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Modeling an adiabatic quantum computer via an exact map to a gas of particles

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posted on 17.12.2015 by Alexandre Zagoskin, Sergey Saveliev, Franco Nori
We map adiabatic quantum evolution on the classical Hamiltonian dynamics of a 1D gas (Pechukas gas) and simulate the latter numerically. This approach turns out to be both insightful and numerically efficient, as seen from our example of a CNOT gate simulation. For a general class of Hamiltonians we show that the escape probability from the initial state scales no faster than |\dot{\lambda}|^{\gamma}, where |\dot{\lambda}| is the adiabaticity parameter. The scaling exponent for the escape probability is \gamma = 1/2 for all levels, except the edge (bottom and top) ones, where \gamma <~1/3. In principle, our method can solve arbitrarily large adiabatic quantum Hamiltonians.

Funding

This work was supported by NSA, LPS, ARO, NSF grant No. EIA-0130383, JSPS-RFBR 06-02-91200, MEXT Grant-in-Aid No. 18740224, EPSRC via No. EP/D072581/1 and the NSERC Discovery Grants Program (Canada)

History

School

  • Science

Department

  • Physics

Published in

Phys. Rev. Lett.

Volume

98

Pages

120503 - ?

Citation

ZAGOSKIN, A.M., SAVEL'EV, S. and NORI, F., 2007. Modeling an adiabatic quantum computer via an exact map to a gas of particles. Physical Review Letters, 98, 120503.

Publisher

© American Physical Society

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2007

Notes

This article was published in the journal, Physical Review Letters [© American Physical Society] and the definitive version is available at: http://dx.doi.org/10.1103/PhysRevLett.98.120503

ISSN

0031-9007

eISSN

1079-7114

Language

en

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