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Entanglement in Graph States and its Applications
Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows onlyExpand
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Graphical description of the action of local Clifford transformations on graph states
We translate the action of local Clifford operations on graph states into transformations on their associated graphs, i.e., we provide transformation rules, stated in purely graph theoretical terms,Expand
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Simulating quantum computers with probabilistic methods
  • M. V. D. Nest
  • Computer Science, Physics
  • Quantum Inf. Comput.
  • 9 November 2009
TLDR
We investigate the boundary between classical and quantum computational power. Expand
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Measurement-based quantum computation
Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics are harnessed and exploited. A number of models of quantum computationExpand
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Classical simulation of quantum computation, the gottesman-Knill theorem, and slightly beyond
  • M. V. D. Nest
  • Physics, Mathematics
  • Quantum Inf. Comput.
  • 6 November 2008
TLDR
We study classical simulation of quantum computation, taking the Gottesman-Knill theorem as a starting point. Expand
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Classical simulation complexity of extended Clifford circuits
TLDR
A class of classically simulatable quantum circuits which yields universal quantum computation if extended by a purely classical additional ingredient. Expand
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Fundamentals of universality in one-way quantum computation
In this paper, we build a framework allowing for a systematic investigation of the fundamental issue: 'Which quantum states serve as universal resources for measurement-based (one-way) quantumExpand
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Classical simulation versus universality in measurement-based quantum computation
We investigate for which resource states an efficient classical simulation of measurement-based quantum computation is possible. We show that the Schmidt-rank width, a measure recently introduced toExpand
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Simulating Quantum Circuits with Sparse Output Distributions
TLDR
We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one where only a polynomially small, a priori unknown subset of the measurement probabilities are nonzero. Expand
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Edge-local equivalence of graphs
The local complement G*i of a simple graph G at one of its vertices i is obtained by complementing the subgraph induced by the neighborhood of i and leaving the rest of the graph unchanged. IfExpand
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