A. Abeyesinghe

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The Markov Chain Monte Carlo method is at the heart of most fully-polynomial randomized approximation schemes for #P-complete problems such as estimating the permanent or the value of a polytope. It is therefore very natural and important to determine whether quantum computers can speed-up classical mixing processes based on Markov chains. To this end, we(More)
In this paper, we present a one-shot method for preparing pure entangled states between a sender and a receiver at a minimal cost of entanglement and quantum communication. In the case of preparing unentangled states, an earlier paper showed that a 2l-qubit quantum state could be communicated to a receiver by physically transmitting only l+o(l) qubits in(More)
We achieve a quantum speed-up of fully polynomial randomized approximation schemes (FPRAS) for estimating partition functions that combine simulated annealing with the Monte-Carlo Markov Chain method and use non-adaptive cooling schedules. The improvement in time complexity is twofold: a quadratic reduction with respect to the spectral gap of the underlying(More)
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