Quantum Information Processing, Vol. 6, No. 2, April 2007 (© 2006)
Improved Gap Estimates for Simulating Quantum
Circuits by Adiabatic Evolution
Mary Beth Ruskai,
and Wolfgang Spitzer
Received May 23, 2006; accepted August 27, 2006; Published online December 12, 2006
We use elementary variational arguments to prove, and improve on, gap estimates
which arise in simulating quantum circuits by adiabatic evolution.
KEY WORDS: Adiabatic quantum computation; Quantum circuit simulation;
There are several models for quantum computation.
The quantum Tur-
ing machine model and the quantum circuit model are equivalent in the
sense that any algorithm that runs in polynomial time in one requires only
polynomial time in the other. There are also several “one-way” measure-
such as the cluster state model,
which can simu-
late any polynomial time quantum circuit in polynomial time.
In Ref. (4), Farhi et al. introduced quantum computation by adia-
batic evolution of a Hamiltonian and showed that it could be simulated
by a suitable quantum circuit. In this model, the time required is assumed
by authors. Reproduction permitted for non-commercial purposes.
Partially supported by the National Science Foundation under Grants DMS-0296084 and
Partially supported by the National Science Foundation under Grant DMS-0314228 and
by the National Security Agency and Advanced Research and Development Activity under
Army Research Ofﬁce contract number DAAD19-02-1-0065.
Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY 10012 USA.
Department of Mathematics, Tufts University, Medford, MA 02155 USA.
Department of Physics, International University of Bremen Campus Ring 8, 28759 Bremen,
Germany. E-mail: email@example.com
To whom correspondence should be addressed. E-mail: firstname.lastname@example.org
1570-0755/07/0400-0121/0 © 2006 Springer Science+Business Media, LLC