We study how two pieces of localized quantum information can be delocalized across a composite Hilbert space when a global unitary operation is applied. We classify the delocalization power of global unitary operations on quantum information by investigating the possibility of relocalizing one piece of the quantum information without using any global quantum resource. We show that one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent of a controlled-unitary operation. The delocalization power turns out to reveal different aspect of the non-local properties of global unitary operations characterized by their entangling power.
{"title":"Classification of delocalization power of global unitary operations in terms of LOCC one-piece relocalization","authors":"A. Soeda, M. Murao","doi":"10.4204/EPTCS.26.11","DOIUrl":"https://doi.org/10.4204/EPTCS.26.11","url":null,"abstract":"We study how two pieces of localized quantum information can be delocalized across a composite Hilbert space when a global unitary operation is applied. We classify the delocalization power of global unitary operations on quantum information by investigating the possibility of relocalizing one piece of the quantum information without using any global quantum resource. We show that one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent of a controlled-unitary operation. The delocalization power turns out to reveal different aspect of the non-local properties of global unitary operations characterized by their entangling power.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"32 1","pages":"117-126"},"PeriodicalIF":0.0,"publicationDate":"2010-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79284076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same quantum algorithm can also be used to learn which input variables other types of Boolean functions depend on, with a success probability that depends on the form of the Boolean function that is tested, but does not depend on the total number of input variables. We also outline a procedure to futher amplify the success probability, based on another quantum algorithm, the Grover search.
{"title":"Quantum algorithms for testing Boolean functions","authors":"Dominik F. Floess, E. Andersson, M. Hillery","doi":"10.4204/EPTCS.26.9","DOIUrl":"https://doi.org/10.4204/EPTCS.26.9","url":null,"abstract":"We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same quantum algorithm can also be used to learn which input variables other types of Boolean functions depend on, with a success probability that depends on the form of the Boolean function that is tested, but does not depend on the total number of input variables. We also outline a procedure to futher amplify the success probability, based on another quantum algorithm, the Grover search.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"1 3 1","pages":"101-108"},"PeriodicalIF":0.0,"publicationDate":"2010-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76282706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We sketch the relation with two established vectorial lambda-calculi. Then we study the problems arising from the addition of a fixed point combinator and how to modify the equational theory to solve them. We sketch an algebraic vectorial PCF and its possible denotational interpretations.
{"title":"Semantics of a Typed Algebraic Lambda-Calculus","authors":"B. Valiron","doi":"10.4204/EPTCS.26.14","DOIUrl":"https://doi.org/10.4204/EPTCS.26.14","url":null,"abstract":"Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We sketch the relation with two established vectorial lambda-calculi. Then we study the problems arising from the addition of a fixed point combinator and how to modify the equational theory to solve them. We sketch an algebraic vectorial PCF and its possible denotational interpretations.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"258 1","pages":"147-158"},"PeriodicalIF":0.0,"publicationDate":"2010-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73480321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We report recent research on computing with biology-based neural network models by means of physics-based opto-electronic hardware. New technology provides opportunities for very-high-speed computation and uncovers problems obstructing the wide-spread use of this new capability. The Computation Modeling community may be able to offer solutions to these cross-boundary research problems.
{"title":"Computing by Means of Physics-Based Optical Neural Networks","authors":"A. S. Younger, E. Redd","doi":"10.4204/EPTCS.26.15","DOIUrl":"https://doi.org/10.4204/EPTCS.26.15","url":null,"abstract":"We report recent research on computing with biology-based neural network models by means of physics-based opto-electronic hardware. New technology provides opportunities for very-high-speed computation and uncovers problems obstructing the wide-spread use of this new capability. The Computation Modeling community may be able to offer solutions to these cross-boundary research problems.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"94 1","pages":"159-167"},"PeriodicalIF":0.0,"publicationDate":"2010-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84305059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.
