Quantum Computers, Factoring, and Decoherence

In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large numbers -- a problem of great practical significance because of its cryptographic applications. Instead of the nearly exponential ($\sim \exp L^{1/3}$, for a number with $L$ digits) time required by the fastest classical algorithm, the quantum algorithm gives factors in a time polynomial in $L$ ($\sim L^2$). This enormous speed-up is possible in principle because quantum computation can simultaneously follow all of the paths corresponding to the distinct classical inputs, obtaining the solution as a result of coherent quantum interference between the alternatives. Hence, a quantum computer is sophisticated interference device, and it is essential for its quantum state to remain coherent in the course of the operation. In this report we investigate the effect of decoherence on the quantum factorization algorithm and establish an upper bound on a ``quantum factorizable'' $L$ based on the decoherence suffered per operational step.Comment: 7 pages,LaTex + 2 postcript figures in a uuencoded fil

Divergent nematic susceptibility in an iron arsenide superconductor

Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition is often a more subtle matter due to coupling between otherwise distinct order parameters. In this paper we show how measurement of the divergent nematic susceptibility of an iron pnictide superconductor unambiguously distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also reveal an electronic nematic quantum phase transition at the composition with optimal superconducting transition temperature.Comment: 8 pages, 8 figure

Cryogenic-coolant He4-superconductor dynamic and static interactions

A composite superconducting material (NbTi-Cu) was evaluated with emphasis on post quench solid cooling interaction regimes. The quasi-steady runs confirm the existence of a thermodynamic limiting thickness for insulating coatings. Two distinctly different post quench regimes of coated composites are shown to relate to the limiting thickness. Only one regime,, from quench onset to the peak value, revealed favorable coolant states, in particular in He2. Transient recovery shows favorable recovery times from this post quench regime (not drastically different from bare conductors) for both single coated specimens and a coated conductor bundle

Unusual electronic ground state of a prototype cuprate: band splitting of single CuO_2-plane Bi_2 Sr_(2-x) La_x CuO_(6+delta)

By in-situ change of polarization a small splitting of the Zhang-Rice singlet state band near the Fermi level has been resolved for optimum doped (x=0.4) Bi$_{2}$Sr$_{2-x}$La$_{x}$CuO$_{6+\delta}$ at the (pi,0)-point (R.Manzke et al. PRB 63, R100504 (2001). Here we treat the momentum dependence and lineshape of the split band by photoemission in the EDC-mode with very high angular and energy resolution. The splitting into two destinct emissions could also be observed over a large portion of the major symmetry line $\Gamma$M, giving the dispersion for the individual contributions. Since bi-layer effects can not be present in this single-layer material the results have to be discussed in the context of one-particle removal spectral functions derived from current theoretical models. The most prominent are microscopic phase separation including striped phase formation, coexisting antiferromagnetic and incommensurate charge-density-wave critical fluctuations coupled to electrons (hot spots) or even spin charge separation within the Luttinger liquid picture, all leading to non-Fermi liquid like behavior in the normal state and having severe consequences on the way the superconducting state forms. Especially the possibilty of observing spinon and holon excitations is discussed.Comment: 5 pages, 4 figure

Two Qubits in the Dirac Representation

A general two qubit system expressed in terms of the complete set of unit and fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features of this system. The well-known physical interpretations associated with the relativistic Dirac equation involving the symmetry operations of time-reversal T, charge conjugation C, parity P, and their products are reinterpreted here by examining their action on the basic Bell states. The transformation properties of the Bell basis states under these symmetry operations also reveal that C is the only operator that does not mix the Bell states whereas all others do. In a similar fashion, expressing the various logic gates introduced in the subject of quantum computers in terms of the Dirac matrices shows for example, that the NOT gate is related to the product of time-reversal and parity operators.Comment: 11 page

Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance

Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm to find the low-lying spectrum of a Hamiltonian. While the number of elementary quantum gates does scale polynomially with the size of the system, it increases inversely to the desired error bound $\epsilon$. Making such simulations robust to decoherence using fault-tolerance constructs requires an additional factor of $1/ \epsilon$ gates. These constraints are illustrated by using a three qubit nuclear magnetic resonance system to simulate a pairing Hamiltonian, following the algorithm proposed by Wu, Byrd, and Lidar.Comment: 6 pages, 2 eps figure

Complete quantum teleportation using nuclear magnetic resonance

Quantum mechanics provides spectacular new information processing abilities (Bennett 1995, Preskill 1998). One of the most unexpected is a procedure called quantum teleportation (Bennett et al 1993) that allows the quantum state of a system to be transported from one location to another, without moving through the intervening space. Partial implementations of teleportation (Bouwmeester et al 1997, Boschi et al 1998) over macroscopic distances have been achieved using optical systems, but omit the final stage of the teleportation procedure. Here we report an experimental implementation of the full quantum teleportation operation over inter-atomic distances using liquid state nuclear magnetic resonance (NMR). The inclusion of the final stage enables for the first time a teleportation implementation which may be used as a subroutine in larger quantum computations, or for quantum communication. Our experiment also demonstrates the use of quantum process tomography, a procedure to completely characterize the dynamics of a quantum system. Finally, we demonstrate a controlled exploitation of decoherence as a tool to assist in the performance of an experiment.Comment: 15 pages, 2 figures. Minor differences between this and the published versio

Weak Bond Screening System

The most commonly used nondestructive inspection (NDI) technique for adhesively bonded and composite structures is the ultrasonic C-scan technique operating in a pulse-echo or through-transmission mode. They are most effective in detecting disbonds, voids, delamination and foreign inslusions, but are ineffective for the detection of weak bonds at the adhesive points. Weak bonds are mostly caused by improper surface cleaning of substrates. There is no air space at the adhesive joints where the substrate and the adhesive are in intimate contact with each other. This results in a lack of interface for ultrasound reflection required for their detection by conventional ultrasonic NDI techniques. Other ultrasonic techniques such as ultrasonic spectroscopy and ultrasonic resonance testers also suffer from the same disadvantage

THE RESPONSE OF WHOLE BODY VIBRATION ON TAI CHI AND WEIGHT-LIFTING ATHLETES

Whole body vibration (WBV) is a new technique which may improve leg muscle strength. Many researchers have studied the effect of whole body vibration recently. But study of effects of vibration stimulus to different activity type athletes, such as Tai Chi (N=12) and Weight-lifting (N=15) athletes is lacking. In this study we examine that question. The subjects were asked to stand in a half-squat posture without additional load on a vibration platform with 7 vibration frequencies (5, 9, 12, 16, 20, 24, 30 Hz) at 4 mm amplitude and maintained for 30 seconds. The effect of WBV would be different on different sport subjects’ perceived exertion. We discovered that the subject’s perception may be related with the acceleration of the subject’s head. Using whole body vibration training to improve muscle power and strength depends on the particular sport’s training emphasis to setup the appropriate training protocol such as amplitude and frequency