Quantum Information Processing, Vol. 6, No. 5, October 2007 (© 2007)
Quantum Mechanical Search and Harmonic
Jie-Hong R. Jiang,
and Cheng-En Wu
Received: February 5, 2007; accepted: August 5, 2007; Published online: September 21, 2007
Perturbation theory in quantum mechanics studies how quantum systems inter-
act with their environmental perturbations. Harmonic perturbation is a rare spe-
cial case of time-dependent perturbations in which exact analysis exists. Some
important technology advances, such as masers, lasers, nuclear magnetic reso-
nance, etc., originated from it. Here we add quantum computation to this list with
a theoretical demonstration. Based on harmonic perturbation, a quantum mechan-
ical algorithm is devised to search the ground state of a given Hamiltonian. The
intrinsic complexity of the algorithm is continuous and parametric in both time
T and energy E . More precisely, the probability of locating a search target of a
Hamiltonian in N -dimensional vector space is shown to be 1/(1 + cNE
for some constant c. This result is optimal. As harmonic perturbation provides
a different computation mechanism, the algorithm may suggest new directions in
realizing quantum computers.
KEY WORDS: quantum computation; complexity; Grover database search;
PACS : 03.67.Lx.
Quantum physics can in principle speed up solving the unsorted-database
search problem with a quadratic improvement over classical algorithms, as
was ﬁrst demonstrated by Grover
. This problem was originally formu-
lated as to identify a target item in the fewest queries to a black-box data-
base. An important reformulation by Farhi et al.
phrased the prob-
lem as to search the target state with some special eigenvalue of a given
Department of Electrical Engineering, National Taiwan University, Taipei 10617, Taiwan.
Department of Physics, University of California, Berkeley, CA 94720, USA.
Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan.
To whom correspondence should be addressed. E-mail: email@example.com
1570-0755/07/1000-0349/0 © 2007 Springer Science+Business Media, LLC