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Alexandria digital library
 Communications of the ACM
, 1995
"... We investigate definitions of and protocols for multiparty quantum computing in the scenario where the secret data are quantum systems. We work in the quantum informationtheoretic model, where no assumptions are made on the computational power of the adversary. For the slightly weaker task of veri ..."
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Cited by 36 (6 self)
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We investigate definitions of and protocols for multiparty quantum computing in the scenario where the secret data are quantum systems. We work in the quantum informationtheoretic model, where no assumptions are made on the computational power of the adversary. For the slightly weaker task of verifiable quantum secret sharing, we give a protocol which tolerates any t < n/4 cheating parties (out of n). This is shown to be optimal. We use this new tool to establish that any multiparty quantum computation can be securely performed as long as the number of dishonest players is less than n/6.
Braiding operators are universal quantum gates
 New J. Phys
, 2004
"... doi:10.1088/13672630/6/1/134 Abstract. This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of theYang–Baxter equation is a universal gate for quantum computing, in the presence of local unitary tra ..."
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Cited by 36 (10 self)
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doi:10.1088/13672630/6/1/134 Abstract. This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of theYang–Baxter equation is a universal gate for quantum computing, in the presence of local unitary transformations.We show that this same R generates a new nontrivial invariant of braids, knots and links. Other solutions of the Yang– Baxter equation are also shown to be universal for quantum computation. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, and the structure of braiding in a topological quantum field theory.
An introduction to measurement based quantum computation, ArXiv: quantph/0508124
, 2005
"... In the formalism of measurement based quantum computation we start with a given fixed entangled state of many qubits and perform computation by applying a sequence of measurements to designated qubits in designated bases. The choice of basis for later measurements may depend on earlier measurement o ..."
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Cited by 32 (1 self)
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In the formalism of measurement based quantum computation we start with a given fixed entangled state of many qubits and perform computation by applying a sequence of measurements to designated qubits in designated bases. The choice of basis for later measurements may depend on earlier measurement outcomes and the final result of the computation is determined from the classical data of all the measurement outcomes. This is in contrast to the more familiar gate array model in which computational steps are unitary operations, developing a large entangled state prior to some final measurements for the output. Two principal schemes of measurement based computation are teleportation quantum computation (TQC) and the socalled cluster model or oneway quantum computer (1WQC). We will describe these schemes and show how they are able to perform universal quantum computation. We will outline various possible relationships between the models which serve to clarify their workings. We will also discuss possible novel computational benefits of the measurement based models compared to the gate array model, especially issues of parallelisability of algorithms. 1
A practical architecture for reliable quantum computers
 IEEE Computer
, 2002
"... Quantum computers offer the prospect of computation that scales exponentially with data size. Unfortunately, a single bit error can corrupt an exponential amount of data. Quantum mechanics can seem more suited to science fiction than system engineering, yet small quantum devices of 5 to 7 bits have ..."
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Cited by 29 (7 self)
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Quantum computers offer the prospect of computation that scales exponentially with data size. Unfortunately, a single bit error can corrupt an exponential amount of data. Quantum mechanics can seem more suited to science fiction than system engineering, yet small quantum devices of 5 to 7 bits have nevertheless been built in the laboratory, 1,2 100bit devices are on the drawing table now, and emerging quantum technologies promise even greater scalability. 3,4 More importantly, improvements in quantum errorcorrection codes have established a threshold theorem, 5 according to which scalable quantum computers can be built from faulty components as
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.
The Compositional Structure of Multipartite Quantum Entanglement
 IN: PROCEEDINGS OF THE 37TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP), LECTURE NOTES IN COMPUTER SCIENCE
, 2010
"... While multipartite quantum states constitute a (if not the) key resource for quantum computations and protocols, obtaining a highlevel, structural understanding of entanglement involving arbitrarily many qubits is a longstanding open problem in quantum computer science. In this paper we expose th ..."
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Cited by 27 (12 self)
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While multipartite quantum states constitute a (if not the) key resource for quantum computations and protocols, obtaining a highlevel, structural understanding of entanglement involving arbitrarily many qubits is a longstanding open problem in quantum computer science. In this paper we expose the algebraic and graphical structure of the GHZstate and the Wstate, as well as a purely graphical distinction that characterises the behaviours of these states. In turn, this structure yields a compositional graphical model for expressing general multipartite states. We identify those states, named Frobenius states, which canonically induce an algebraic structure, namely the structure of a commutative Frobenius algebra (CFA). We show that all SLOCCmaximal tripartite qubit states are locally equivalent to Frobenius states. Those that are SLOCCequivalent to the GHZstate induce special commutative Frobenius algebras, while those that are SLOCCequivalent to the Wstate induce what we call antispecial commutative Frobenius algebras. From the SLOCCclassification of tripartite qubit states follows a representation theorem for two dimensional CFAs. Together, a GHZ and a W Frobenius state form the primitives of a graphical calculus. This calculus is expressive enough to generate and reason about arbitrary multipartite states, which are obtained by “composing” the GHZ and Wstates, giving rise to a rich graphical paradigm for general multipartite entanglement.
Generalized Flow and Determinism in Measurementbased Quantum Computation
 New J. Physics
, 2007
"... Abstract. We extend the notion of quantum information flow defined by Danos and Kashefi [1] for the oneway model [2] and present a necessary and sufficient condition for the deterministic computation in this model. The generalized flow also applied in the extended model with measurements in the (X, ..."
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Cited by 26 (13 self)
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Abstract. We extend the notion of quantum information flow defined by Danos and Kashefi [1] for the oneway model [2] and present a necessary and sufficient condition for the deterministic computation in this model. The generalized flow also applied in the extended model with measurements in the (X, Y), (X, Z) and (Y, Z) planes. We apply both measurement calculus and the stabiliser formalism to derive our main theorem which for the first time gives a full characterization of the deterministic computation in the oneway model. We present several examples to show how our result improves over the traditional notion of flow, such as geometries (entanglement graph with input and output) with no flow but having generalized flow and we discuss how they lead to an optimal implementation of the unitaries. More importantly one can also obtain a better quantum computation depth with the generalized flow rather than with flow. We believe our characterization result is particularly essential for the study of the algorithms and complexity in the oneway model. Generalized Flow and Determinism 2 1.
Complementarity in categorical quantum mechanics
, 2010
"... We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that ( ..."
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Cited by 23 (7 self)
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We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a ‘pointfree’ definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.
TemperleyLieb Algebra: From Knot Theory to . . .
"... Our aim in this paper is to trace some of the surprising and beautiful connections which are beginning to emerge between a number of apparently disparate topics. ..."
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Cited by 20 (4 self)
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Our aim in this paper is to trace some of the surprising and beautiful connections which are beginning to emerge between a number of apparently disparate topics.