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Quantum entanglement
, 2007
"... Contents All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism — entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger — waited over 70 years to enter to laborat ..."
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Contents All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism — entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger — waited over 70 years to enter to laboratories as a new resource as real as energy.
Simulating quantum computation by contracting tensor networks
 SIAM Journal on Computing
, 2005
"... The treewidth of a graph is a useful combinatorial measure of how close the graph is to a tree. We prove that a quantum circuit with T gates whose underlying graph has treewidth d can be simulated deterministically in T O(1) exp[O(d)] time, which, in particular, is polynomial in T if d = O(logT). Am ..."
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Cited by 30 (1 self)
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The treewidth of a graph is a useful combinatorial measure of how close the graph is to a tree. We prove that a quantum circuit with T gates whose underlying graph has treewidth d can be simulated deterministically in T O(1) exp[O(d)] time, which, in particular, is polynomial in T if d = O(logT). Among many implications, we show efficient simulations for quantum formulas, defined and studied by Yao (Proceedings of the 34th Annual Symposium on Foundations of Computer Science, 352–361, 1993), and for logdepth circuits whose gates apply to nearby qubits only, a natural constraint satisfied by most physical implementations. We also show that oneway quantum computation of Raussendorf and Briegel (Physical Review Letters, 86:5188– 5191, 2001), a universal quantum computation scheme with promising physical implementations, can be efficiently simulated by a randomized algorithm if its quantum resource is derived from a smalltreewidth graph.
Synthesis of quantum logic circuits
 IEEE Trans. on ComputerAided Design
"... The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits [10] to the attention of the Electronic Design Automation community [18, 28, 7, 27, 17]. We discuss efficient quantum logic circuits which p ..."
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Cited by 28 (5 self)
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The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits [10] to the attention of the Electronic Design Automation community [18, 28, 7, 27, 17]. We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the statespace of an nqubit register is not finite and contains exponential superpositions of classical bit strings. Our proposed circuits are asymptotically optimal for respective tasks and improve earlier published results by at least a factor of two. The circuits for generic quantum computation constructed by our algorithms are the most efficient known today in terms of the number of most expensive gates (quantum controlledNOTs). They are based on an analogue of the Shannon decomposition of Boolean functions and a new circuit block, quantum multiplexor, that generalizes several known constructions. A theoretical lower bound implies that our circuits cannot be improved by more than a factor of two. We additionally show how to accommodate the severe architectural limitation of using only nearestneighbor gates that is representative of current implementation technologies. This increases the number of gates by almost an order of magnitude, but preserves the asymptotic optimality of gate counts. 1
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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Cited by 28 (7 self)
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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
Quantum computing without entanglement
, 2004
"... It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability of the outcome after a fixed number of oracle calls. Using ..."
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Cited by 12 (1 self)
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It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability of the outcome after a fixed number of oracle calls. Using a separable (that is, unentangled) state, we show that the Deutsch–Jozsa problem and the Simon problem can be solved more reliably by a quantum computer than by the best possible classical algorithm, even probabilistic. We conclude that: (a) entanglement is not essential for quantum computing; and (b) some advantage of quantum algorithms over classical algorithms persists even when the quantum state contains an arbitrarily small amount of information—that is, even when the state is arbitrarily close to being totally mixed.
Communication Links for Distributed Quantum Computation
, 2007
"... Distributed quantum computation requires quantum operations that act over a distance on errorcorrection encoded states of logical qubits, such as the transfer of qubits via teleportation. We evaluate the performance of several quantum error correction codes, and find that teleportation failure rat ..."
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Cited by 10 (2 self)
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Distributed quantum computation requires quantum operations that act over a distance on errorcorrection encoded states of logical qubits, such as the transfer of qubits via teleportation. We evaluate the performance of several quantum error correction codes, and find that teleportation failure rates of one percent or more are tolerable when two levels of the [[23,1,7]] code are used. We present an analysis of performing quantum error correction (QEC) on QECencoded states that span two quantum computers, including the creation of distributed logical zeroes. The transfer of the individual qubits of a logical state may be multiplexed in time or space, moving serially across a single link, or in parallel across multiple links. We show that the performance and reliability penalty for using serial links is small for a broad range of physical parameters, making serial links preferable for a large, distributed quantum multicomputer when engineering difficulties are considered. Such a multicomputer will be able to factor a 1,024bit number using Shor’s algorithm with a high probability of success.
Quantum convolutional codes: fundamentals
, 2004
"... We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used in similar circumstances in classical communication. In this ..."
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Cited by 9 (0 self)
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We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used in similar circumstances in classical communication. In this article, we provide an efficient polynomial formalism for describing their stabilizer group, derive an online encoding circuit with linear gate complexity and study error propagation together with the existence of online decoding. Finally, we provide a maximum likelihood error estimation algorithm with linear classical complexity for any memoryless channel. 1
Climbing mount scalable: Physical resource requirements for a scalable quantum computer
 Found. Phys
, 2002
"... The primary resource for quantum computation is Hilbertspace dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources pl ..."
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Cited by 8 (0 self)
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The primary resource for quantum computation is Hilbertspace dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubitbased quantum computer. KEY WORDS: quantum information; quantum computation; entanglement; quantum mechanics; scalability.