Intrinsically universal one-dimensional quantum cellular automata in two flavours

We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial configuration of the universal QCA. Several steps of the universal QCA will then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA. The encoding is linear and hence does not carry any of the cost of the computation. We do this in two flavours: a weak one which requires an infinite but periodic initial configuration and a strong one which needs only a finite initial configuration. KEYWORDS: Quantum cellular automata, Intrinsic universality, Quantum computation.Comment: 27 pages, revtex, 23 figures. V3: The results of V1-V2 are better explained and formalized, and a novel result about intrinsic universality with only finite initial configurations is give

A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the intrinsically universal QCA. Several steps of the intrinsically universal QCA then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA.Comment: 13 pages, 7 figures. In Proceedings of the 4th International Conference on Language and Automata Theory and Applications (LATA 2010), Lecture Notes in Computer Science (LNCS). Journal version: arXiv:0907.382

A Quantum Game of Life

This research describes a three dimensional quantum cellular automaton (QCA) which can simulate all other 3D QCA. This intrinsically universal QCA belongs to the simplest subclass of QCA: Partitioned QCA (PQCA). PQCA are QCA of a particular form, where incoming information is scattered by a fixed unitary U before being redistributed and rescattered. Our construction is minimal amongst PQCA, having block size 2 x 2 x 2 and cell dimension 2. Signals, wires and gates emerge in an elegant fashion.Comment: 13 pages, 10 figures. Final version, accepted by Journ\'ees Automates Cellulaires (JAC 2010)

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

Proceedings of JAC 2010. Journées Automates Cellulaires

The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast

The Block Universe: A Philosophical Investigation in Four Dimensions

The aim of this doctoral dissertation is to closely explore the nature of Einstein’s block universe and to tease out its implications for the nature of time and human freedom. Four questions, in particular, are central to this dissertation, and set out the four dimensions of this philosophical investigation: (1) Does the block universe view of time follow inevitably from the theory of special relativity? (2) Is there room for the passage of time in the block universe? (3) Can we distinguish past from future in the block universe? (4) Is there room for human freedom in the block universe? Although the answer of most philosophers would be yes, triple no, my own answer, controversially, is no, triple yes. I thereby challenge the status quo with respect to each of these metaphysical questions, and argue that none of these questions can be answered from looking at physics alone. Physics may constrain our metaphysics, but it certainly does not settle it. What is needed in order to answer these questions, are additional metaphysical assumptions that fall outside the scope of modern physics. My primary goal in this dissertation, therefore, is not to settle the debates on the nature of time and human freedom, but to clarify them by expliciting the metaphysical assumptions that are otherwise left implicit

T-cell epitope frequency in ordered and disordered protein regions

Frequently asked question in immunology is whether the immunodominance of T-cell epitopes is dependent to their localization in the antigen 3D structure or epitope-intrinsic. Using epitope prediction algorithms we have found that both HLA-I and HLA-II epitope frequencies were higher in ordered protein regions, for all analysed taxonomic categories (archaea, bacteria, eukarya, and viridae) and that epitopes appertaining to ordered protein regions were prevalently hydrophobic. Epitope frequency in disordered protein regions of various lengths was constant while in ordered regions had shown a rising trend with prolonging region length. The comparison between predicted and experimentally evaluated epitopes of several tumor associated antigens of cancer/testis antigen group, revealed that majority of epitopes presented by HLA-I and HLA-II molecules were localized in ordered protein regions

Diverse and robust molecular algorithms using reprogrammable DNA self-assembly

Molecular biology provides an inspiring proof-of-principle that chemical systems can store and process information to direct molecular activities such as the fabrication of complex structures from molecular components. To develop information-based chemistry as a technology for programming matter to function in ways not seen in biological systems, it is necessary to understand how molecular interactions can encode and execute algorithms. The self-assembly of relatively simple units into complex products is particularly well suited for such investigations. Theory that combines mathematical tiling and statistical–mechanical models of molecular crystallization has shown that algorithmic behaviour can be embedded within molecular self-assembly processes, and this has been experimentally demonstrated using DNA nanotechnology with up to 22 tile types. However, many information technologies exhibit a complexity threshold—such as the minimum transistor count needed for a general-purpose computer—beyond which the power of a reprogrammable system increases qualitatively, and it has been unclear whether the biophysics of DNA self-assembly allows that threshold to be exceeded. Here we report the design and experimental validation of a DNA tile set that contains 355 single-stranded tiles and can, through simple tile selection, be reprogrammed to implement a wide variety of 6-bit algorithms. We use this set to construct 21 circuits that execute algorithms including copying, sorting, recognizing palindromes and multiples of 3, random walking, obtaining an unbiased choice from a biased random source, electing a leader, simulating cellular automata, generating deterministic and randomized patterns, and counting to 63, with an overall per-tile error rate of less than 1 in 3,000. These findings suggest that molecular self-assembly could be a reliable algorithmic component within programmable chemical systems. The development of molecular machines that are reprogrammable—at a high level of abstraction and thus without requiring knowledge of the underlying physics—will establish a creative space in which molecular programmers can flourish