Hamiltonian and measuring time for analog quantum search

We derive in this study a Hamiltonian to solve with certainty the analog quantum search problem analogue to the Grover algorithm. The general form of the initial state is considered. Since the evaluation of the measuring time for finding the marked state by probability of unity is crucially important in the problem, especially when the Bohr frequency is high, we then give the exact formula as a function of all given parameters for the measuring time.Comment: 5 page

Measuring Energy, Estimating Hamiltonians, and the Time-Energy Uncertainty Relation

Suppose that the Hamiltonian acting on a quantum system is unknown and one wants to determine what is the Hamiltonian. We show that in general this requires a time $\Delta t$ which obeys the uncertainty relation $\Delta t \Delta H \gtrsim 1$ where $\Delta H$ is a measure of how accurately the unknown Hamiltonian must be estimated. We then apply this result to the problem of measuring the energy of an unknown quantum state. It has been previously shown that if the Hamiltonian is known, then the energy can in principle be measured in an arbitrarily short time. On the other hand we show that if the Hamiltonian is not known then an energy measurement necessarily takes a minimum time $\Delta t$ which obeys the uncertainty relation $\Delta t \Delta E \gtrsim 1$ where $\Delta E$ is the precision of the energy measurement. Several examples are studied to address the question of whether it is possible to saturate these uncertainty relations. Their interpretation is discussed in detail.Comment: 12pages, revised version with small correction

Preparing ground states of quantum many-body systems on a quantum computer

Preparing the ground state of a system of interacting classical particles is an NP-hard problem. Thus, there is in general no better algorithm to solve this problem than exhaustively going through all N configurations of the system to determine the one with lowest energy, requiring a running time proportional to N. A quantum computer, if it could be built, could solve this problem in time sqrt(N). Here, we present a powerful extension of this result to the case of interacting quantum particles, demonstrating that a quantum computer can prepare the ground state of a quantum system as efficiently as it does for classical systems.Comment: 7 pages, 1 figur

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.Comment: 13 pages, 3 figure

A Hybrid Quantum Encoding Algorithm of Vector Quantization for Image Compression

Many classical encoding algorithms of Vector Quantization (VQ) of image compression that can obtain global optimal solution have computational complexity O(N). A pure quantum VQ encoding algorithm with probability of success near 100% has been proposed, that performs operations 45sqrt(N) times approximately. In this paper, a hybrid quantum VQ encoding algorithm between classical method and quantum algorithm is presented. The number of its operations is less than sqrt(N) for most images, and it is more efficient than the pure quantum algorithm. Key Words: Vector Quantization, Grover's Algorithm, Image Compression, Quantum AlgorithmComment: Modify on June 21. 10pages, 3 figure

Quantum Algorithm for Molecular Properties and Geometry Optimization

It is known that quantum computers, if available, would allow an exponential decrease in the computational cost of quantum simulations. We extend this result to show that the computation of molecular properties (energy derivatives) could also be sped up using quantum computers. We provide a quantum algorithm for the numerical evaluation of molecular properties, whose time cost is a constant multiple of the time needed to compute the molecular energy, regardless of the size of the system. Molecular properties computed with the proposed approach could also be used for the optimization of molecular geometries or other properties. For that purpose, we discuss the benefits of quantum techniques for Newton's method and Householder methods. Finally, global minima for the proposed optimizations can be found using the quantum basin hopper algorithm, which offers an additional quadratic reduction in cost over classical multi-start techniques.Comment: 6 page

New Samarium and Neodymium based admixed ferromagnets with near zero net magnetization and tunable exchange bias field

Rare earth based intermetallics, SmScGe and NdScGe, are shown to exhibit near zero net magnetization with substitutions of 6 to 9 atomic percent of Nd and 25 atomic percent of Gd, respectively. The notion of magnetic compensation in them is also elucidated by the crossover of zero magnetization axis at low magnetic fields (less than 103 Oe) and field-induced reversal in the orientation of the magnetic moments of the dissimilar rare earth ions at higher magnetic fields. These magnetically ordered materials with no net magnetization and appreciable conduction electron polarization display an attribute of an exchange bias field, which can be tuned. The attractively high magnetic ordering temperatures of about 270 K, underscore the importance of these materials for potential applications in spintronics.Comment: 6 page text + 5 figure

Effectiveness of BaTiO3 dielectric patches on YBa2Cu3O7 thin films for MEM switches

A micro-electro-mechanical (MEM) switch built on a superconducting microstrip filter will be utilized to investigate BaTiO3 dielectric patches for functional switching points of contact. Actuation voltage resulting from the MEM switch provokes static friction between the bridge membrane and BaTiO3 insulation layer. The dielectric patch crystal structure and roughness affect the ability of repetitively switching cycles and lifetime. A series of experiments have been performed using different deposition methods and RF magnetron sputtering was found to be the best deposition process for the BaTiO3 layer. The effect examination of surface morphology will be presented using characterization techniques as x-ray diffraction, SEM and AFM for an optimum switching device. The thin film is made of YBa2Cu3O7 deposited on LaAlO3 substrate by pulsed laser deposition. For this work, the dielectric material sputtering pressure is set at 9.5x10-6 Torr. The argon gas is released through a mass-flow controller to purge the system prior to deposition. RF power is 85 W at a distance of 9 cm. The behavior of Au membranes built on ultimate BaTiO3 patches will be shown as part of the results. These novel surface patterns will in turn be used in modelling other RF MEM switch devices such as distributed-satellite communication system operating at cryogenic temperatures

Quantum Search with Two-atom Collisions in Cavity QED

We propose a scheme to implement two-qubit Grover's quantum search algorithm using Cavity Quantum Electrodynamics. Circular Rydberg atoms are used as quantum bits (qubits). They interact with the electromagnetic field of a non-resonant cavity . The quantum gate dynamics is provided by a cavity-assisted collision, robust against decoherence processes. We present the detailed procedure and analyze the experimental feasibility.Comment: 4 pages, 2 figure