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Can quantum mechanics help distributed computing
 SIGACT News
"... We present a brief survey of results where quantum information processing is useful to solve distributed computation tasks. We describe problems that are impossible to solve using classical resources but that become feasible with the help of quantum mechanics. We also give examples where the use of ..."
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We present a brief survey of results where quantum information processing is useful to solve distributed computation tasks. We describe problems that are impossible to solve using classical resources but that become feasible with the help of quantum mechanics. We also give examples where the use of quantum information significantly reduces the need for communication. The main focus of the survey is on communication complexity but we also address other distributed tasks.
What Can Be Observed Locally? RoundBased Models for Quantum Distributed Computing
 COMPUTING, IN "23RD INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING (DISC) DISC, ESPAGNE ELCHE/ELX
, 2009
"... It is a wellknown fact that, by resorting to quantum processing in addition to manipulating classical information, it is possible to reduce the time complexity of some centralized algorithms, and also to decrease the bit size of messages exchanged in tasks requiring communication among several agen ..."
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It is a wellknown fact that, by resorting to quantum processing in addition to manipulating classical information, it is possible to reduce the time complexity of some centralized algorithms, and also to decrease the bit size of messages exchanged in tasks requiring communication among several agents. Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed computation is extended so as to apply quantum processing. This has been achieved in one of two distinct ways: (1) by initializing the system in a quantum entangled state, and/or (2) by applying quantum communication channels. In this paper, we explain why some of these prior claims are misleading, in the sense that they rely on changes to the model unrelated to quantum processing. On the positive side, we consider the aforementioned quantum extensions when applied to Linial’s wellestablished LOCAL model of distributed computing. For both types of extensions, we put forward valid proofofconcept examples of distributed problems whose round complexity
An algebraic language for distributed quantum computing
 IEEE Transactions on Computers
"... Abstract—A classical circuit can be represented by a circuit graph or equivalently by a Boolean expression. The advantage of a circuit graph is that it can help us to obtain an intuitive understanding of the circuit under consideration, whereas the advantage of a Boolean expression is that it is sui ..."
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Abstract—A classical circuit can be represented by a circuit graph or equivalently by a Boolean expression. The advantage of a circuit graph is that it can help us to obtain an intuitive understanding of the circuit under consideration, whereas the advantage of a Boolean expression is that it is suited to various algebraic manipulations. In the literature, however, quantum circuits are mainly drawn as circuit graphs, and a formal language for quantum circuits that has a function similar to that of Boolean expressions for classical circuits is still missing. Certainly, quantum circuit graphs will become unmanageable when complicated quantum computing problems are encountered, and in particular when they have to be solved by employing the distributed paradigm where complex quantum communication networks are involved. In this paper, we design an algebraic language for formally specifying quantum circuits in distributed quantum computing. Using this language, quantum circuits can be represented in a convenient and compact way, similar to the way that we use Boolean expressions in dealing with classical circuits. Moreover, some fundamental algebraic laws for quantum circuits expressed in this language are established. These laws form a basis of rigorously reasoning about distributed quantum computing and quantum communication protocols. Index Terms—Quantum computing, circuits, distributed systems I.
Distinguishing Views in Symmetric Networks: A Tight Lower Bound
, 2013
"... The view of a node in a portlabeled network is an infinite tree encoding all walks in the network originating from this node. We prove that for any integers n ≥ D ≥ 1, there exists a portlabeled network with at most n nodes and diameter at most D which contains a pair of nodes whose (infinite) vie ..."
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The view of a node in a portlabeled network is an infinite tree encoding all walks in the network originating from this node. We prove that for any integers n ≥ D ≥ 1, there exists a portlabeled network with at most n nodes and diameter at most D which contains a pair of nodes whose (infinite) views are different, but whose views truncated to depth Ω(D log(n/D)) are identical.
Model checking quantum Markov chains
, 2012
"... Although security of quantum cryptography is provable based on principles of quantum mechanics, it can be compromised by flaws in the design of quantum protocols. So, it is indispensable to develop techniques for verifying and debugging quantum cryptographic systems. Modelchecking has proved to be ..."
