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We examine the impact of the intrinsic molecular reorganization energy on switching in two-state quantum-dot cellular automata (QCA) cells. Switching a bit involves an electron transferring between charge centers within the molecule. This in turn causes the other atoms in the molecule to rearrange their positions in response. We capture this in a model that treats the electron motion quantum-mechanically, but the motion of nuclei semiclassically. This results in a non-linear Hamiltonian for the electron system. Interaction with a thermal environment is included by solving the Lindblad equation for the time-dependent density matrix. The calculated response of a molecule to the local electric field shows hysteresis during switching when the sweep direction is reversed. The relaxation of neighboring nuclei increases localization of the electron, which provides an intrinsic source of enhanced bistability and single-molecule memory. This comes at the cost of increased power dissipation., Comment: 14 pages, 17 figures

We examine the energy dissipated by a two-state quantum system during a switching operation when interacting with a thermal environment. For an isolated system, the excess energy decreases exponentially with switching time. For classically damped systems, the energy dissipation decreases linearly with switching time. We model the quantum system coupled to a thermal environment using a Lindblad equation for the density matrix. For rapid switching, the exponential quantum adiabaticity holds. For slow enough switching, the damping from the bath yields linear dissipation, as in the classical limit. Between these two limits, when the switching time is comparable to the characteristic energy transfer time to the thermal bath, there is an inverted region when dissipation increases with longer switching times. Consequences for the design of molecular quantum-dot cellular automata are discussed.

For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum operator entropy, which is the Shannon entropy of the probability distribution for the eigenvalues of a Hermitian operator. These entropies characterize the missing information about a particular observable inherent in the quantum state itself. The von Neumann entropy is the quantum operator entropy for the case when the operator is the density matrix. We examine pure state unitary evolution in a simple model system comprised of a set of highly-interconnected topologically disordered states and a time-independent Hamiltonian. An initially confined state is subject to free expansion into available states. The time development is completely reversible with no loss of quantum information and no course graining is applied. The positional entropy increases in time in a way that is consistent with both the classical statistical mechanical entropy and the second law., Comment: 10 pages, 10 figures

Mixed-valence complexes are potential candidates for the molecular quantum-dot cellular automata (QCA) approach, which encodes binary information using the configuration of localized and mobile charges. In the Robin–Day classification of mixed-valence complexes, charge localization/delocalization is determined by the ratio of the nuclear reorganization energy and the electron transfer (ET) matrix element. We point out that the driving force for charge localization in molecular QCA is the Coulomb interaction between neighboring molecules rather than nuclear relaxation. This suggests a different criterion for the relevant charge localization, one based on the ET matrix element and the driving bias of a neighboring molecule.

We study quantum entanglement loss due to environmental interaction in a condensed matter system with a complex geometry relevant to recent proposals for computing with single electrons at the nanoscale. We consider a system consisting of two qubits, each realized by an electron in a double quantum dot, which are initially in an entangled Bell state. The qubits are widely separated and each interacts with its own environment. The environment for each is modeled by surrounding double quantum dots placed at random positions with random orientations. We calculate the unitary evolution of the joint system and environment. The global state remains pure throughout. We examine the time dependence of the expectation value of the bipartite Clauser-Horne-Shimony-Holt (CHSH) and Brukner-Paunkovi\'c-Rudolph-Vedral (BPRV) Bell operators and explore the emergence of correlations consistent with local realism. Though the details of this transition depend on the specific environmental geometry, we show how the results can be mapped on to a universal behavior with appropriate scaling. We determine the relevant disentanglement times based on realistic physical parameters for molecular double-dots., Comment: 14 pages, 3 figures

Quantum-dot cellular automata (QCA) is a low-power, non-von-Neumann, general- purpose paradigm for classical computing using transistor-free logic. Here, classical bits are encoded on the charge configuration of individual computing primitives known as &ldquo, cells.&rdquo, A cell is a system of quantum dots with a few mobile charges. Device switching occurs through quantum mechanical inter-dot charge tunneling, and devices are interconnected via the electrostatic field. QCA devices are implemented using arrays of QCA cells. A molecular implementation of QCA may support THz-scale clocking or better at room temperature. Molecular QCA may be clocked using an applied electric field, known as a clocking field. A time-varying clocking field may be established using an array of conductors. The clocking field determines the flow of data and calculations. Various arrangements of clocking conductors are laid out, and the resulting electric field is simulated. It is shown that that control of molecular QCA can enable feedback loops, memories, planar circuit crossings, and versatile circuit grids that support feedback and memory, as well as data flow in any of the ordinal grid directions. Logic, interconnect and memory now become indistinguishable, and the von Neumann bottleneck is avoided.

