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Quadratic Fermionic Interactions Yield Hamiltonians with Large Ground-state Energy Gaps

Published

Author(s)

Dianne M. O'Leary, Michael J. O'Hara

Abstract

Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but required for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians, first considered by Lieb et al. We then prove that adiabatic quantum computing can realize the ground states of Hamiltonians with certain random interactions, as well as the ground states of one, two, and three-dimensional fermionic interaction lattices, in polynomial time. Finally, we use the Jordan-Wigner transformation to show that our results can be restated with Pauli operators in a surprisingly simple manner.
Citation
Physical Review A (Atomic, Molecular and Optical Physics)
Volume
79

Keywords

adiabatic quantum computing, fermionic interaction lattices, Jordan-Wigner transformation, Pauli operators, quadratic fermionic Hamiltonians

Citation

O'Leary, D. and O'Hara, M. (2009), Quadratic Fermionic Interactions Yield Hamiltonians with Large Ground-state Energy Gaps, Physical Review A (Atomic, Molecular and Optical Physics), [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=890014 (Accessed July 20, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created March 24, 2009, Updated February 19, 2017