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Eigenlevel statistics of the quantum adiabatic algorithm
Marko Znidaric
We study the eigenlevel spectrum of quantum adiabatic algorithm for 3-satisfiability problem, focusing on single-solution instances. The properties of the ground state and the asso…
Exponential complexity of an adiabatic algorithm for an NP-complete problem
Marko Znidaric, Martin Horvat
We prove an analytical expression for the size of the gap between the ground and the first excited state of quantum adiabatic algorithm for the 3-satisfiability, where the initial…
Decoherence in regular systems
Marko Znidaric, Tomaz Prosen
We consider unitary evolution of finite bipartite quantum systems and study time dependence of purity for initial cat states -- coherent superpositions of Gaussian wave-packets. We…
Scaling of running time of quantum adiabatic algorithm for propositional satisfiability
Marko Znidaric
We numerically study quantum adiabatic algorithm for the propositional satisfiability. A new class of previously unknown hard instances is identified among random problems. We nume…