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Anderson localization makes adiabatic quantum optimization fail
TLDR
It turns out 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, which implies that unfortunately, adiABatic quantum optimization fails: the system gets trapped in one of the numerous local minima.
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 time
Quantum Walks Can Find a Marked Element on Any Graph
TLDR
This work solves an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph by introducing a notion of interpolation between the random walk P and the absorbing walk P, whose marked states are absorbing.
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.
Routing entanglement in the quantum internet
TLDR
This work considers how a quantum network—nodes equipped with limited quantum processing capabilities connected via lossy optical links—can distribute high-rate entanglement simultaneously between multiple pairs of users, and develops protocols for such quantum “repeater” nodes, which enable a pair of users to achieve large gains inEntanglement rates over using a linear chain of quantum repeaters by exploiting the diversity of multiple paths in the network.
Efficient quantum algorithm for dissipative nonlinear differential equations
TLDR
A lower bound on the worst-case complexity of quantum algorithms for general quadratic differential equations is provided, showing that the problem is intractable for $R \ge \sqrt{2}$.
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 an
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 this
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 quantum
Adiabatic quantum optimization fails for random instances of NP-complete problems
TLDR
It is shown that because of a phenomenon similar to Anderson localization, 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, which implies that adi abatic quantum optimization also fails for these instances by getting stuck in a local minimum, unless the computation is exponentially long.
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