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Although security of quantum cryptography is provable based on principles of quantum mechanics, it can be compromised by flaws in the design of quantum protocols. So, it is indispensable to develop techniques for verifying and debugging quantum cryptographic systems. Modelchecking has proved to be effective in the verification of classical cryptographic protocols, but an essential difficulty arises when it is applied to quantum systems: the state space of a quantum system is always a continuum even when its dimension is finite. To overcome this difficulty, we introduce a novel notion of quantum Markov chain, especially suited for modelling quantum cryptographic protocols, in which quantum effects are encoded as superoperators labelling transitions, leaving the location information (nodes) being classical. Then we define a quantum extension of probabilistic computation tree logic (PCTL) and develop a modelchecking algorithm for quantum Markov chains.
Quantum leader election
, 2009
"... A group of n individuals A1,... An who do not trust each other and are located far away from each other, want to select a leader. This is the leader election problem, a natural extension of the coin flipping problem to n players. We want a protocol which will guarantee that an honest player will hav ..."
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A group of n individuals A1,... An who do not trust each other and are located far away from each other, want to select a leader. This is the leader election problem, a natural extension of the coin flipping problem to n players. We want a protocol which will guarantee that an honest player will have at least 1 n − chance of winning (∀ > 0), regardless of what the other players do (whether they are honest, cheating alone or in groups). It is known to be impossible classically. This work gives a simple algorithm that does it, based on the weak coin flipping protocol with arbitrarily small bias recently derived by Mochon [Moc]. The protocol is quite simple to achieve if the number of rounds is linear; We provide an improvement to logarithmic number of rounds. 1
66 Can Quantum Mechanics Help Distributed Computing?
"... After two columns on practical problems arising in current day technologies (multicores in Column 29; systems research in Column 30), this column takes a sharp turn towards the futuristic realm of quantum computations. More specifically, the column features two surveys of distributed quantum computi ..."
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After two columns on practical problems arising in current day technologies (multicores in Column 29; systems research in Column 30), this column takes a sharp turn towards the futuristic realm of quantum computations. More specifically, the column features two surveys of distributed quantum computing, which, unbeknownst to many distributed computing folks, is an active area of research. First, Anne Broadbent and Alain Tapp provide a broad overview of distributed computations and multiparty protocols that can benefit from quantum mechanics, most notably from entanglement. Some of these are unsolvable with classical computing, for example, pseudotelepathy. In other cases, like appointment scheduling, the problem’s communication complexity can be reduced by quantum means. Next, Vasil Denchev and Gopal Pandurangan critically examine the joint future of quantum computers and distributed computing, asking whether this is a new frontier... or science fiction. They give background to the lay reader on quantum mechanics concepts that provide added value over classical computing, (again, entanglement figures prominently). They also elaborate on the practical difficulties of implementing them. They then illustrate how these concepts can be exploited for two goals: (1) to distribute centralized quantum algorithms over multiple small quantum computers; and (2) to solve leader election in various distributed computing models. They conclude that the jury is still out on the costeffectiveness of quantum distributed computing. Both surveys outline open questions and directions for future research. Many thanks to Anne, Alain, Vasil and Gopal for their contributions! Call for contributions: I welcome suggestions for material to include in this column, including news, reviews, open problems, tutorials and surveys, either exposing the community to new and interesting topics, or providing new insight on wellstudied topics by organizing them in new ways.
Applications of an Entangled Quantum Internet
"... Physicists and engineers are making technical progress toward the creation of intercontinental quantum networks. But if they succeed, what new applications will a quantum Internet enable? This paper presents a series of potential uses, some fairly wellestablished and some highly speculative. The en ..."
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Physicists and engineers are making technical progress toward the creation of intercontinental quantum networks. But if they succeed, what new applications will a quantum Internet enable? This paper presents a series of potential uses, some fairly wellestablished and some highly speculative. The entanglement generated by a quantum network will be useful both as a digital computational resource, and as a gyroscopic reference, providing both phase (time) and directional information. Computational applications include the wellknown quantum key distribution (QKD) process and distributed leader election, as well as the traditional uses of networks to connect geographically distributed resources. The gyroscopic reference uses are more speculative, but include the possibility of improving some “Big Science ” projects by utilizing quantum entanglement to beat singlesystem quantum limits on precision measurements, including the accuracy of clocks. 1