arXiv subjects

K. Birgitta Whaley

Publications and source records attributed to K. Birgitta Whaley.

At least 163 records · Page 9Linked to original sources

arXiv2004

Effect of electron-nuclear spin interactions on electron-spin qubits localized in self-assembled quantum dots

The effect of electron-nuclear spin interactions on qubit operations is investigated for a qubit represented by the spin of an electron localized in a self-assembled quantum dot. The localized electron wave function is evaluated within the atomistic tight-binding model. The magnetic field generated by the nuclear spins is estimated in the presence of an inhomogeneous environment characterized by a random nuclear spin configuration, by the dot-size distribution, by alloy disorder, and by interface disorder. Due to these inhomogeneities, the magnitude of the nuclear magnetic field varies from one qubit to another by the order of 100 G, 100 G, 10 G, and 0.1 G, respectively. The fluctuation of the magnetic field causes errors in exchange operations due to the inequality of the Zeeman splitting between two qubits. We show that the errors can be made lower than the quantum error threshold if an exchange energy larger than 0.1 meV is used for the operation.

quant-ph↗

arXiv2003

Implementing a Quantum Algorithm with Exchange-Coupled Quantum Dots: a Feasibility study

We present Monte Carlo wavefunction simulations for quantum computations employing an exchange-coupled array of quantum dots. Employing a combination of experimentally and theoretically available parameters, we find that gate fidelities greater than 98 % may be obtained with current experimental and technological capabilities. Application to an encoded 3 qubit (nine physical qubits) Deutsch-Josza computation indicates that the algorithmic fidelity is more a question of the total time to implement the gates than of the physical complexity of those gates.

quant-ph↗

arXiv2003

Nanoscale Quantum Solvation of para-H$_2$ around the Linear OCS Molecule inside $^4$He Droplets

We present a microscopic analysis of the quantum solvation structures of para-H$_2$ around the OCS molecule when embedded in low temperature $^4$He droplets. The structures of clusters containing M=5 and 6 para-H$_2$ molecules are compared with corresponding structures for M=1 (OCS-H$_2$ complex) and M=17 (a full solvation shell), as well as with the clusters in the absence of helium. We find that the helium has negligible effect on the structures for the small and large OCS(H$_2$)$_M$ clusters, but that it modifies the cluster structure for M=6. We discuss implications of these results for the onset of superfluidity in the solvating hydrogen shell and for spectroscopic measurements.

cond-mat↗

arXiv2003

Effects of Noisy Oracle on Search Algorithm Complexity

Grover's algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover's search algorithm to a random phase error in the oracle and analyzes the complexity of the search process as a function of the scaling of the oracle error with database or library size. Both the discrete- and continuous-time implementations of the search algorithm are investigated. It is shown that unless the oracle phase error scales as O(N^(-1/4)), neither the discrete- nor the continuous-time implementation of Grover's algorithm is scalably robust to this error in the absence of error correction.

quant-ph↗

arXiv2003

Structure and energetics of helium adsorption on nanosurfaces

The ground and excited state properties of small helium clusters, 4He_N, containing nanoscale (~3-10 Angstroms) planar aromatic molecules have been studied with quantum Monte Carlo methods. Ground state structures and energies are obtained from importance-sampled, rigid-body diffusion Monte Carlo. Excited state energies due to helium vibrational motion are evaluated using the projection operator, imaginary time spectral evolution technique. We examine the adsorption of N helium atoms (N less than or equal to 24) on a series of planar aromatic molecules (benzene, naphthalene, anthracene, tetracene, phthalocyanine). The first layer of helium atoms is well-localized on the molecule surface, and we find well-defined localized excitations due to in-plane vibrational motion of helium on the molecule surface. We discuss the implications of these confined excitations for the molecule spectroscopy.

physics.chem-ph↗

arXiv2003

Transmission Spectrum of an Optical Cavity Containing N Atoms

The transmission spectrum of a high-finesse optical cavity containing an arbitrary number of trapped atoms is presented. We take spatial and motional effects into account and show that in the limit of strong coupling, the important spectral features can be determined for an arbitrary number of atoms, N. We also show that these results have important ramifications in limiting our ability to determine the number of atoms in the cavity.

quant-ph↗

arXiv2003

Optimal quantum circuit synthesis from Controlled-U gates

From a geometric approach, we derive the minimum number of applications needed for an arbitrary Controlled-Unitary gate to construct a universal quantum circuit. A new analytic construction procedure is presented and shown to be either optimal or close to optimal. This result can be extended to improve the efficiency of universal quantum circuit construction from any entangling gate. Specifically, for both the Controlled-NOT and Double-CNOT gates, we develop simple analytic ways to construct universal quantum circuits with three applications, which is the least possible.

