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Quantum Walks on Graphs
, 2002
"... We set the ground for a theory of quantum walks on graphsthe generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible. However, by suitably relaxing the definition, we can obtain a meas ..."
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Cited by 122 (6 self)
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We set the ground for a theory of quantum walks on graphsthe generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible. However, by suitably relaxing the definition, we can obtain a
UNIVERSAL MIXING OF QUANTUM WALK ON GRAPHS
, 2007
"... We study the set of probability distributions visited by a continuoustime quantum walk on graphs. An edgeweighted graph G is universal mixing if the instantaneous or average probability distribution of the quantum walk on G ranges over all probability distributions on the vertices as the weights a ..."
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Cited by 5 (0 self)
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We study the set of probability distributions visited by a continuoustime quantum walk on graphs. An edgeweighted graph G is universal mixing if the instantaneous or average probability distribution of the quantum walk on G ranges over all probability distributions on the vertices as the weights
DYNAMICS AND CONTROL THEORY OF QUANTUM WALKS ON GRAPHS By
, 2010
"... Abstract. We present a study on the control theory and the dynamics of quantum walks on graphs. A controllability analysis is provided to characterize the set of possible states for such systems using algebraic and graph theoretic methods. Algorithms are described to drive the state of quantum walks ..."
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Abstract. We present a study on the control theory and the dynamics of quantum walks on graphs. A controllability analysis is provided to characterize the set of possible states for such systems using algebraic and graph theoretic methods. Algorithms are described to drive the state of quantum
2002), Mixing in continuous quantum walk on graphs
"... Classical random walks on wellbehaved graphs are rapidly mixing towards the uniform distribution. Moore and Russell showed that a continuous quantum walk on the hypercube is instantaneously uniform mixing. We show that the continuoustime quantum walks on other wellbehaved graphs do not exhibit th ..."
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Cited by 2 (1 self)
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Classical random walks on wellbehaved graphs are rapidly mixing towards the uniform distribution. Moore and Russell showed that a continuous quantum walk on the hypercube is instantaneously uniform mixing. We show that the continuoustime quantum walks on other wellbehaved graphs do not exhibit
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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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
Results 1  10
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238,406