Employing online quantum random number generators for generating truly random quantum states in Mathematica

We present a new version of TRQS package for Mathematica computing system. The package allows harnessing quantum random number generators (QRNG) for investigating the statistical properties of quantum states. It implements a number of functions for generating random states. The new version of the package adds the ability to use the on-line quantum random number generator service and implements new functions for retrieving lists of random numbers. Thanks to the introduced improvements, the new version provides faster access to high-quality sources of random numbers and can be used in simulations requiring large amount of random data.Comment: New version of the package described in arXiv:1102.4598. Software available at http://www.iitis.pl/~miszczak/trq

Improving randomness characterization through Bayesian model selection

Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other probabilistic algorithms. In this context, a crucial scientific endeavour is to develop effective methods that allow the characterization of random number generators. However, commonly employed methods either lack formality (e.g. the NIST test suite), or are inapplicable in principle (e.g. the characterization derived from the Algorithmic Theory of Information (ATI)). In this letter we present a novel method based on Bayesian model selection, which is both rigorous and effective, for characterizing randomness in a bit sequence. We derive analytic expressions for a model's likelihood which is then used to compute its posterior probability distribution. Our method proves to be more rigorous than NIST's suite and the Borel-Normality criterion and its implementation is straightforward. We have applied our method to an experimental device based on the process of spontaneous parametric downconversion, implemented in our laboratory, to confirm that it behaves as a genuine quantum random number generator (QRNG). As our approach relies on Bayesian inference, which entails model generalizability, our scheme transcends individual sequence analysis, leading to a characterization of the source of the random sequences itself.Comment: 25 page

Symbolic quantum programming for supporting applications of quantum computing technologies

The goal of this paper is to deliver the overview of the current state of the art, to provide experience report on developing quantum software tools, and to outline the perspective for developing quantum programming tools supporting symbolic programming for the needs of quantum computing technologies. The main focus of this paper is on quantum computing technologies, as they can in the most direct way benefit from developing tools enabling the symbolic manipulation of quantum circuits and providing software tools for creating, optimizing, and testing quantum programs. We deliver a short survey of the most popular approaches in the field of quantum software development and we aim at pointing their strengths and weaknesses. This helps to formulate a list of desirable characteristics which should be included in quantum computing frameworks. Next, we describe a software architecture and its preliminary implementation supporting the development of quantum programs using symbolic approach, encouraging the functional programming paradigm, and, at the same, time enabling the integration with high-performance and cloud computing. The described software consists of several packages developed to address different needs, but nevertheless sharing common design concepts. We also outline how the presented approach could be used in tasks in quantum software engineering, namely quantum software testing and quantum circuit construction.Comment: 14 pages, contribution to QP2023 Workshop, Programming'23, Tokyo, JP, March 13-17, 202

Theoretical Analysis of Single Molecule Spectroscopy Lineshapes of Conjugated Polymers

Conjugated Polymers(CPs) exhibit a wide range of highly tunable optical properties. Quantitative and detailed understanding of the nature of excitons responsible for such a rich optical behavior has significant implications for better utilization of CPs for more efficient plastic solar cells and other novel optoelectronic devices. In general, samples of CPs are plagued with substantial inhomogeneous broadening due to various sources of disorder. Single molecule emission spectroscopy (SMES) offers a unique opportunity to investigate the energetics and dynamics of excitons and their interactions with phonon modes. The major subject of the present thesis is to analyze and understand room temperature SMES lineshapes for a particular CP, called poly(2,5-di-(2\u27-ethylhexyloxy)-1,4-phenylenevinylene)(DEH-PPV). A minimal quantum mechanical model of a two-level system coupled to a Brownian oscillator bath is utilized. The main objective is to identify the set of model parameters best fitting a SMES lineshape for each of about 200 samples of DEH-PPV, from which new insight into the nature of exciton-bath coupling can be gained. This project also entails developing a reliable computational methodology for quantum mechanical modeling of spectral lineshapes in general. Well-known optimization techniques such as gradient descent, genetic algorithms, and heuristic searches have been tested, employing an $L^2$ measure between theoretical and experimental lineshapes for guiding the optimization. However, all of these tend to result in theoretical lineshapes qualitatively different from experimental ones. This is attributed to the ruggedness of the parameter space and inadequateness of the $L^2$ measure. On the other hand, when the dynamic reduction of the original parameter space to a 2-parameter space through feature searching and visualization of the search space paths using directed acyclic graphs(DAGs), the qualitative nature of the fitting improved significantly. For a more satisfactory fitting, it is shown that the inclusion of an additional energetic disorder is essential, representing the effect of quasi-static disorder accumulated during the SMES of each polymer. Various technical details, ambiguous issues, and implication of the present work are discussed

