Quantum Computation as Geometry

Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms, or to prove limitations on the power of quantum computers.Comment: 13 Pages, 1 Figur

Towards Quantifying Complexity with Quantum Mechanics

While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified by the complexity of its simplest mathematical model - the model that requires the least past information for optimal future prediction. Here we review how such models, known as $\epsilon$-machines can be further simplified through quantum logic, and explore the resulting consequences for understanding complexity. In particular, we propose a new measure of complexity based on quantum $\epsilon$-machines. We apply this to a simple system undergoing constant thermalization. The resulting quantum measure of complexity aligns more closely with our intuition of how complexity should behave.Comment: 10 pages, 6 figure, Published in the Focus Point on Quantum information and complexity edition of EPJ Plu

Surveying structural complexity in quantum many-body systems

Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and entanglement alone. Using tools from complexity science, we characterise such structure. We investigate the structural complexities that can be found within the patterns that manifest from the observational data of these systems. In particular, using two prototypical quantum many-body systems as test cases - the one-dimensional quantum Ising and Bose-Hubbard models - we explore how different information-theoretic measures of complexity are able to identify different features of such patterns. This work furthers the understanding of fully-quantum notions of structure and complexity in quantum systems and dynamics.Comment: 9 pages, 5 figure

Finite element modelling and experimental validation in radiative heat transfer.

The work presented in this thesis can be divided into two parts: numerical modelling and experimental validation. The first part considers a finite element computer code called Pharo which has been developed to simulates heat transfer exchanged in an enclosure via thermal radiation and conduction. This finite element heat transfer code has been written for the Defence, Science and Technology Laboratory (DSTL). Face to face (zonal) thermal radiation which operates with diffuse surface properties of materials without a participating media is analyzed and included in Pharo. To analyze the net heat exchanged within an enclosure several methods for view factor calculation, such as the Monte Carlo and Hemi-cube methods were included in Pharo. During heat transfer simulations a better accuracy of results has been demonstrated using a new approach called the Multiple Reflection of View Factors 'MRV' method. Transient heat flow is solved using both finite difference and finite element time stepping. Also, an analysis of transient heat flow using different solvers (direct and iterative) to find the most appropriate one was carried out. The second part of the work considers experimental validation of numerical results obtained using Pharo. Special attention was given to the analysis of the relationship between view factors and measured heat transfer. To make the experimental data complete the measurements of surface properties including emissivity, reflectivity for different wavelengths as well as roughness of materials is presented. These experimental results can be used as experimental benchmark data for model users and developers

Effects of recombinations on variability and heritability of traits in maize populations with exotic germplasm

The following maize populations were encompassed by the study: a population with 25% of exotic germplasm (1601/5xZPL913)F2R0 and populations developed after three (1601/5xZPL913)F2R3, that is, five (1601/5xZPL913)F2R5, gene recombination cycles. The S, progeny trial was set lip according to the nested design in two replications and two locations during two years (2001 and 2002). The average values for all traits except moisture at harvest increased. The changes of mean values of yields and other traits can be very important from the aspect of long-term breeding programmes. Different agroecological conditions, genotype, family x location interaction and family x location interaction within the set signficantly affected all observed traits of populations. Genetic and phenotypic variances for all traits except the 1000-kernel weight decreased under the effects of the number of recombination cycles, which was confirmed by the coefficients of heritability. A significant decrease was not detected in yields and ear lengths, which is particularly important for practical breeding. Three cycles of gene recombination are sufficient for this population prior to the application by various breeding methods

A reduced complexity numerical method for optimal gate synthesis

Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate design problem is equivalent to the solution of an associated optimal control problem, the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality free techniques) that determine the optimal control thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, used in previous literature. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on $SU(4)$- a problem that is computationally intractable by grid based approaches.Comment: 8 pages, 4 figure

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, subriemannian, and Finslerian manifolds. These results generalize the results of Nielsen, Dowling, Gu, and Doherty, Science 311, 1133-1135 (2006), which showed that the gate complexity can be related to distances on a Riemannian manifoldComment: 7 Pages Added Full Names to Author

Quantum Computing with Continuous-Variable Clusters

Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.Comment: 17 pages, 5 figure

RPLL - RENDEZVOUS PROTOCOL FOR LONG-LIVING SENSOR NODE

Sensor nodes (SNs), as constituents of wireless sensor network (WSN), are battery-powered not rechargeable devices and have limited amount of energy available. Since lifetime of SNs is crucial parameter for energy-efficient WSN design, it is essential to extend their lifetimes as much as possible. Here we propose a rendezvous scheme called Rendezvous Protocol for Long-Living SN, RPLL. This scheme is based on implementation of a duty-cycling technique. For each SN within WSN a unique identification number (ID) is allocated, thanks to which a collision problem is effectively remedied. The RPLL provides on time wake-up of SNs in fully decentralized way and fast detection of new appended SNs. Taking into account the WSN and SN working parameters, such as beacon time, beacon period, number of active SNs, and quartz oscillator instability, by using the proposed method, WSN designer can determine the maximal lifetime of a SN, i.e. to achieve optimal energy consumption