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Daniel Koch

Publications and source records attributed to Daniel Koch.

28 records · Page 2Linked to original sources
arXiv2019

Introduction to Coding Quantum Algorithms: A Tutorial Series Using Pyquil

As the field of Quantum Computing continues to grow, so too has the general public's interest in testing some of the publicly available quantum computers. However, many might find learning all of the supplementary information that goes into quantum algorithms to be a daunting task, and become discouraged. This tutorial is a series of lessons, aimed to teach the basics of quantum algorithms to those who may have little to no background in quantum physics and/or minimal knowledge of coding in python. Each lesson covers select physics/coding topics needed for writing quantum algorithms, eventually building up a toolset for tackling more and more challenging quantum algorithms. This tutorial series is designed to provide readers from any background with two services: 1) A concise and thorough understanding of some of the most popular/academically important quantum algorithms. 2) A fluent understanding of how to write code for quantum algorithms, using Rigetti's publicly available Pyquil.

quant-ph↗
arXiv2018

Scattering Quantum Random Walks on Square Grids and Randomly Generated Mazes

The Scattering Quantum Random Walk scheme has found success as a basis for search algorithms on highly symmetric graph structures. In this paper we examine its effectiveness at locating a specially marked vertex on square grid graphs, consisting of N$^2$ nodes. We simulate these quantum systems using classical computational methods, and find that the probability distributions that arise are very favorable for a hybrid quantum / classical algorithm. We then examine how this hybrid algorithm handles varying types of randomness in both location of the special vertex and later random obstacles placed throughout the geometry, showing that that the algorithm is resilient to both cases.

quant-ph↗
arXiv2018

Stability of charges in titanium compounds and charge transfer to oxygen in titanium dioxide

We investigate the charge density distribution in titanium dioxide, molecular titanium complexes and a variety of periodic titanium compounds using delocalization indices and Bader charge analysis. Our results are in agreement with previous experimental and theoretical investigations on the charge stability and deviation from formal oxidation states in transition metal compounds. We present examples for practically relevant redox processes, using molecular titanium dioxide model systems, that illustrate the failure of formal oxidation states to account for some redox phenomena. We observe a pronounced charge stability on titanium for trial systems which are expected to be mainly ionic. No environment tested by us is capable to reduce the local titanium charge remainder below one electron.

cond-mat.mtrl-sci↗
arXiv2017

Finding paths in tree graphs with a quantum walk

In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to find a selected final node as quickly as possible, faster than any classical search algorithm. We show that this can be done using a quantum random walk, both exactly through numerical calculations as well as analytically using eigenvectors and eigenvalues of the quantum system.

quant-ph↗
arXiv2017

Finding paths with quantum walks or quantum walking through a maze

We show that it is possible to use a quantum walk to find a path from one marked vertex to another. In the specific case of $M$ stars connected in a chain, one can find the path from the first star to the last one in $O(M\sqrt{N})$ steps, where $N$ is the number of spokes of each star. First we provide an analytical result showing that by starting in a phase-modulated highly superposed initial state we can find the path in $O(M\sqrt{N}\log M)$ steps. Next, we improve this efficiency by showing that the recovery of the path can also be performed by a series of successive searches when we start at the last known position and search for the next connection in $O(\sqrt{N})$ steps leading to the overall efficiency of $O(M\sqrt{N})$. For this result we use the analytical solution that can be obtained for a ring of stars of double the length of the chain.

quant-ph↗
arXiv2017

Ab initio study of Li, Mg and Al insertion into rutile VO2: Fast diffusion and enhanced voltages

Vanadium oxides are among the most promising materials that can be used as electrodes in rechargeable metal-ion batteries. In this work, we systematically investigate thermodynamic, electronic and kinetic properties associated with the insertion of Li, Mg and Al atoms in rutile VO2. Using first-principles calculations, we systematically study the structural evolution and voltage curves of LixVO2, MgxVO2 and AlxVO2 (0<x<1) compounds. The calculated lithium intercalation voltage starts at 3.50 V for single-atom insertion and decreases to 2.23 V for full lithiation, to the LiVO2 compound, which agrees well with experimental results. The Mg insertion features a plateau about 1.6 V up to Mg0.5VO2 and then another plateau-like region at around 0.5 V up to Mg1VO2. The predicted voltage curve for Al insertion starts at 1.98 V, followed by two plateaus at 1.48 V and 1.17 V. The diffusion barrier of Li, Mg and Al in the tunnel structure of VO2 is 0.06, 0.33 and 0.50 eV, respectively. The demonstrated excellent Li, Mg and Al mobility, high structural stability and high specific capacity suggest a promising potential of rutile VO2 electrodes especially for multivalent batteries.

cond-mat.mtrl-sci↗
arXiv2017

On the oxidation state of titanium in titanium dioxide

The oxidation state of titanium in titanium dioxide is commonly assumed to be +4. This assumption is used ubiquitously to rationalize phenomena observed with TiO2. We present a comprehensive electronic structure investigation of Ti ions, TiO2 molecules and TiO2 bulk crystals, using different density functional theory and wave function-based approaches, which suggests a lower oxidation state (+3). Specifically, there is evidence of a significant remaining contribution from valence s and d electrons of Ti, including the presence of a nuclear cusp around the Ti core. The charge corresponding to valence s and d states of Ti amounts to 1 e. The commonly assumed picture may therefore have to be revised.

cond-mat.mtrl-sci↗
arXiv2016

Retrodiction of a sequence of measurement results in qubit interferometers

We study how well we can retrodict results of measurements made on a quantum system if we can make measurements on its final state. We know what measurements were made, but not their results. An initial examination shows that we can gain anywhere from no information to perfect information about the results of previous measurements, depending on the measurements and the initial state of the system. The case of two two-outcome measurements, the second of which is a projective measurement, is examined in some detail. We then look at a model of a qubit interferometer in which measurements are made in order to determine the path the qubit followed. The measurement made on the final state of the qubit depends on the information about previous measurement results that we are trying to determine. One can attempt to find the result of just one of the measurements, all of them, or find a measurement sequence that was not realized. We study all three possibilities.

quant-ph↗
arXiv2009

Dynamics of a stiff biopolymer in an actively contractile background: buckling, stiffening and negative dissipation

We present a generic theory for the dynamics of a stiff filament under tension, in an active medium with orientational correlations, such as a microtubule in contractile actin. In sharp contrast to the case of a passive medium, we find the filament can stiffen, and possibly oscillate, \textit{or} buckle, depending on the contractile or tensile nature of the activity \textit{and} the filament-medium anchoring interaction. We present experiments on the behaviour of microtubules in the growth cone of a neuron, which provide evidence for these apparently opposing behaviours. We also demonstrate a strong violation of the fluctuation-dissipation (FD) relation in the effective dynamics of the filament, including a negative FD ratio. Our approach is also of relevance to the dynamics of axons, and our model equations bear a remarkable formal similarity to those in recent work [PNAS (2001) {\bf 98}:14380-14385] on auditory hair cells. Detailed tests of our predictions can be made using a single filament in actomyosin extracts or bacterial suspensions.

cond-mat.soft↗