Local Unitary Quantum Cellular Automata

In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this model is to act as a theoretical model of quantum computation, similar to the quantum circuit model. It is also shown to be an appropriate abstraction for space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains and others. Some results that show the benefits of basing the model on local unitary operators are shown: universality, strong connections to the circuit model, simple implementation on quantum hardware, and a wealth of applications.Comment: To appear in Physical Review

Investigation of Molecular FCN for Beyond-CMOS: Technology, design, and modeling for nanocomputing

L'abstract è presente nell'allegato / the abstract is in the attachmen

Cellular Automata

Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented

SCERPA: a Self-Consistent Algorithm for the Evaluation of the Information Propagation in Molecular Field-Coupled Nanocomputing

Among the emerging technologies that are intended to outperform the current CMOS technology, the field-coupled nanocomputing (FCN) paradigm is one of the most promising. The molecular quantum-dot cellular automata (MQCA) has been proposed as possible FCN implementation for the expected very high device density and possible room temperature operations. The digital computation is performed via electrostatic interactions among nearby molecular cells, without the need for charge transport, extremely reducing the power dissipation. Due to the lack of mature analysis and design methods, especially from an electronics standpoint, few attempts have been made to study the behavior of logic circuits based on real molecules, and this reduces the design capability. In this article, we propose a novel algorithm, named self-consistent electrostatic potential algorithm (SCERPA), dedicated to the analysis of molecular FCN circuits. The algorithm evaluates the interaction among all molecules in the system using an iterative procedure. It exploits two optimizations modes named Interaction Radius and Active Region which reduce the computational cost of the evaluation, enabling SCERPA to support the simulation of complex molecular FCN circuits and to characterize consequentially the technology potentials. The proposed algorithm fulfills the need for modeling the molecular structures as electronic devices and provides important quantitative results to analyze the information propagation, motivating and supporting further research regarding molecular FCN circuits and eventual prototype fabrication

Quantum Cellular Automata: Theory and Applications

This thesis presents a model of Quantum Cellular Automata (QCA). The presented formalism is a natural quantization of the classical Cellular Automata (CA). It is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this model is to act as a theoretical model of quantum computation, similar to the quantum circuit model. The main advantage that QCA have over quantum circuits is that QCA make considerably fewer demands on the underlying hardware. In particular, as opposed to direct implementations of quantum circuits, the global evolution of the lattice in the QCA model does not assume independent control over individual \emph{qudits}. Rather, all qudits are to be addressed collectively in parallel. The QCA model is also shown to be an appropriate abstraction for space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains and others. Some results that show the benefits of basing the model on local unitary operators are shown: computational universality, strong connections to the circuit model, simple implementation on quantum hardware, and a series of applications. A detailed discussion will be given on one particular application of QCA that lies outside either computation or simulation: single-spin measurement. This algorithm uses the techniques developed in this thesis to achieve a result normally considered hard in physics. It serves well as an example of why QCA are interesting in their own right

On Algorithms, Separability and Cellular Automata in Quantum Computing

In Part I of this thesis, we present a new model of quantum cellular automata (QCA) based on local unitary operations. We will describe a set of desirable properties for any QCA model, and show that all of these properties are satisfied by the new model, while previous models of QCA do not. We will also show that the computation model based on Local Unitary QCA is equivalent to the Quantum Circuit model of computation, and give a number of applications of this new model of QCA. We also present a physical model of classical CA, on which the Local Unitary QCA model is based, and Coloured QCA, which is an alternative to the Local Unitary QCA model that can be used as the basis for implementing QCA in actual physical systems. In Part II, we explore the quantum separability problem, where we are given a density matrix for a state over two quantum systems, and we are to determine whether the state is separable with respect to these systems. We also look at the converse problem of finding an entanglement witness, which is an observable operator which can give a verification that a particular quantum state is indeed entangled. Although the combined problem is known to be NP-hard in general, it reduces to a convex optimization problem, and by exploiting specific properties of the set of separable states, we introduce a classical algorithm for solving this problem based on an Interior Point Algorithm introduced by Atkinson and Vaidya in 1995. In Part III, we explore the use of a low-depth AQFT (approximate quantum Fourier transform) in quantum phase estimation. It has been shown previously that the logarithmic-depth AQFT is as effective as the full QFT for the purposes of phase estimation. However, with sub-logarithmic depth, the phase estimation algorithm no longer works directly. In this case, results of the phase estimation algorithm need classical post-processing in order to retrieve the desired phase information. A generic technique such as the method of maximum likelihood can be used in order to recover the original phase. Unfortunately, working with the likelihood function analytically is intractable for the phase estimation algorithm. We develop some computational techniques to handle likelihood functions that occur in phase estimation algorithms. These computational techniques may potentially aid in the analysis of certain likelihood functions

A review of quantum cellular automata

Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally arose as an alternative paradigm for quantum computation, though more recently they have found application in understanding topological phases of matter and have been proposed as models of periodically driven (Floquet) quantum systems, where QCA methods were used to classify their phases. QCAs have also been used as a natural discretization of quantum field theory, and some interesting examples of QCAs have been introduced that become interacting quantum field theories in the continuum limit. This review discusses all of these applications, as well as some other interesting results on the structure of quantum cellular automata, including the tensor-network unitary approach, the index theory and higher dimensional classifications of QCAs. © 2020 Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. All rights reserved

Fault and Defect Tolerant Computer Architectures: Reliable Computing With Unreliable Devices

This research addresses design of a reliable computer from unreliable device technologies. A system architecture is developed for a fault and defect tolerant (FDT) computer. Trade-offs between different techniques are studied and yield and hardware cost models are developed. Fault and defect tolerant designs are created for the processor and the cache memory. Simulation results for the content-addressable memory (CAM)-based cache show 90% yield with device failure probabilities of 3 x 10(-6), three orders of magnitude better than non fault tolerant caches of the same size. The entire processor achieves 70% yield with device failure probabilities exceeding 10(-6). The required hardware redundancy is approximately 15 times that of a non-fault tolerant design. While larger than current FT designs, this architecture allows the use of devices much more likely to fail than silicon CMOS. As part of model development, an improved model is derived for NAND Multiplexing. The model is the first accurate model for small and medium amounts of redundancy. Previous models are extended to account for dependence between the inputs and produce more accurate results

Advanced Information Processing Methods and Their Applications

This Special Issue has collected and presented breakthrough research on information processing methods and their applications. Particular attention is paid to the study of the mathematical foundations of information processing methods, quantum computing, artificial intelligence, digital image processing, and the use of information technologies in medicine