Topological quantum computing has largely evolved toward a paradigm of manipulating edge-localized Majorana within p-wave topological superconducting nanowires. To bridge the gap between physical qubit systems and quantum algorithms, we perform a dynamical analysis to extend what is known in the adiabatic regime, providing time-dependent gate elements for further qubit and algorithm modeling efforts. Our analysis covers dynamical considerations for two methods of shuttling domain edge bound Majoranas in a single nanowire system, which both function by applying spatiotemporally dependent onsite and hopping parameters within the system’s Hamiltonian. We then complicate this model by converting it into the T-qubit to calculate the finite-time gate representation of the shuttling techniques used in a more practical setting. These contributions provide insight into realistic experimental setups in the next-generation of qubit implementation and will hopefully facilitate fault tolerant scalable systems and universal gate design.

The current state of Quantum computing (QC) is extremely optimistic, and we are at a point where researchers have produced highly sophisticated quantum algorithms to address far reaching problems. However, it is equally apparent that the noisy quantum environment is a larger threat than many may realize. The noisy intermediate scale quantum era can be viewed as an inflection point for the enterprise of QC where decoherence could stagnate progress if left unaddressed. One tactic for handling decoherence is to address the problem from a hardware level by implementing topological materials into the design. In this work, we model several Josephson junctions that are modified by the presence of topological superconducting nanowires in between the host superconductors. Our primary result is a numerical calculation of the energy-phase relationship for topological nanowire junctions which is a key parameter of interest for the dynamics of qubit circuits. In addition to this, we report on the qualitative physical behavior of the bound states as a function of superconducting phase. These results can be used to further develop and inform the construction of more complicated systems, and it is hopeful that these types of designs could manifest as a fault tolerant qubit.

A semiclassical model based on the Gryzinski theory is used to compute vibrationally resolved electron-impact ionization cross sections for molecular nitrogen. This model extends the approach used by Wünderlich for molecular hydrogen and its isotopomeres. The multireference configuration interaction (MRCI) method in Molpro is used with complete active space self-consistent field reference wave functions to compute potential energy curves (PECs) and electronic wave functions for several states of interest. Nuclear wave functions and vibrational energy levels are computed from the MRCI PECs using the Fourier grid Hamiltonian method. The target orbital electron kinetic energies, Franck-Condon factors, and transition energies are parameters for the semiclassical model and are calculated directly from the computed electronic and nuclear wave functions and vibrational energy levels. The target electron kinetic energies are computed as the expectation value of the one-electron kinetic energy operator for the product of the appropriate nuclear vibrational wave function and the MRCI natural orbital for a particular state-to-state ionization process. From the fully vibrationally resolved ionization cross sections, lumped and total cross sections are calculated by summing the partial cross sections over the closure relationship of the Franck-Condon theory.

Cross sections for electron impact dissociative excitation and ionization in scattering on vibrationally excited levels of the ground electronic state of H_{3}^{+} and its isotopologues are reported in the energy range of 8 to 1000 eV. Calculations have been performed using a newly developed version of the molecular convergent close-coupling code. Cross sections for total dissociative excitation, ionization yielding atomic fragments such as D^{+}, and the total inelastic cross section are presented. Good agreement with available experiments has been demonstrated.

Cross sections for electron impact dissociative excitation and ionization in scattering on vibrationally excited levels of the ground electronic state of H3+, D3+, and T3+ are reported in the energy range of 8-1000 eV. Calculations have been performed using a newly developed version of the molecular convergent close-coupling code. Convergence of the cross sections with the size of the projectile partial-wave and close-coupling expansions is examined. Branching ratios and cross sections for the yields of D2+ and D+ from dissociative excitation of D3+ are presented and isotope effects are investigated. Cross sections for total dissociative ionization yielding atomic fragments such as D+ are presented and the total inelastic cross section is produced. Good agreement with available experiments has been demonstrated.