{"title":"Measurement Based Quantum Computation on Fractal Lattices","authors":"D. Markham, J. Anders, M. Hajdušek, V. Vedral","doi":"10.4204/EPTCS.26.10","DOIUrl":"https://doi.org/10.4204/EPTCS.26.10","url":null,"abstract":"In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"5 1","pages":"109-115"},"PeriodicalIF":0.0,"publicationDate":"2010-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90651901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Indexed monoidal algebras are introduced as an equivalent structure for self-dual compact closed categories, and a coherence theorem is proved for the category of such algebras. Turing automata and Turing graph machines are defined by generalizing the classical Turing machine concept, so that the collection of such machines becomes an indexed monoidal algebra. On the analogy of the von Neumann data-flow computer architecture, Turing graph machines are proposed as potentially reversible low-level universal computational devices, and a truly reversible molecular size hardware model is presented as an example.
{"title":"Turing Automata and Graph Machines","authors":"M. Bartha","doi":"10.4204/EPTCS.26.3","DOIUrl":"https://doi.org/10.4204/EPTCS.26.3","url":null,"abstract":"Indexed monoidal algebras are introduced as an equivalent structure for self-dual compact closed categories, and a coherence theorem is proved for the category of such algebras. Turing automata and Turing graph machines are defined by generalizing the classical Turing machine concept, so that the collection of such machines becomes an indexed monoidal algebra. On the analogy of the von Neumann data-flow computer architecture, Turing graph machines are proposed as potentially reversible low-level universal computational devices, and a truly reversible molecular size hardware model is presented as an example.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"519 1","pages":"19-31"},"PeriodicalIF":0.0,"publicationDate":"2010-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85621965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
DCM 2010 provides a forum for ideas about new computing means and models, with a particular emphasis in 2010 on computational and causal models related to physics and biology. We believe that bringing together different approaches - in a community with the strong foundational background characteristic of FLoC - results in inspirational cross-boundary exchanges, and innovative further research. Day two of this pre-FLoC 2010 workshop is given over to physics and quantum related computation. The content of day one is more typical of previous DCM workshops - covering a full spectrum of topics related to the development of new computational models or new features for traditional computational models. DCM 2010 was designed to foster interactions, and provide a forum for presenting new ideas and work in progress. It is also intended to enable newcomers to learn about current research in this area.
{"title":"Algebraic characterisation of one-way patterns","authors":"V. Dunjko, E. Kashefi","doi":"10.4204/EPTCS.26.8","DOIUrl":"https://doi.org/10.4204/EPTCS.26.8","url":null,"abstract":"DCM 2010 provides a forum for ideas about new computing means and models, with a particular emphasis in 2010 on computational and causal models related to physics and biology. We believe that bringing together different approaches - in a community with the strong foundational background characteristic of FLoC - results in inspirational cross-boundary exchanges, and innovative further research. Day two of this pre-FLoC 2010 workshop is given over to physics and quantum related computation. The content of day one is more typical of previous DCM workshops - covering a full spectrum of topics related to the development of new computational models or new features for traditional computational models. DCM 2010 was designed to foster interactions, and provide a forum for presenting new ideas and work in progress. It is also intended to enable newcomers to learn about current research in this area.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"70 1","pages":"85-100"},"PeriodicalIF":0.0,"publicationDate":"2010-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83918833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a reduction of the termination problem for a Turing machine (in the simplified form of the Post correspondence problem) to the problem of determining whether a continuous-time Markov chain presented as a set of Kappa graph-rewriting rules has an equilibrium. It follows that the problem of whether a computable CTMC is dissipative (ie does not have an equilibrium) is undecidable.
