Quantum Information Processing

, Volume 14, Issue 12, pp 4731–4749 | Cite as

Challenges of adiabatic quantum evaluation of NAND trees

Article

Abstract

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 \(O(\sqrt{N})\) 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 \(\frac{N^{2}}{\log {N^{2}}}\) gap.

Keywords

Quantum adiabatic computation Tree evaluation Spectrum evaluation Numerical analysis 

Mathematics Subject Classification

81P68 68Q05 68Q10 68Q12 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.QCG/LNCCPetrópolisBrazil

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