Quantum computing resources have been known to provide speed-ups in computational complexity in many algorithms. The impact of these resources in communication, however, has not attracted much attention. We investigate the impact of quantum entanglement on communication complexity. We provide a positive result, by presenting a class of multi-party communication problems wherein the presence of a suitable quantum entanglement lowers the classical communication complexity. We show that, in evaluating certains function whose parameters are distributed among various parties, the presence of prior entanglement can help in reducing the required communication. We also present an outline of realizing the required entanglement through optical photon quantum computing. We also suggest the possible impact of our results on network information flow problems, by showing an instance of a lower bound which can be broken by adding limited power to the communication model.

First-principles electronic structure theory explains properties of atoms, molecules and solids from underlying physical principles without input from empirical parameters. Time-dependent density functional theory (TDDFT) has emerged as arguably the most widely used first-principles method for describing the time-dependent quantum mechanics of many-electron systems. In this thesis, we will show how the fundamental principles of TDDFT can be extended and applied in two novel directions: The theory of open quantum systems (OQS) and quantum computation (QC). In the first part of this thesis, we prove theorems that establish the foundations of TDDFT for open quantum systems (OQS-TDDFT). OQS-TDDFT allows for a first principles description of non-equilibrium systems, in which the electronic degrees of freedom undergo relaxation and decoherence due to coupling with a thermal environment, such as a vibrational or photon bath. We then discuss properties of functionals in OQS-TDDFT and investigate how these differ from functionals in conventional TDDFT using an exactly solvable model system. Next, we formulate OQS-TDDFT in the linear-response regime, which gives access to environmentally broadened excitation spectra. Lastly, we present a hybrid approach in which TDDFT can be used to construct master equations from first-principles for describing energy transfer in condensed phase systems. In the second part of this thesis, we prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. TDDFT applied to universal Hamiltonians implies that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. This offers the possibility of simplifying computations by using the principles of TDDFT similar to how it is applied in electronic structure theory. Lastly, we discuss a related result; the computational complexity of TDDFT. / Physics

Josh Folk explains how the traditional rules of physics don't make sense at the quantum-mechanical level - and how those discrepancies can be turned into opportunities.

ESR quantum computing presents faster means to perform gates on nuclear spins than the traditional NMR methods. This means ESR is a test-bed that can potentially be useful in ways that are not possible with NMR. The first step is to demonstrate universal control in the ESR system. This work focuses on spin systems with one electron spin and two nuclear spins. We try to demonstrate control over the nuclear spins using the electron as an actuator. In order to perform the experiments, a customized ESR spectrometer was built in the lab. The main advantage of the home-built system is the ability to send arbitrary pulses to the spins. This ability is the key to perform high fidelity controls on the spin system. A customized low temperature probe was designed and built to have three features necessary for the experiments. First, it is possible to orient the sample, thus to change the spin Hamiltonian of the system, in situ. Second, the combined system is able to perform ESR experiments at liquid nitrogen and liquid helium temperatures and rotate the sample while it is cold. Last, the pulse bandwidth of the microwave resonator, which directly affects the fidelity of the gates, is held constant with respect to the sample temperature. Simulations of the experiments have been carried out and the results are promising. Preliminary experiments have been performed, the final set of experiments, demonstrating full quantum control of a three-spin system, are underway at present.

Thesis (MTech (Electrical Engineering))--Cape Peninsula University of Technology, 2018. / In this research, we undertake a numerical study of the interaction between laser beams and two as well as multi-level atoms. The main aim of this research is to obtain a deeper understanding of laser-atom interactions and non-linear processes such as optical four-wave mixing. This work will supplement experiments to be conducted by other members of the group, who are involved in generating entangled photons via four-wave mixing in cold rubidium atoms. We begin by performing a basic study of the interaction between laser beams and two-level atoms as an aid to gain knowledge of numerical techniques, as well as an understanding of the physics behind light-atom interactions. We make use of a semi-classical approach to describe the system where the atoms are treated quantum mechanically and the laser beams are treated classically. We study the interaction between atoms and laser beams using the density matrix operator and Maxwell's equations respectively. By solving the optical Bloch equations for two-level atoms we examine the atomic populations and coherences and present plots of the density matrix elements as a function of time. The e ects of various parameters such as laser intensity, detuning and laser modulation have been tested. The behaviour of the laser beam as it propagates through the atomic sample is also studied. This is determined by Maxwell's equation where the atomic polarization is estimated from the coherence terms of the density matrix elements. / French South African Institute of Technology National Research Foundation

