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Hitting time for quantum walks on the hypercube (8 pages)
Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting timeExpand
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Quantum Walks Can Find a Marked Element on Any Graph
TLDR
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. Expand
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Anderson localization makes adiabatic quantum optimization fail
TLDR
We show that due to a phenomenon similar to Anderson localization, exponentially small gaps appear close to the end of the adiabatic algorithm for large random instances of NP-complete problems. Expand
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Quantum walks with infinite hitting times
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite.Expand
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Hitting time for the continuous quantum walk
We define the hitting (or absorbing) time for the case of continuous quantum walks by measuring the walk at random times, according to a Poisson process with measurement rate $\lambda$. From thisExpand
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Routing entanglement in the quantum internet
TLDR
We develop protocols for such quantum “repeater” nodes, which enable a pair to achieve large gains in entanglement rates over using a linear chain of quantum repeaters, by exploiting the diversity of multiple paths in the network. Expand
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Rate-distance tradeoff and resource costs for all-optical quantum repeaters
We present a resource-performance tradeoff of an all-optical quantum repeater that uses photon sources, linear optics, photon detectors and classical feedforward at each repeater node, but no quantumExpand
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Quantum walks on quotient graphs
A discrete-time quantum walk on a graph {gamma} is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has anExpand
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Adiabatic quantum optimization fails for random instances of NP-complete problems
TLDR
We show that an exponentially small eigenvalue gap appears in the spectrum of the adiabatic Hamiltonian for large random instances, very close to the end of the algorithm. Expand
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Quantum enigma machines and the locking capacity of a quantum channel
TLDR
The locking effect is a phenomenon which is unique to quantum information theory and represents one of the strongest separations between the classical and quantum theories of information. Expand
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