In the molecular quantum-dot cellular automata (QCA) paradigm clocking wires are used to produce an electric field which is perpendicular to the device plane of surface-bound molecules and is sinusoidally modulated in space and time. This clocking field guides the data flow through the molecular QCA array. Power is dissipated in clocking wires due to the non-zero resistance of the conductors. We analyze quantitatively the amount of power dissipated in the clocking wires and find that in the relevant parameter range it is fairly small. Dissipation in the molecular devices themselves will likely dominate the energy budget.

The computational paradigm known as quantum-dot cellular automata (QCA) encodes binary information in the charge configuration of Coulomb-coupled quantum-dot cells. Functioning QCA devices made of metal-dot cells have been fabricated and measured. We focus here on the issue of robustness in the presence of disorder and thermal fluctuations. We examine the performance of a semi-infinite QCA shift register as a function of both clock period and temperature. The existence of power gain in QCA cells acts to restore signal levels even in situations where high speed operation and high temperature operation threaten signal stability. Random variations in capacitance values can also be tolerated.

Quantum-dot cellular automata (QCA) is an approach to computing that eliminates the need for current switches by representing binary information as the configuration of charge among quantum dots. For molecular QCA, redox sites of molecules serve as the quantum dots. The Coulomb interaction between neighboring molecules provides device-device coupling. By introducing clocked control of the QCA cell, power gain, reduced power dissipation, and computational pipelining can be achieved. We present an ab initio analysis of a simple molecular system, which acts as a clocked molecular QCA cell. The intrinsic bistability of the molecular charge configuration results in dipole or quadrupole fields that couple strongly to the state of neighboring molecules. We show how clocked control of the molecular QCA can be accomplished with a local electric field.

The Nano-Devices Group at the University of Notre Dame proposed a new device that encodes information in the geometrical charge distribution of artificial (or natural) molecules. Functional units are composed by electrostatic coupling. In these units, processing takes place by reshaping the electron density of the molecules, and not by switching currents. Signal processing potential of next-neighbor-coupled cellular nonlinear networks (CNNs) has been recently explored with the conclusion that local-activity of the cells is necessary to exhibit complexity. It will be shown that Coulomb-coupled time-invariant artificial molecules behave like nonlinear locally passive devices, thus signal-power-gain or multiple equilibria cannot be achieved by integrating them. However, the signal input-output relation of strongly nonlinear molecules can be varied in time by adiabatic pumping, called clock control. It will be shown that strongly nonlinear time-varying molecules can transform the necessary amount of clock energy into the signal flow, thereby enabling the network of molecules to perform signal processing.

An introduction to the operation of quantum-dot cellular automata (QCA) is presented, along with recent experimental results. QCA is a transistorless computation paradigm that addresses the issues of device density and interconnection. The basic building blocks of the QCA architecture, such as AND, OR, and NOT are presented. The experimental device is a four-dot QCA cell with two electrometers. The dots are metal islands, which are coupled by capacitors and tunnel junctions. An improved design of the cell is presented in which all four dots of the cell are coupled by tunnel junctions. A noninvasive electrometer is presented which improves the sensitivity and linearity of dot potential measurements. The operation of this basic cell is confirmed by an externally controlled polarization change of the cell.

We present experimental demonstration of a basic cell of Quantum-dot Cellular Automata, a transistorless computation paradigm which addresses the issues of device density and interconnection. The devices presented consist of four and six-dot quantum-dot cellular systems where the metal dots are connected by capacitors and tunnel junctions. The operation of a basic cell is confirmed by the externally controlled polarization change of the cell. The cell exhibits a bistable response and voltage gain. We present an experimental technique which cancels the parasitic cross-talk capacitors in the system.

Scanning tunnelling microscopy reveals that molecules of ferrocenecarboxylic acid can self-assemble into quasicrystal monolayers containing highly unusual cyclic hydrogen-bonded pentamers; this molecular framework could form the basis of a large range of supramolecular assemblies. The range of systems in which non-periodic quasicrystalline ordering has been observed continues to increase, with small-molecule self-assembled monolayers now entering the arena. Specifically, Natalie Wasio and colleagues find that the hydrogen-bonding patterns of ferrocenecarboxylic acid drive the assembly of these molecules into unusual cyclic pentamers, whose five-fold symmetry facilitates a two-dimensional quasicrystalline arrangement. The authors anticipate that a large range of novel quasicrystalline supramolecular assemblies could be formed based on this molecular framework. The process of molecular self-assembly on solid surfaces is essentially one of crystallization in two dimensions, and the structures that result depend on the interplay between intermolecular forces and the interaction between adsorbates and the underlying substrate1. Because a single hydrogen bond typically has an energy between 15 and 35 kilojoules per mole, hydrogen bonding can be a strong driver of molecular assembly; this is apparent from the dominant role of hydrogen bonding in nucleic-acid base pairing, as well as in the secondary structure of proteins. Carboxylic acid functional groups, which provide two hydrogen bonds, are particularly promising and reliable in creating and maintaining surface order, and self-assembled monolayers of benzoic acids produce structure that depends on the number and relative placement of carboxylic acid groups2,3,4,5,6. Here we use scanning tunnelling microscopy to study self-assembled monolayers of ferrocenecarboxylic acid (FcCOOH), and find that, rather than producing dimeric or linear structures typical of carboxylic acids, FcCOOH forms highly unusual cyclic hydrogen-bonded pentamers, which combine with simultaneously formed FcCOOH dimers to form two-dimensional quasicrystallites that exhibit local five-fold symmetry and maintain translational and rotational order (without periodicity) for distances of more than 400 angstroms.