An investigation of the electronic structure of some transition metal clusters comprising anti-ferromagnetically coupled, heterometallic arrays of eight metal ions that are wheel-shaped, is reported. The compounds were synthesized and provided by Dr. Grigore Timco of The University of Manchester and are formulated by their metal content as Cr7M, where M = a divalent 3d metal. Two families of wheels are the subject of this research, defined ‘green’ and ‘purple’ from their physical appearance. Within each family, the compounds are all isostructural. From simulation using a single Hamiltonian for Cr7M-purple compounds, where M = Zn, Mn, or Ni, it is shown that with only two exchange parameters, one JCr-Cr and one JCr-M, data from bulk magnetization, neutron scattering, Electron Paramagnetic Resonance (EPR) spectroscopy at multiple frequencies and specific heat measurements can be modelled and that there is transferability of parameters. Preliminary attempts to measure electron spin relaxation times for two of the purple wheels have shown values of T1 and T2 that are comparable with those of the more extensively studied green wheels and hence further studies in this area are warranted. Variable temperature Q- and W-band EPR spectra for a series of nine heterodimers comprising one green and one purple wheel, M=Zn, Mn or Ni in each case, are reported. For Cr7Zn-purple there is no magnetic exchange detected, whereas weak and quantifiable exchange is required to interpret the spectra from the other six dimers. EPR studies of three trimers of the form purple-green-purple are reported and the presence of magnetic exchange is identified by comparison with the spectra of the component single and double wheel compounds, although this is not quantified because of the numerical size of the simulations that are required. The process of comparing simulated to experimental spectra is a complex problem and one which is central to the work reported in this thesis. The problem of fitting has been investigated and two novel solutions, one based upon pixel mapping and the other based on wavelet transformation are proposed.

An adversary armed with a quantum computer has algorithms[66, 33, 34] at their disposal, which are capable of breaking our current methods of encryption. Even with the birth of post-quantum cryptography[52, 62, 61], some of best cryptanalytic algorithms are still quantum [45, 8]. This thesis contains several experiments on the efficacy of lattice reduction algorithms, BKZ and LLL. In particular, the difficulty of solving Learning With Errors is assessed by reducing the problem to an instance of the Unique Shortest Vector Problem. The results are used to predict the behavior these algorithms may have on actual cryptographic schemes with security based on hard lattice problems. Lattice reduction algorithms require several floating-point operations including multiplication. In this thesis, I consider the resource requirements of a quantum circuit designed to simulate floating-point multiplication with high precision. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2020. / FAU Electronic Theses and Dissertations Collection

This project was motivated by the following question: what information do the properties of a random graph contain about the performance of a quantum search acting on it? To investigate this problem, we define a notion of search time to quantify the behavior of a quantum search, and find strong evidence of a relation between its distribution and the model of random graph on which the search was performed. Surprisingly, we also find strong evidence that the return time of a classical random walk initialized at the marked vertex is closely related to its search time, and that the distribution of degrees over the graph vertices may play a significant role in this relation. / Mathematics

In this dissertation we discuss decoherence in charge qubits formed by multiple lateral quantum dots in the framework of the spin-boson model and the Born-Markov approximation. We consider the intrinsic decoherence caused by the coupling to bulk phonon modes and electromagnetic environmental fluctuations. In the case of decoherence caused by phonon coupling, two distinct quantum dot configurations are studied and proposed as setups that mitigate its nocive effects : (i) Three quantum dots in a ring geometry with one excess electron in total and (ii) arrays of quantum dots where the computational basis states form multipole charge configurations. For the three-dot qubit, we demonstrate the possibility of performing one- and two-qubit operations by solely tuning gate voltages. Compared to a previous proposal involving a linear three-dot spin qubit, the three-dot charge qubit allows for less overhead on two-qubit operations. For small interdot tunnel amplitudes, the three-dot qubits have Q factors much higher than those obtained for double-dot systems. The high-multipole dot configurations also show a substantial decrease in decoherence at low operation frequencies when compared to the double-dot qubit. We also discuss decoherence due to electromagnetic fluctuations in charge qubits formed by two lateral quantum dots. We use effective circuit models to evaluate correlations of voltage fluctuations in the qubit setup. These correlations allows us to estimate energy (T1) and phase (T2) relaxation times of the the qubit system. We also discuss the dependence the quality factor Q shows with respect to parameters of the setup, such as temperature and capacitive coupling between the electrodes.

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