Quantum computers can search rapidly by using almost any transformation

A quantum computer has a clear advantage over a classical computer for exhaustive search. The quantum mechanical algorithm for exhaustive search was originally derived by using subtle properties of a particular quantum mechanical operation called the Walsh-Hadamard (W-H) transform. This paper shows that this algorithm can be implemented by replacing the W-H transform by almost any quantum mechanical operation. This leads to several new applications where it improves the number of steps by a square-root. It also broadens the scope for implementation since it demonstrates quantum mechanical algorithms that can readily adapt to available technology.Comment: This paper is an adapted version of quant-ph/9711043. It has been modified to make it more readable for physicists. 9 pages, postscrip

Hilbert Space Average Method and adiabatic quantum search

We discuss some aspects related to the so-called Hilbert space Average Method, as an alternative to describe the dynamics of open quantum systems. First we present a derivation of the method which does not make use of the algebra satisfied by the operators involved in the dynamics, and extend the method to systems subject to a Hamiltonian that changes with time. Next we examine the performance of the adiabatic quantum search algorithm with a particular model for the environment. We relate our results to the criteria discussed in the literature for the validity of the above-mentioned method for similar environments.Comment: 6 pages, 1 figur

Performance of Equal Phase-Shift Search for One Iteration

Grover presented the phase-shift search by replacing the selective inversions by selective phase shifts of $\pi /3$. In this paper, we investigate the phase-shift search with general equal phase shifts. We show that for small uncertainties, the failure probability of the Phase-$\pi /3$ search is smaller than the general phase-shift search and for large uncertainties, the success probability of the large phase-shift search is larger than the Phase-$\pi /3$ search. Therefore, the large phase-shift search is suitable for large-size of databases.Comment: 10 pages, 4 figure

Stress Concentrations: Their Effect on Design for Repeated Loading

Changes of section, such as fillets, grooves, oil holes, keyways, and the like, are necessary in many machine parts. These are sources of stress concentration when a part is under load, Stress concentrations may also occur near bolts, pins, rivets, spot welds, and other discrete fasteners in joints of structural members. Flaws, inclu-sions, and other discontinuities in a metal may also interrupt the stress pattern under load. The general term "stress raiser" has been coined to describe any such irregularity or inhomogeneity which produces it local concentration of stress in a loaded part

Equivalent qubit dynamics under classical and quantum noise

We study the dynamics of quantum systems under classical and quantum noise, focusing on decoherence in qubit systems. Classical noise is described by a random process leading to a stochastic temporal evolution of a closed quantum system, whereas quantum noise originates from the coupling of the microscopic quantum system to its macroscopic environment. We derive deterministic master equations describing the average evolution of the quantum system under classical continuous-time Markovian noise and two sets of master equations under quantum noise. Strikingly, these three equations of motion are shown to be equivalent in the case of classical random telegraph noise and proper quantum environments. Hence fully quantum-mechanical models within the Born approximation can be mapped to a quantum system under classical noise. Furthermore, we apply the derived equations together with pulse optimization techniques to achieve high-fidelity one-qubit operations under random telegraph noise, and hence fight decoherence in these systems of great practical interest.Comment: 5 pages, 2 figures; converted to PRA format, added Fig. 2, corrected typo

Anisotropic dehydration of hydrogel surfaces

Efforts to develop tissue-engineered skin for regenerative medicine have explored natural, synthetic, and hybrid hydrogels. The creation of a bilayer material, with the stratification exhibited by native skin is a complex problem. The mechanically robust, waterproof epidermis presents the stratum corneum at the tissue/air interface, which confers many of these protective properties. In this work we explore the effect of high temperatures on alginate hydrogels, which are widely employed for tissue engineering due to their excellent mechanical properties and cellular compatibility. In particular, we investigate the rapid dehydration of the hydrogel surface which occurs following local exposure to heated surfaces with temperatures in the range 100-200 oC. We report the creation of a mechanically strengthened hydrogel surface, with improved puncture resistance and increased coefficient of friction, compared to the unheated surface. The use of a mechanical restraint during heating promoted differences in the rate of mass loss; the rate of temperature increase within the hydrogel, in the presence and absence of restraint, is simulated and discussed. It is hoped that the results will be of use in the development of processes suitable for preparing skin-like analogues; application areas could include wound healing and skin restoration

Grover's Quantum Search Algorithm and Diophantine Approximation

In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, M<K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using only iterations of Grover's basic step (and no other algorithm). Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m < (2N^{1/2})/(K^{1/2}-M^{1/2}) obtains. This bound sharpens previous results and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.Comment: 8 pages, revtex, Title change

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

Self-magnetic compensation and Exchange Bias in ferromagnetic Samarium systems

For Sm(3+) ions in a vast majority of metallic systems, the following interesting scenario has been conjured up for long, namely, a magnetic lattice of tiny self (spin-orbital) compensated 4f-moments exchange coupled (and phase reversed) to the polarization in the conduction band. We report here the identification of a self-compensation behavior in a variety of ferromagnetic Sm intermetallics via the fingerprint of a shift in the magnetic hysteresis (M-H) loop from the origin. Such an attribute, designated as exchange bias in the context of ferromagnetic/antiferromagnetic multilayers, accords these compounds a potential for niche applications in spintronics. We also present results on magnetic compensation behavior on small Gd doping (2.5 atomic percent) in one of the Sm ferromagnets (viz. SmCu(4)Pd). The doped system responds like a pseudo-ferrimagnet and it displays a characteristic left-shifted linear M-H plot for an antiferromagnet.Comment: 7 pages and 7 figure