Challenges of adiabatic quantum evaluation of NAND trees

Challenges of adiabatic quantum evaluation of NAND trees The quantum adiabatic algorithm solves problems by evolving a known initial state towards the ground state of a Hamiltonian encoding the answer to a problem. Although continuous- and discrete-time quantum algorithms exist capable of evaluating tree graphs consisting of N vertexes in $$O(\sqrt{N})$$ O ( N ) time, a quadratic improvement over their classical counterparts, no quantum adiabatic procedure is known to exist. In this work, we present a study of the main issues and challenges surrounding quantum adiabatic evaluation of NAND trees. We focus on a number of issues ranging from: (1) mapping mechanisms; (2) spectrum analysis and remapping; (3) numerical evaluation of spectrum gaps; and (4) algorithmic procedures. These concepts are then used to provide numerical evidence for the existence of a $$\frac{N^{2}}{\log {N^{2}}}$$ N 2 log N 2 gap. Quantum Information Processing Springer Journals

Challenges of adiabatic quantum evaluation of NAND trees

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Springer US
Copyright © 2015 by Springer Science+Business Media New York
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
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