Theory of Quantum Annealing of an Ising Spin Glass
Giuseppe E. Santoro,1
Roman Marto
ák,23
Erio Tosatti,14*
Roberto Car5
Probing the lowest energy configuration of a complex system by
quantum annealing was recently found to be more effective than its
classical, thermal counterpart. By comparing classical and quantum
Monte Carlo annealing protocols on the two-dimensional random Ising
model (a prototype spin glass), we confirm the superiority of quantum
annealing relative to classical annealing. We also propose a theory of
quantum annealing based on a cascade of Landau-Zener tunneling events.
For both classical and quantum annealing, the residual energy after
annealing is inversely proportional to a power of the logarithm of the
annealing time, but the quantum case has a larger power that makes it
faster.
1 Scuola Internazionale Superiore di Studi
Avanzati (SISSA) and Istituto Nazionale per la Fisica della Materia
(INFM) (Unità di Ricerca SISSA), I-34014 Trieste, Italy.
2 Swiss Centre for Scientific Computing, CH-6928
Manno, Switzerland, and Department of Physical Chemistry,
ETH-Zürich, CH-8093 Zürich, Switzerland.
3 Department of Physics, Slovak Technical University
(FEI), 81219 Bratislava, Slovakia.
4 International
Center for Theoretical Physics (ICTP), Post Office Box 586, I-34100
Trieste, Italy.
5 Department of Chemistry and
Princeton Materials Institute, Princeton University, Princeton, NJ
08544, USA.
*
To whom correspondence should be addressed. E-mail:
tosatti{at}sissa.it