One of the greatest challenges when designing new technologies that make use of non-trivial quantum materials is the difficulty associated with predicting material-specific properties, such as critical temperature, gap parameter, etc. There is naturally a great amount of interest in these types of condensed matter systems because of their application to quantum sensing, quantum electronics, and quantum computation; however, they are exceedingly difficult to address from first principles because of the famous many-body problem. For this reason, a full electron-nuclear quantum calculation will likely remain completely out of reach for the foreseeable future. A practical alternative is provided by finite temperature, multi component density functional theory, which is a formally exact method of computing the equilibrium state energy of a many-body quantum system. In this work, we use this construction alongside a perturbative scheme to demonstrate that the phenomena Peierls effect and Kohn anomaly are both natural features of the Kohn-Sham (KS) equations without additional structure needed. We find the temperature dependent ionic density for a simple 1D lattice which is then used to derive the ionic densities temperature dependent affect on the electronic band structure. This is accomplished by Fourier transforming the ionic density term found within this KS electronic equation. Using the Peierls effect phonon distortion gap openings in relation to the Fermi level, we then perturb the KS ionic equation with a conduction electron density, deriving the Kohn anomaly. This provides a workable predictive strategy for interesting electro-phonon related material properties which could be extended to 2D and 3D real materials while retaining the otherwise complicated temperature dependence.

Among the list of major threats to quantum computation, quantum decoherence poses one of the largest because it generates losses to the environment within a computational system which cannot be recovered via error correction methods. These methods require the assumption that the environmental interaction forces the qubit state into some linear combination of qubit eigenstates. In reality, the environment causes the qubit to enter into a mixed state where the original is no longer recoverable. A promising solution to this problem bases the computational states on the low lying energy excitations within topological materials. The existence of these states is protected by a global parameter within the Hamiltonian which prevents the computational states from coupling locally and decohering. In this paper, the qubit is based on nonlocal, topological Majorana fermions (MF), and the gate operations are generated by swapping or braiding the positions of said MF. The algorithmic calculation for such gate operations is well known, but, the opposite gates-to-braid calculation is currently underdeveloped. Additionally, because one may choose from a number of different possible qubit definitions, the resultant gate operations from calculation to calculation appear different. Here, the calculations for the two- and four-MF cases are recapitulated for the sake of logical flow. This set of gates serves as the foundation for the understanding and construction of the six-MF cases. Using these, a full characterization of the system is made by completely generalizing the list of gates and transformations between possible qubit definitions. A complete description of this system is desirable and will hopefully serve future iterations of topological qubits.

We fabricate nanolayer alumina capacitor and apply high electric fields, close to 1 GV m −1 , to inject charges in the dielectric. Asymmetric charge distributions have been achieved due to the selectivity of the quantum tunneling process. Namely, the electrons near the Fermi level cannot tunnel intoregions near the cathode, where the total energy would be less than the potential energy. This mechanism exhibits a strong tendency to populate charge traps located near the anode, i.e. the regions where their potential energy is the lowest. Such spatially selective charging of the dielectric allows a permanent bulk charge storage in the dielectric layer, even if the capacitor plates are short-circuited, provided that the temperature is sufficiently low so that the conductivity of the dielectric is negligible. The stored charge can be recovered if the temperature is increased above ~250 K for the dielectric tested, i.e. Al 2 O 3 . In our experiments, the total charge stored in the dielectric was up to seven and a half times higher than the charge stored on the capacitor plates. Also, measurements of the breakdown voltage show that the breakdown electric field, i.e. the dielectric strength, is independent of the thickness of the dielectric.

Sandstone mechanical stability is of key concern in projects involving injections of CO2 in sandstone geological reservoirs, for the purpose of long-term storage. We developed a method to measure nanometer-scale deformations of sandstones in real time. We demonstrate that Berea sandstone, when hydrated, changes dimensions with a relative deformation of the order of 10^(-4). If the moisture content increases, sandstone samples exhibit an extension and if the moisture content decreases then the samples shrink. We also discover that, immediately after exposure to water, the sandstone temporarily shrinks, just for a few seconds, after which a slow extension begins, and continues until about half of the fluid evaporates. Such shrinkage followed by an extension has been observed also when the sample was exposed to acetone, Mineral Spirits or Vacuum Oil. The results are obtained using a high-resolution nano-positioner technique and, in independent experiments, confirmed using the technique of coda wave interferometry.

