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

Effects of Private Insurance on Forest Landowners' Incentives to Sequester and Trade Carbon under Uncertainty: Impact of Hurricanes

We evaluate incentives of forest landowners for sequestering and trading carbon, given the risk of carbon loss from hurricanes, and an opportunity to insure their losses. Results of simulation model reveal that the effect of hurricane risk depends on the variability of returns from carbon and timber and landowners' ability to mitigate risk by diversifying forest holdings across regions or transferring risk by purchasing insurance.Carbon Sequestration, Emissions Trading, Natural Disaster, Risk, Insurance, Risk and Uncertainty, Q54, Q58,

Water balance complexities in ephemeral catchments with different land uses: Insights from monitoring and distributed hydrologic modeling

Although ephemeral catchments are widespread in arid and semiarid climates, the relationship of their water balance with climate, geology, topography, and land cover is poorly known. Here we use 4 years (2011–2014) of rainfall, streamflow, and groundwater level measurements to estimate the water balance components in two adjacent ephemeral catchments in south-eastern Australia, with one catchment planted with young eucalypts and the other dedicated to grazing pasture. To corroborate the interpretation of the observations, the physically based hydrological model CATHY was calibrated and validated against the data in the two catchments. The estimated water balances showed that despite a significant decline in groundwater level and greater evapotranspiration in the eucalypt catchment (104–119% of rainfall) compared with the pasture catchment (95–104% of rainfall), streamflow consistently accounted for 1–4% of rainfall in both catchments for the entire study period. Streamflow in the two catchments was mostly driven by the rainfall regime, particularly rainfall frequency (i.e., the number of rain days per year), while the downslope orientation of the plantation furrows also promoted runoff. With minimum calibration, the model was able to adequately reproduce the periods of flow in both catchments in all years. Although streamflow and groundwater levels were better reproduced in the pasture than in the plantation, model-computed water balance terms confirmed the estimates from the observations in both catchments. Overall, the interplay of climate, topography, and geology seems to overshadow the effect of land use in the study catchments, indicating that the management of ephemeral catchments remains highly challenging

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

Nested quantum search and NP-complete problems

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown here that an improved quantum search algorithm can be devised that exploits the structure of a tree search problem by nesting this standard search algorithm. The number of iterations required to find the solution of an average instance of a constraint satisfaction problem scales as $\sqrt{d^\alpha}$, with a constant $\alpha<1$ depending on the nesting depth and the problem considered. When applying a single nesting level to a problem with constraints of size 2 such as the graph coloring problem, this constant $\alpha$ is estimated to be around 0.62 for average instances of maximum difficulty. This corresponds to a square-root speedup over a classical nested search algorithm, of which our presented algorithm is the quantum counterpart.Comment: 18 pages RevTeX, 3 Postscript figure

Implementation of quantum search algorithm using classical Fourier optics

We report on an experiment on Grover's quantum search algorithm showing that {\em classical waves} can search a $N$-item database as efficiently as quantum mechanics can. The transverse beam profile of a short laser pulse is processed iteratively as the pulse bounces back and forth between two mirrors. We directly observe the sought item being found in $\sim\sqrt{N}$ iterations, in the form of a growing intensity peak on this profile. Although the lack of quantum entanglement limits the {\em size} of our database, our results show that entanglement is neither necessary for the algorithm itself, nor for its efficiency.Comment: 4 pages, 3 figures; minor revisions plus extra referenc

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

Extending scientific computing system with structural quantum programming capabilities

We present a basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantum-octave, providing a library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate high-level programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for high-level quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantum-octave package. This is possible thanks to the ability to operate on density matrices

Ultrahigh Transmission Optical Nanofibers

We present a procedure for reproducibly fabricating ultrahigh transmission optical nanofibers (530 nm diameter and 84 mm stretch) with single-mode transmissions of 99.95 $\pm$ 0.02%, which represents a loss from tapering of 2.6 $\,\times \,$ 10$^{-5}$ dB/mm when normalized to the entire stretch. When controllably launching the next family of higher-order modes on a fiber with 195 mm stretch, we achieve a transmission of 97.8 $\pm$ 2.8%, which has a loss from tapering of 5.0 $\,\times \,$ 10$^{-4}$ dB/mm when normalized to the entire stretch. Our pulling and transfer procedures allow us to fabricate optical nanofibers that transmit more than 400 mW in high vacuum conditions. These results, published as parameters in our previous work, present an improvement of two orders of magnitude less loss for the fundamental mode and an increase in transmission of more than 300% for higher-order modes, when following the protocols detailed in this paper. We extract from the transmission during the pull, the only reported spectrogram of a fundamental mode launch that does not include excitation to asymmetric modes; in stark contrast to a pull in which our cleaning protocol is not followed. These results depend critically on the pre-pull cleanliness and when properly following our pulling protocols are in excellent agreement with simulations.Comment: 32 pages, 10 figures, accepted to AIP Advance