair oscillations in a super-ohmic bath. A finite bond-bond interaction $W$ alters the transfer rate: it increases as function of $W$ when the effective Coulomb repulsion exceeds the reorganization energy (inverted regime) and decreases for smaller Coulomb repulsion

Anisotropic Superexchange for nearest and next nearest coppers in chain, ladder and lamellar cuprates

We present a detailed calculation of the magnetic couplings between nearest-neighbor and next-nearest-neighbor coppers in the edge-sharing geometry, ubiquitous in many cuprates. In this geometry, the interaction between nearest neighbor coppers is mediated via two oxygens, and the Cu-O-Cu angle is close to 90 degrees. The derivation is based on a perturbation expansion of a general Hubbard Hamiltonian, and produces numerical estimates for the various magnetic energies. In particular we find the dependence of the anisotropy energies on the angular deviation away from the 90 degrees geometry of the Cu-O-Cu bonds. Our results are required for the correct analysis of the magnetic structure of various chain, ladder and lamellar cuprates.Comment: 13 pages, Latex, 7 figure

Functional modules by relating protein interaction networks and gene expression

Genes and proteins are organized on the basis of their particular mutual relations or according to their interactions in cellular and genetic networks. These include metabolic or signaling pathways and protein interaction, regulatory or co-expression networks. Integrating the information from the different types of networks may lead to the notion of a functional network and functional modules. To find these modules, we propose a new technique which is based on collective, multi-body correlations in a genetic network. We calculated the correlation strength of a group of genes (e.g. in the co-expression network) which were identified as members of a module in a different network (e.g. in the protein interaction network) and estimated the probability that this correlation strength was found by chance. Groups of genes with a significant correlation strength in different networks have a high probability that they perform the same function. Here, we propose evaluating the multi-body correlations by applying the superparamagnetic approach. We compare our method to the presently applied mean Pearson correlations and show that our method is more sensitive in revealing functional relationships

Dissipative exciton transfer in donor–bridge–acceptor systems: numerical renormalization group calculation of equilibrium properties

We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.Comment: 10 pages, 12 figure

Dissipative two-electron transfer: a numerical renormalization group study

We investigate non-equilibrium two-electron transfer in a model redox system represented by a two-site extended Hubbard model and embedded in a dissipative environment. The influence of the electron-electron interactions and the coupling to a dissipative bosonic bath on the electron transfer is studied in different temperature regimes. At high temperatures Marcus transfer rates are evaluated and at low temperatures, we calculate equilibrium and non-equilibrium population probabilities of the donor and acceptor with the non-perturbative Numerical Renormalization Group approach. We obtain the non-equilibrium dynamics of the system prepared in an initial state of two electrons at the donor site and identify conditions under which the electron transfer involves one concerted two-electron step or two sequential single-electron steps. The rates of the sequential transfer depend non-monotonically on the difference between the inter-site and on-site Coulomb interaction which become renormalized in the presence of the bosonic bath. If this difference is much larger than the hopping matrix element, the temperature as well as the reorganization energy, simultaneous transfer of both electrons between donor and acceptor can be observed