We study one-dimensional chains of superconducting islands with a particular emphasis on the regime in which every second island is switched into its normal state, thus forming a superconductor-insulator-normal metal (S-I-N) repetition pattern. As is known since Giaever tunneling experiments, tunneling charge transport between a superconductor and a normal metal becomes exponentially suppressed, and zero-bias resistance diverges, as the temperature is reduced and the energy gap of the superconductor grows larger than the thermal energy. Here we demonstrate that this physical phenomenon strongly impacts transport properties of inhomogeneous superconductors made of weakly coupled islands with fluctuating values of the critical temperature. We observe a nonmonotonous dependence of the chain resistance on both temperature and magnetic field, with a pronounced resistance peak at temperatures at which some but not all islands are superconducting. We explain this phenomenon by the inhomogeneity of the chains, in which neighboring superconducting islands have slightly different critical temperatures. We argue that the Giaever's resistance divergence can also occur in the zero-temperature limit. Such quantum transition can occur if the magnetic field is tuned such that it suppresses superconductivity in the islands with the weaker critical field, while the islands with stronger energy gap remain superconducting. In such a field, the system acts as a chain of S-I-N junctions.

The development of approximate exchange-correlation functionals is critical for modern density functional theory. A recent analysis of atomic systems suggested that some modern functionals are straying from the path toward the exact functional because electron densities are becoming less accurate while energies are becoming more accurate since the year 2000. To investigate this trend for more chemically relevant systems, the electron densities in the bonding regions and the atomization energies are analyzed for a series of diatomic molecules with 90 different functionals. For hybrid generalized gradient approximation functionals developed since the year 2000, the errors in densities and atomization energies are decoupled; the accuracy of the energies remains relatively consistent while the accuracy of the densities varies significantly. Such decoupling is not observed for generalized gradient and meta-generalized gradient approximation functionals. Analysis of electron densities in bonding regions is found to be important for the evaluation of functionals for chemical systems.

Multicomponent density functional theory (DFT) enables the consistent quantum mechanical treatment of both electrons and protons. A major challenge has been the design of electron-proton correlation (epc) functionals that produce even qualitatively accurate proton densities. Herein an electron-proton correlation functional, epc17, is derived analogously to the Colle-Salvetti formalism for electron correlation and is implemented within the nuclear-electronic orbital (NEO) framework. The NEO-DFT/epc17 method produces accurate proton densities efficiently and is promising for diverse applications.

Although the binding of a positron to a neutral atom has not been directly observed experimentally, high-level theoretical methods have predicted that a positron will bind to a neutral atom. In the present study, the binding" energies of a positron to lithium, sodium, beryllium, and magnesium, as well as the electron positron annihilation rates for these systems, are calculated using the reduced explicitly correlated Hartree-Fock (RXCHF) method within the nuclear-electronic orbital (NEO) framework. Due to the lack of explicit electron-positron correlation, NEO Hartree-Fock and full configuration interaction calculations with reasonable electronic and positronic basis sets do not predict positron binding to any of these atoms. In contrast, the RXCHF calculations predict positron binding energies and electron-positron annihilation rates in qualitative agreement with previous highly accurate but computationally expensive stochastic variational method calculations. These results illustrate that the RXCHF method can successfully describe the binding of a positron to a neutral species with no dipole moment. Moreover, the RXCHF method will be computationally tractable for calculating positron binding to molecular systems. The RXCHF approach offers a balance of accuracy and computational tractability for studying these types of positronic systems.

Electric capacitors are commonly used in electronic circuits for the short-term storage of small amounts of energy. It is desirable however to use capacitors to store much larger energy amounts to replace rechargeable batteries. Unfortunately existing capacitors cannot store sufficient energy to be able to replace common electrochemical energy storage systems. Here we examine the energy storage capabilities of graphene nanocapacitors, which are tri-layer devices involving an Al film, Al2O3 dielectric layer, and a single layer of carbon atoms, i.e., graphene. This is a purely electronic capacitor and therefore it can function in a wide temperature interval. The capacitor shows a high dielectric breakdown electric field strength, of the order of 1000 kV mm(-1) (i.e., 1GVm(-1)), which is much larger than the table value of the Al2O3 dielectric strength. The corresponding energy density is 10-100 times larger than the energy density of a common electrolytic capacitor. Moreover, we discover that the amount of charge stored in the dielectric layer can be equal or can even exceed the amount of charge stored on the capacitor plates. The dielectric discharge current follows a power-law time dependence. We suggest a model to explain this behavior.

Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF(-) molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.

