Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 114, Issue 20, Pages E3909-E3916Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1619826114
Keywords
counterdiabatic driving; adiabatic gauge; transitionless driving; variational principle; complex systems
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Funding
- Fonds Wetenschappelijk Onderzoek
- Air Force Office of Scientific Research [FA9550-16-1-0334]
- National Science Foundation [DMR-1506340]
- Army Research Office [W911NF1410540]
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Counterdiabatic driving protocols have been proposed [Demirplak M, Rice SA (2003) J Chem Phys A 107: 9937-9945; Berry M (2009) J Phys A Math Theor 42: 365303] as a means to make fast changes in the Hamiltonian without exciting transitions. Such driving in principle allows one to realize arbitrarily fast annealing protocols or implement fast dissipationless driving, circumventing standard adiabatic limitations requiring infinitesimally slow rates. These ideas were tested and used both experimentally and theoretically in small systems, but in larger chaotic systems, it is known that exact counterdiabatic protocols do not exist. In this work, we develop a simple variational approach allowing one to find the best possible counterdiabatic protocols given physical constraints, like locality. These protocols are easy to derive and implement both experimentally and numerically. We show that, using these approximate protocols, one can drastically suppress heating and increase fidelity of quantum annealing protocols in complex many-particle systems. In the fast limit, these protocols provide an effective dual description of adiabatic dynamics, where the coupling constant plays the role of time and the counterdiabatic term plays the role of the Hamiltonian.
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