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Quantum Information Theory and the Foundations of Quantum Mechanics
, 2004
"... This thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. In Part I an attempt is made to shed some light on the nature of information and quantum information theory. It is emphasized that the everyday notion of ..."
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This thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. In Part I an attempt is made to shed some light on the nature of information and quantum information theory. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; noun, hence does not refer to a particular or substance. The popular claim ‘Information is Physical ’ is assessed and it is argued that this proposition faces a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. A novel argument is provided against Dretske’s (1981) attempt to base a semantic notion of information on ideas from information theory. The function of various measures of information content for quantum systems is explored and the applicability of the Shannon information in the quantum context maintained against the challenge of Brukner and Zeilinger (2001). The phenomenon of quantum teleportation is then explored as a case study serving to emphasize the value of
Architectural implications of quantum computing technologies
 ACM Journal on Emerging Technologies in Computing Systems (JETC
, 2006
"... In this article we present a classification scheme for quantum computing technologies that is based on the characteristics most relevant to computer systems architecture. The engineering tradeoffs of execution speed, decoherence of the quantum states, and size of systems are described. Concurrency, ..."
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Cited by 27 (4 self)
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In this article we present a classification scheme for quantum computing technologies that is based on the characteristics most relevant to computer systems architecture. The engineering tradeoffs of execution speed, decoherence of the quantum states, and size of systems are described. Concurrency, storage capacity, and interconnection network topology influence algorithmic efficiency, while quantum error correction and necessary quantum state measurement are the ultimate drivers of logical clock speed. We discuss several proposed technologies. Finally, we use our taxonomy to explore architectural implications for common arithmetic circuits, examine the implementation of quantum error correction, and discuss clusterstate quantum computation.
Quantum walks: a comprehensive review
, 2012
"... Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting ..."
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Cited by 24 (0 self)
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Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists and engineers. In this paper we review theoretical advances on the foundations of both discrete and continuoustime quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discretetime quantum walks. Furthermore, we have reviewed several algorithms based on both discrete and continuoustime quantum walks as well as a most important result: the computational universality of both continuous and discretetime quantum walks.
A quantum computing primer for operator theorists
 Linear Algebra Appl
, 2005
"... Abstract. This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum channels, or equivalently, completely positive trace pre ..."
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Cited by 15 (3 self)
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Abstract. This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum channels, or equivalently, completely positive trace preserving maps. The main theorems for quantum error detection and correction are presented and we conclude with a description of a particular passive method of quantum error correction. 1.
On the existence of truly autonomic computing systems and the link with quantum computing
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What is Geometry in Quantum Theory
 Int. J. Geom. Methods Mod. Phys
"... Abstract. In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics1, we briefly survey some peculiarities of geometric techniques in quantum models. Contemporary quantum theory meets an explosion of different types of quantization. Some of them (g ..."
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Abstract. In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics1, we briefly survey some peculiarities of geometric techniques in quantum models. Contemporary quantum theory meets an explosion of different types of quantization. Some of them (geometric quantization, deformation quantization, noncommutative geometry, topological field theory etc.) speak the language of geometry, algebraic and differential topology. We do not pretend for any comprehensive analysis of these quantization techniques, but aims to formulate and illustrate their main peculiarities. As in any survey, a selection of topics has to be done, and we apologize in advance if some relevant works are omitted. Geometry of classical mechanics and field theory is mainly differential geometry of finitedimensional smooth manifolds, fiber bundles and Lie groups. The key point why geometry plays a prominent role in classical field theory lies in the fact that it enables one to deal with invariantly defined objects. Gauge theory has shown clearly that this is a basic physical principle. At first, a pseudoRiemannian metric has been identified to a gravitational field in the framework of Einstein’s General Relativity. In 6070th, one has observed that connections on a principal bundle provide the mathematical model of classical gauge potentials [13].
Physics and metaphysics look at computation
"... As far as algorithmic thinking is bound by symbolic paperandpencil operations, the ChurchTuring thesis appears ..."
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As far as algorithmic thinking is bound by symbolic paperandpencil operations, the ChurchTuring thesis appears
Topological Color Codes and TwoBody Quantum Lattice Hamiltonians
, 2009
"... Topological color codes are among the stabilizer codes with remarkable properties from quantum information perspective. In this paper we construct a lattice, the so called ruby lattice, with coordination number four governed by a 2body Hamiltonian. In a particular regime of coupling constants, in t ..."
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Topological color codes are among the stabilizer codes with remarkable properties from quantum information perspective. In this paper we construct a lattice, the so called ruby lattice, with coordination number four governed by a 2body Hamiltonian. In a particular regime of coupling constants, in the triangular limit, degenerate perturbation theory implies that the low energy spectrum of the model can be described by a manybody effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to vortexfree sector. The gauge symmetry Z2 × Z2 of color code could already be realized by identifying three distinct plaquette operators on the lattice. All plaquette operators commute with each other and with the Hamiltonian being integrals of motion. Plaquettes are extended to closed strings or stringnet structures. Noncontractible closed strings winding the space commute with Hamiltonian but not always with each other giving rise to exact topological degeneracy of the model. Connection to 2colexes can be established via the coloring of the strings. We discuss it at the nonperturbative level. The particular structure of the 2body Hamiltonian provides a fruitful interpretation in terms of mapping to bosons coupled to effective spins. We show that high energy excitations of the model
Strategic Insights From Playing the Quantum TicTacToe
, 1007
"... Abstract. Inthispaper,weperformaminimalisticquantizationoftheclassicalgame of tictactoe, by allowing superpositions of classical moves. In order for the quantum game to reduce properly to the classical game, we require legal quantum moves to be orthogonal to all previous moves. We also admit inter ..."
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Abstract. Inthispaper,weperformaminimalisticquantizationoftheclassicalgame of tictactoe, by allowing superpositions of classical moves. In order for the quantum game to reduce properly to the classical game, we require legal quantum moves to be orthogonal to all previous moves. We also admit interference effects, by squaring the sum ofamplitudes overallmovesby aplayertocompute his orheroccupationlevelofa given site. A player wins when the sums of occupations along any of the eight straight lines we can draw in the 3×3 grid is greater than three. We play the quantum tictactoe first randomly, and then deterministically, to explore the impact different opening moves, end games, and different combinationsof offensive and defensive strategieshave on the outcome of the game. In contrast to the classical tictactoe, the deterministic quantum game does not always end in a draw. In contrast also to most classical twoplayer games of no chance, it is possible for Player 2 to win. More interestingly, we find that Player 1 enjoys an overwhelming quantum advantage when he opens with a quantum move, but loses this advantage when he opens with a classical move. We also find the quantum blocking move, which consists of a weighted superposition of moves that the opponent could use to win the game, to be very effective in denying the opponent his or her victory. We then speculate what implications these results might have on quantum information transfer and portfolio optimization. PACS numbers: 03.65.w, 03.67.aStrategic Insights From Playing the Quantum TicTacToe 2 1.