Capriccio For Strings: Collision-Mediated Parallel Transport in Curved Landscapes and Conifold-Enhanced Hierarchies Among Mirror Quintic Flux Vacua

This dissertation begins with a review of Calabi-Yau manifolds and their moduli spaces, flux compactification largely tailored to the case of type IIb supergravity, and Coleman-De Luccia vacuum decay. The three chapters that follow present the results of novel research conducted as a graduate student. Our first project is concerned with bubble collisions in single scalar field theories with multiple vacua. Lorentz boosted solitons traveling in one spatial dimension are used as a proxy to the colliding 3-dimensional spherical bubble walls. Recent work found that at sufficiently high impact velocities collisions between such bubble vacua are governed by "free passage" dynamics in which field interactions can be ignored during the collision, providing a systematic process for populating local minima without quantum nucleation. We focus on the time period that follows the bubble collision and provide evidence that, for certain potentials, interactions can drive significant deviations from the free passage bubble profile, thwarting the production of a new patch with different field value. However, for simple polynomial potentials a fine-tuning of vacuum locations is required to reverse the free passage kick enough that the field in the collision region returns to the original bubble vacuum. Hence we deem classical transitions mediated by free passage robust. Our second project continues with soliton collisions in the limit of relativistic impact velocity, but with the new feature of nontrivial field space curvature. We establish a simple geometrical interpretation of such collisions in terms of a double family of field profiles whose tangent vector fields stand in mutual parallel transport. This provides a generalization of the well-known limit in flat field space (free passage). We investigate the limits of this approximation and illustrate our analytical results with numerical simulations. In our third and final project we investigate the distribution of field theories that arise from the low energy limit of flux vacua built on type IIb string theory compactified on the mirror quintic. For a large collection of these models, we numerically determine the distribution of Taylor coefficients in a polynomial expansion of each model's scalar potential to fourth order. We provide an analytic explanation of the proncounced hierarchies exhibited by the random sample of masses and couplings generated numerically. The analytic argument is based on the structure of masses in no scale supergravity and the divergence of the Yukawa coupling at the conifold point in the moduli space of the mirror quintic. Our results cast the superpotential vev as a random element whose capacity to cloud structure vanishes as the conifold is approached

Symmetries in Quantum Mechanics

Symmetry and quantum mechanics are two of the most fundamental probes we have of nature. This collection of eleven papers discusses new quantum phenomena in atoms, galaxies, and people (quantum cognition), which is a testimonial to the breadth of the influence of symmetry and quantum mechanics. The book represents an international effort of researchers from educational and research institutions in nine countries, including India, Finland, France, Mexico, Norway, Russia, Spain, Turkey, and the United States. The papers can be divided into four broad categories: Fundamentals of quantum systems, including a new derivation of the uncertainty principle from optimal stochastic control theory, a new model of energy transfer between atoms with no wave function collapse, a new asymmetric optical micro-device with the remarkable property of showing a current with no applied voltage, and a model of quantum cognition to predict the effect of irrelevant information on decision making. 2. Algebraic methods in quantum mechanics, describing an elegant derivation of hydrogen atom Stark effect matrix elements, and a new group theoretical method for the computation of radiative shifts. Teleportation and scattering, including a method to improve the information transfer in teleportation, and the use of permutation symmetry to compute scattering cross sections. Cosmology, including scalar-tensor theory applied to inflation, the characterization of new Levi-Cevita space-times, and a comprehensive analysis of gravitational dispersion forces