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Quantum complexity theory
 in Proc. 25th Annual ACM Symposium on Theory of Computing, ACM
, 1993
"... Abstract. In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s model of a quantum Turing machine (QTM) [Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 97–117]. This constructi ..."
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Cited by 582 (5 self)
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Abstract. In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s model of a quantum Turing machine (QTM) [Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 97
An introduction to quantum complexity theory
 Collected Papers on Quantum Computation and Quantum Information Theory
, 2000
"... ..."
11 Quantum Complexity Theory II
"... In this section we introduce basic techniques for performing quantum computations. We will apply them to two problems: a problem by Deutsch and Jozsa and the prime factoring problem. 11.1 Quantum bits The simplest unit to apply quantum operations to is a single bit, called quantum bit or qubit in th ..."
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In this section we introduce basic techniques for performing quantum computations. We will apply them to two problems: a problem by Deutsch and Jozsa and the prime factoring problem. 11.1 Quantum bits The simplest unit to apply quantum operations to is a single bit, called quantum bit or qubit
10 Quantum Complexity Theory I
"... Just as the theory of computability had its foundations in the ChurchTuring thesis, computational complexity theory rests upon a modern strengthening of this thesis, which asserts that any “reasonable ” model of computation can be efficiently simulated on a probabilistic Turing machine (by “efficie ..."
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Just as the theory of computability had its foundations in the ChurchTuring thesis, computational complexity theory rests upon a modern strengthening of this thesis, which asserts that any “reasonable ” model of computation can be efficiently simulated on a probabilistic Turing machine (by
Parallelized Solution to Semidefinite Programmings in Quantum Complexity Theory
, 2010
"... In this paper we present an equilibrium value based framework for solving SDPs via the multiplicative weight update method which is different from the one in Kale’s thesis [Kal07]. One of the main advantages of the new framework is that we can guarantee the convertibility from approximate to exact ..."
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Cited by 3 (2 self)
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results QIP(2)⊆PSPACE [JUW09] and QMAM=PSPACE [JJUW09]. Furthermore, we provide a generic form of SDPs which can be solved in the similar way. By parallelizing every step in our solution, we are able to solve a class of SDPs in NC. Although our motivation is from quantum computing, our result will also
Quantum Gravity
, 2004
"... We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string theor ..."
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Cited by 566 (11 self)
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integral quantizations, coupling to matter, extensions to supergravity and higher dimensional theories, as well as applications to black holes, cosmology and Plank scale phenomenology. We describe the near term prospects for observational tests of quantum theories of gravity and the expectations that loop
The Jones polynomial: quantum algorithms and applications in quantum complexity theory
"... We analyze relationships between the Jones polynomial and quantum computation. First, we present two polynomialtime quantum algorithms which give additive approximations of the Jones polynomial, in the sense of Bordewich, Freedman, Lovász and Welsh, of any link obtained from a certain general famil ..."
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Cited by 37 (5 self)
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of the braid group which makes the underlying representation theory apparent, allowing us to provide an algorithm for approximating the HOMFLYPT twovariable polynomial of the trace closure of a braid at certain pairs of values as well. Next, we provide a selfcontained proof that any quantum computation can
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a
Quantum theory, the ChurchTuring principle and the universal quantum computer
, 1985
"... computer ..."
Axiomatic quantum field theory in curved spacetime
, 2008
"... The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincare invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globa ..."
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Cited by 692 (18 self)
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The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincare invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary
Results 1  10
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