quant-ph↗

arXiv2003

Magneto-optical response of CdSe nanostructures

We present theoretical calculations of the Landé g-factors of semiconductor nanostructures using a time-dependent empirical tight-binding method. The eigenenergies and eigenfunctions of the band edge states are calculated as a function of an external magnetic field with the electromagnetic field incorporated into the tight-binding Hamiltonian in a gauge-invariant form. The spin-orbit interaction and magnetic field are treated non-perturbatively. The g-factors are extracted from the energy splitting of the eigenstates induced by the applied magnetic field. Both electron and hole g-factors are investigated for CdSe nanostructures. The size and aspect ratio dependence of g-factors is studied. We observe that the electron g-factors are anisotropic and find that the calculated values agree quantitatively with experimental data. We conclude that the two distinct g-factor values extracted from time resolved Faraday rotation experiments should be assigned to the anisotropic in plane ($g_\parallel$) and out of plane ($g_z$) electron g-factors, rather than to isotropic electron and exciton g-factors. We find that the anisotropy in the electron g-factor depends on the aspect ratio of the nanocrystal. The g-factor anisotropy derived from the wurtzite structure and from the non-unity aspect ratio may cancel each other in some regime. We observe that hole g-factors oscillate as a function of size, due to size dependent mixing between the heavy hole-light hole components of the valence band edge states. Extension to the calculation of exciton g-factors is discussed.

cond-mat↗

arXiv2003

A Simple Model for Magnetization Ratios in Doped Nanocrystals

Recent experiments on Mn-doped ZnS nanocrystals have shown unusual magnetization properties. We describe a nearest-neighbor Heisenberg exchange model for calculating the magnetization ratios of these antiferromagnetically doped crystals, in which the dopant atoms are distributed inhomogeneously within the nanocrystal. This simple inhomogeneous doping model is capable of reproducing the experimental results, and suggests that interior dopant atoms are localized within the crystal.

cond-mat↗

arXiv2003

Tight-binding g-Factor Calculations of CdSe Nanostructures

The Lande g-factors for CdSe quantum dots and rods are investigated within the framework of the semiempirical tight-binding method. We describe methods for treating both the n-doped and neutral nanostructures, and then apply these to a selection of nanocrystals of variable size and shape, focusing on approximately spherical dots and rods of differing aspect ratio. For the negatively charged n-doped systems, we observe that the g-factors for near-spherical CdSe dots are approximately independent of size, but show strong shape dependence as one axis of the quantum dot is extended to form rod-like structures. In particular, there is a discontinuity in the magnitude of g-factor and a transition from anisotropic to isotropic g-factor tensor at aspect ratio ~1.3. For the neutral systems, we analyze the electron g-factor of both the conduction and valence band electrons. We find that the behavior of the electron g-factor in the neutral nanocrystals is generally similar to that in the n-doped case, showing the same strong shape dependence and discontinuity in magnitude and anisotropy. In smaller systems the g-factor value is dependent on the details of the surface model. Comparison with recent measurements of g-factors for CdSe nanocrystals suggests that the shape dependent transition may be responsible for the observations of anomalous numbers of g-factors at certain nanocrystal sizes.

cond-mat↗

arXiv2003

Exact two-qubit universal quantum circuit

We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly simulates arbitrary two-qubit operations in SU(4). Each block in this circuit is given in a closed form solution. We also provide a uniform upper bound of the applications of the given entangling gates, and find that exactly half of all the Controlled-Unitary gates satisfy the same upper bound as the CNOT gate. These results allow for the efficient implementation of operations in SU(4) required for both quantum computation and quantum simulation.

quant-ph↗

arXiv2003

Microscopic two-fluid theory of rotational constants of the OCS-H$_2$ complex in $^4$He droplets

We present a microscopic quantum analysis for rotational constants of the OCS-H$_2$ complex in helium droplets using the local two-fluid theory in conjunction with path integral Monte Carlo simulations. Rotational constants are derived from effective moments of inertia calculated assuming that motion of the H$_2$ molecule and the local non-superfluid helium density is rigidly coupled to the molecular rotation of OCS and employing path integral methods to sample the corresponding H$_2$ and helium densities. The rigid coupling assumption for H$_2$-OCS is calibrated by comparison with exact calculations of the free OCS-H$_2$ complex. The presence of the H$_2$ molecule is found to induce a small local non-superfluid helium density in the second solvation shell which makes a non-negligible contribution to the moment of inertia of the complex in helium. The resulting moments of inertia for the OCS-H$_2$ complex embedded in a cluster of 63 helium atoms are found to be in good agreement with experimentally measured values in large helium droplets. Implications for analysis of rotational constants of larger complexes of OCS with multiple H$_2$ molecules in helium are discussed.

