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The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective

By Victor Bapst, Laura Foini, Florent Krzakala, Guilhem Semerjian and Francesco Zamponi

Abstract

151 pages, 21 figures - submitted to Physics ReportsAmong various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function (ground state energy). Random optimization problems provide a natural testbed to compare its efficiency with that of classical algorithms. These problems correspond to mean field spin glasses that have been extensively studied in the classical case. This paper reviews recent analytical works that extended these studies to incorporate the effect of quantum fluctuations, and presents also some original results in this direction

Topics: [ INFO.INFO-CC ] Computer Science [cs]/Computational Complexity [cs.CC], [ PHYS.COND.CM-SM ] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], [ PHYS.QPHY ] Physics [physics]/Quantum Physics [quant-ph]
Publisher: HAL CCSD
Year: 2012
OAI identifier: oai:HAL:hal-00738108v1
Provided by: Hal-Diderot
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