Several practical issues in the development and operation of quantum-dot cellular automata (QCA) cells and systems are discussed. The need for adiabatic clocking of QCA systems and modeling of electrostatic confinement of quantum dots are presented. Experimental data on dot coupling and applications to QCA detectors in a 2-dimensional electron gas (2DEG) are presented. We report a charge detection scheme where we observe strong modulation in the detector signal, in addition to the detector exhibiting minimal effect on the dot being measured. With this investigation, we demonstrate these two key components required for QCA in AlGaAs/GaAs materials, namely dot coupling and charge-state detection.

Recent experiments in transport through a ballistic constriction with a periodical corrugation on one wall to modulate the width [1] have revealed miniband structure in the presence of a magnetic field. We have previously explored the properties of edge states in a similar structure[2]. Here we present our calculation of bandstructure and edge states on a 1D channel having an array of antidots placed along its central axis. Our interest is to examine the allowed states in such a channel and, by direct calculating the particle current density, to visualize the current flow via magnetic edge states as well as localized Landau states.

We study local potential variations due to self-consistent space-charge effects in calculations of coherent transport in narrow split-gate structures. We present a numerical technique based on calculating the Hartree potential from the charge density obtained by solving the two-dimensional effective-mass Schrodinger equation for scattering states, and from the bound charge density obtained from a semi-classical Thomas-Fermi screening model. This method allows us to obtain the local self-consistent potential variations close to scattering centers exposed to an incident flux of electrons.

A functioning logic gate based on quantum-dot cellular automata is presented, where digital data are encoded in the positions of only two electrons. The logic gate consists of a cell, composed of four dots connected in a ring by tunnel junctions, and two single-dot electrometers. The device is operated by applying inputs to the gates of the cell. The logic AND and OR operations are verified using the electrometer outputs. Theoretical simulations of the logic gate output characteristics are in excellent agreement with experiment.

Quantum-dot Cellular Automata (QCA) may offer a viable alternative of traditional transistor-based technology at the nanoscale. When modeling a QCA circuit, the number of degrees of freedom necessary to describe the quantum mechanical state increases exponentially making modeling even modest size cell arrays difficult. The intercellular Hartree approximation largely reduces the number of state variables and still gives good results especially when the system remains near ground state. This suggests that large part of the correlation degrees of freedom are not essential from the point of view of the dynamics. In certain cases, however, such as for example the majority gate with unequal input legs, the Hartree approximation gives qualitatively wrong results. An intermediate model is constructed between the Hartree approximation and the exact model, based on the coherence vector formalism. By including correlation effects to a desired degree, it improves the results of the Hartree method and gives the approximate dynamics of the correlation terms. It also models the majority gate correctly. Beside QCA cell arrays, our findings are valid for Ising spin chains in transverse magnetic field, and can be straightforwardly generalized for coupled two-level systems with a more complicated Hamiltonian., 45 pre-print style double-spaced pages including 8 figures, accepted for Journal of Applied Physics

The electrostatic interaction between two capacitively-coupled metal double-dots is studied at low temperatures. Experiments show that when the Coulomb blockade is lifted by applying appropriate gate biases to both double-dots, the conductance through each double-dot becomes significantly lower than when only one double-dot is conducting. A master equation is derived for the system and the results obtained agree well with the experimental data. The model suggests that the conductance lowering in each double-dot is caused by a single-electron tunneling in the other double-dot. Here, each double-dot responds to the instantaneous, rather than average, potentials on the other double-dot. This leads to correlated electron motion within the system, where the position of a single electron in one double-dot controls the tunneling rate through the other double-dot., 19 pages [pre-print style], 8 figures, accepted for Phys. Rev. B

The five papers in this special section cover a wide spectrum of techniques which are encountered in nano-scale computing systems. Briefly summarizes the articles included in this section.