# 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Challenges of adiabatic quantum evaluation of NAND trees

, Volume 14 (12) – Oct 5, 2015
19 pages

Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-1137-3
Publisher site
See Article on Publisher Site

### 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 $$O(\sqrt{N})$$ 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.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 5, 2015

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