Visualization of the Quantum Fourier Transform
Using a Quantum Computer Simulator
Ioannis G. Karafyllidis
Received August 4, 2003; accepted September 4, 2003
The quantum Fourier transform (QFT) is a key subroutine of quantum algorithms
for factoring and simulation and is the heart of the hidden-subgroup problem, the
solution of which is expected to lead to the development of new quantum algorithms.
The QFT acts on the Hilbert space and alters the quantum mechanical phases and
probability amplitudes. Unlike its classical counterpart its schematic representation
and visualization are very difﬁcult. The aim of this work is to develop a schematic
representation and visualization of the QFT by running it on a quantum computer
simulator which has been constructed in the framework of this research. Base states,
superpositions of base states and entangled states are transformed and the
corresponding schematic representations are presented. The visualization of the
QFT presented here and the quantum computer simulator developed for this purpose
may become a useful tool for introducing the QFT to students and researches
without a strong background in quantum mechanics or Fourier analysis.
KEY WORDS: Quantum Fourier transform; quantum algorithms; quantum
computing; quantum simulation.
PACS: 03.67.-a, 03.67.Lx.
Quantum computers are far more efﬁcient that their classical counterparts
in factoring large numbers,
The quantum Fourier transform (QFT) is a key
subroutine of quantum algorithms for factoring and simulation and is the
heart of the hidden-subgroup problem, the solution of which is expected to
lead to the development of new quantum algorithms.
The QFT has been
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Quantum Information Processing, Vol. 2, No. 4, August 2003 (# 2004)
1570-0755/03/0800–0271/0 # 2004 Plenum Publishing Corporation