{"title":"Equilibrium and Termination","authors":"V. Danos, N. Oury","doi":"10.4204/EPTCS.26.7","DOIUrl":"https://doi.org/10.4204/EPTCS.26.7","url":null,"abstract":"We present a reduction of the termination problem for a Turing machine (in the simplified form of the Post correspondence problem) to the problem of determining whether a continuous-time Markov chain presented as a set of Kappa graph-rewriting rules has an equilibrium. It follows that the problem of whether a computable CTMC is dissipative (ie does not have an equilibrium) is undecidable.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"63 1","pages":"75-84"},"PeriodicalIF":0.0,"publicationDate":"2010-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83997166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating the ability to de-quantise quantum algorithms into classical simulations of the algorithms which are as efficient in both time and space as the original quantum algorithms. The process of de-quantisation helps formulate conditions to determine if a quantum algorithm provides a real speed-up over classical algorithms. These conditions can be used to develop new quantum algorithms more effectively (by avoiding features that could allow the algorithm to be efficiently classically simulated) and to create new classical algorithms (by using features which have proved valuable for quantum algorithms). Results on many different methods of de-quantisations are presented, as well as a general formal definition of de-quantisation. De-quantisations employing higher-dimensional classical bits, as well as those using matrix-simulations, put emphasis on entanglement in quantum algorithms; a key result is that any algorithm in which the entanglement is bounded is de-quantisable. These methods are contrasted with the stabiliser formalism de-quantisations due to the Gottesman-Knill Theorem, as well as those which take advantage of the topology of the circuit for a quantum algorithm. The benefits and limits of the different methods are discussed, and the importance of utilising a range of techniques is emphasised. We further discuss some features of quantum algorithms which current de-quantisation methods do not cover and highlight several important open questions in the area.
{"title":"Understanding the Quantum Computational Speed-up via De-quantisation","authors":"A. Abbott, Cristian S. Calude","doi":"10.4204/EPTCS.26.1","DOIUrl":"https://doi.org/10.4204/EPTCS.26.1","url":null,"abstract":"While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating the ability to de-quantise quantum algorithms into classical simulations of the algorithms which are as efficient in both time and space as the original quantum algorithms. The process of de-quantisation helps formulate conditions to determine if a quantum algorithm provides a real speed-up over classical algorithms. These conditions can be used to develop new quantum algorithms more effectively (by avoiding features that could allow the algorithm to be efficiently classically simulated) and to create new classical algorithms (by using features which have proved valuable for quantum algorithms). Results on many different methods of de-quantisations are presented, as well as a general formal definition of de-quantisation. De-quantisations employing higher-dimensional classical bits, as well as those using matrix-simulations, put emphasis on entanglement in quantum algorithms; a key result is that any algorithm in which the entanglement is bounded is de-quantisable. These methods are contrasted with the stabiliser formalism de-quantisations due to the Gottesman-Knill Theorem, as well as those which take advantage of the topology of the circuit for a quantum algorithm. The benefits and limits of the different methods are discussed, and the importance of utilising a range of techniques is emphasised. We further discuss some features of quantum algorithms which current de-quantisation methods do not cover and highlight several important open questions in the area.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"4 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2010-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86737964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Provenance, or information about the sources, derivation, custody or history of data, has been studied recently in a number of contexts, including databases, scientific workflows and the Semantic Web. Many provenance mechanisms have been developed, motivated by informal notions such as influence, dependence, explanation and causality. However, there has been little study of whether these mechanisms formally satisfy appropriate policies or even how to formalize relevant motivating concepts such as causality. We contend that mathematical models of these concepts are needed to justify and compare provenance techniques. In this paper we review a theory of causality based on structural models that has been developed in artificial intelligence, and describe work in progress on using causality to give a semantics to provenance graphs.
{"title":"Causality and the Semantics of Provenance","authors":"J. Cheney","doi":"10.4204/EPTCS.26.6","DOIUrl":"https://doi.org/10.4204/EPTCS.26.6","url":null,"abstract":"Provenance, or information about the sources, derivation, custody or history of data, has been studied recently in a number of contexts, including databases, scientific workflows and the Semantic Web. Many provenance mechanisms have been developed, motivated by informal notions such as influence, dependence, explanation and causality. However, there has been little study of whether these mechanisms formally satisfy appropriate policies or even how to formalize relevant motivating concepts such as causality. We contend that mathematical models of these concepts are needed to justify and compare provenance techniques. In this paper we review a theory of causality based on structural models that has been developed in artificial intelligence, and describe work in progress on using causality to give a semantics to provenance graphs.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"128 1","pages":"63-74"},"PeriodicalIF":0.0,"publicationDate":"2010-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88135931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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