cond-mat↗

arXiv2003

Localized helium excitations in 4He_N-benzene clusters

We compute ground and excited state properties of small helium clusters 4He_N containing a single benzene impurity molecule. Ground-state structures and energies are obtained for N=1,2,3,14 from importance-sampled, rigid-body diffusion Monte Carlo (DMC). Excited state energies due to helium vibrational motion near the molecule surface are evaluated using the projection operator, imaginary time spectral evolution (POITSE) method. We find excitation energies of up to ~23 K above the ground state. These states all possess vibrational character of helium atoms in a highly anisotropic potential due to the aromatic molecule, and can be categorized in terms of localized and collective vibrational modes. These results appear to provide precursors for a transition from localized to collective helium excitations at molecular nanosubstrates of increasing size. We discuss the implications of these results for analysis of anomalous spectral features in recent spectroscopic studies of large aromatic molecules in helium clusters.

physics.chem-ph↗

arXiv2003

Decoherence-Free Subspaces and Subsystems

Decoherence is the phenomenon of non-unitary dynamics that arises as a consequence of coupling between a system and its environment. It has important harmful implications for quantum information processing, and various solutions to the problem have been proposed. Here we provide a detailed a review of the theory of decoherence-free subspaces and subsystems, focusing on their usefulness for preservation of quantum information.

quant-ph↗

arXiv2002

A Quantum Random Walk Search Algorithm

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speed-up over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random walk architecture that provides such a speed-up. It will be shown that this algorithm performs an oracle search on a database of $N$ items with $O(\sqrt{N})$ calls to the oracle, yielding a speed-up similar to other quantum search algorithms. It appears that the quantum random walk formulation has considerable flexibility, presenting interesting opportunities for development of other, possibly novel quantum algorithms.

quant-ph↗

arXiv2002

A geometric theory of non-local two-qubit operations

We study non-local two-qubit operations from a geometric perspective. By applying a Cartan decomposition to su(4), we find that the geometric structure of non-local gates is a 3-Torus. We derive the invariants for local transformations, and connect these local invariants to the coordinates of the 3-Torus. Since different points on the 3-Torus may correspond to the same local equivalence class, we use the Weyl group theory to reduce the symmetry. We show that the local equivalence classes of two-qubit gates are in one-to-one correspondence with the points in a tetrahedron except on the base. We then study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some initially separable states. We provide criteria to determine whether a given two-qubit gate is a perfect entangler and establish a geometric description of perfect entanglers by making use of the tetrahedral representation of non-local gates. We find that exactly half the non-local gates are perfect entanglers. We also investigate the non-local operations generated by a given Hamiltonian. We first study the gates that can be directly generated by a Hamiltonian. Then we explicitly construct a quantum circuit that contains at most three non-local gates generated by a two-body interaction Hamiltonian, together with at most four local gates generated by single qubit terms. We prove that such a quantum circuit can simulate any arbitrary two-qubit gate exactly, and hence it provides an efficient implementation of universal quantum computation and simulation.

quant-ph↗

arXiv2002

Structure and spectroscopy of doped helium clusters using quantum Monte Carlo techniques

We present a comparative study of the rotational characteristics of various molecule-doped 4He clusters using quantum Monte Carlo techniques. The theoretical conclusions obtained from both zero and finite temperature Monte Carlo studies confirm the presence of two different dynamical regimes that correlate with the magnitude of the rotational constant of the molecule, i.e., fast or slow rotors. For a slow rotor, the effective rotational constant for the molecule inside the helium droplet can be determined by a microscopic two-fluid model in which helium densities computed by path integral Monte Carlo are used as input, as well as by direct computation of excited energy levels. For a faster rotor, the conditions for application of the two-fluid model for dynamical analysis are usually not fulfilled and the direct determination of excitation energies is then mandatory. Quantitative studies for three molecules are summarized, showing in each case excellent agreement with experimental results.

physics.atm-clus↗

arXiv2002

The finite-temperature Monte Carlo method and its application to superfluid helium clusters

We review the use of the path integral Monte Carlo (PIMC) methodology to the study of finite-size quantum clusters, with particular emphasis on recent applications to pure and impurity-doped He clusters. We describe the principles of PIMC, the use of the multilevel Metropolis method for sampling particle permutations, and the methods used to accurately incorporate anisotropic molecule-helium interactions into the path integral scheme. Applications to spectroscopic studies of embedded atoms and molecules are summarized, with discussion of the new concepts of local and nanoscale superfluidity that have been generated by recent PIMC studies of the impurity-doped He clusters.

physics.chem-ph↗