The nuclear electronic orbital (NEO) reduced explicitly correlated Hartree-Fock (RXCHF) approach couples select electronic orbitals to the nuclear orbital via Gaussian-type geminal functions. This approach is extended to enable the use of a restricted basis set for the explicitly correlated electronic orbitals and an open-shell treatment for the other electronic orbitals. The working equations are derived and the implementation is discussed for both extensions. The RXCHF method with a restricted basis set is applied to HCN and FHF− and is shown to agree quantitatively with results from RXCHF calculations with a full basis set. The number of many-particle integrals that must be calculated for these two molecules is reduced by over an order of magnitude with essentially no loss in accuracy, and the reduction factor will increase substantially for larger systems. Typically, the computational cost of RXCHF calculations with restricted basis sets will scale in terms of the number of basis functions centered on the quantum nucleus and the covalently bonded neighbor(s). In addition, the RXCHF method with an odd number of electrons that are not explicitly correlated to the nuclear orbital is implemented using a restricted open-shell formalism for these electrons. This method is applied to HCN+, and the nuclear densities are in qualitative agreement with grid-based calculations. Future work will focus on the significance of nonadiabatic effects in molecular systems and the further enhancement of the NEO-RXCHF approach to accurately describe such effects.

The nuclear-electronic orbital (NEO) approach treats select nuclei quantum mechanically on the same level as the electrons and includes nonadiabatic effects between the electrons and the quantum nuclei. The practical implementation of this approach is challenging due to the significance of electron-nucleus dynamical correlation. Herein, we present a general extension of the previously developed reduced NEO explicitly correlated Hartree-Fock (RXCHF) approach, in which only select electronic orbitals are explicitly correlated to each quantum nuclear orbital via Gaussian-type geminal functions. Approximations of the electronic exchange between the geminal-coupled electronic orbitals and the other electronic orbitals are also explored. This general approach enables computationally tractable yet accurate calculations on molecular systems with quantum protons. The RXCHF method is applied to the hydrogen cyanide (HCN) and FHF(-) systems, where the proton and all electrons are treated quantum mechanically. For the HCN system, only the two electronic orbitals associated with the CH covalent bond are geminal-coupled to the proton orbital. For the FHF(-) system, only the four electronic orbitals associated with the two FH covalent bonds are geminal-coupled to the proton orbital. For both systems, the RXCHF method produces qualitatively accurate nuclear densities, in contrast to mean field-based NEO approaches. The development and implementation of the RXCHF method provide the framework to perform calculations on systems such as proton-coupled electron transfer reactions, where electron-proton nonadiabatic effects are important.

The nuclear-electronic orbital (NEO) method treats electrons and select nuclei quantum mechanically on the same level to extend beyond the Born-Oppenheimer approximation. Electron-nucleus dynamical correlation has been found to be highly significant due to the attractive Coulomb interaction. The explicitly correlated Hartree-Fock (NEO-XCHF) approach includes explicit electron-nucleus correlation with Gaussian-type geminal functions during the variational optimization of the nuclear-electronic wavefunction. Although accurate for small model systems, the NEO-XCHF method is computationally impractical for larger chemical systems. In this paper, we develop the reduced explicitly correlated Hartree-Fock approach, denoted NEO-RXCHF, where only select electronic orbitals are explicitly correlated to the nuclear orbitals. By explicitly correlating only the relevant electronic orbitals to the nuclear orbitals, the NEO-RXCHF approach avoids problems that can arise when all electronic orbitals are explicitly correlated to the nuclear orbitals in the same manner. We examine three different NEO-RXCHF methods that differ in the treatment of the exchange between the geminal-coupled electronic orbitals and the other electronic orbitals: NEO-RXCHF-fe is fully antisymmetric with respect to exchange of all electronic coordinates and includes all electronic exchange terms; NEO-RXCHF-ne neglects the exchange between the geminal-coupled electronic orbitals and the other electronic orbitals; and NEO-RXCHF-ae includes approximate exchange terms between the geminal-coupled electronic orbitals and the other electronic orbitals. The latter two NEO-RXCHF methods offer substantial computational savings over the NEO-XCHF approach. The NEO-RXCHF approach is applicable to a wide range of chemical systems that exhibit non-Born-Oppenheimer effects between electrons and nuclei, as well as positron-containing molecular systems.