Quantum Information Processing, Vol. 7, No. 1, February 2008 (© 2008)
Controllability and Universal Three-qubit Quantum
Computation with Trapped Electron States
L. H. Pedersen
and C. Rangan
Received August 25, 2007; accepted November 15, 2007; Published online: February 16, 2008
We show how to control and perform universal three-qubit quantum computation
with trapped electron quantum states. The three qubits are the electron spin, and
the ﬁrst two quantum states of the cyclotron and axial harmonic oscillators. We
explicitly show how universal three-qubit gates can be performed. As an exam-
ple of a quantum algorithm, we outline the implementation of the three-qubit
Deutsch-Jozsa algorithm in this system.
KEY WORDS: trapped electron quantum computation; Deutsch-Jozsa
algorithm; inﬁnite-dimensinal quantum control; coherent control.
PACS: 03.67.-a; 32.80.Qk; 42.50.Vk.
Since the eighties, much effort has been put into the study of quan-
tum computers, and various proposals for the physical implementation
have been put forward in very different ﬁelds such as those of cold
, quantum dots
and neutral atoms.
imental implementations have, however, been few and limited to a low
number of qubits. It is therefore interesting to study alternative candidates
for quantum computers.
In the present work we study a scheme put forward for instance in
Ref. 5 in which an electron trapped in a Penning trap is considered a pos-
sible realization of quantum logic. Advantages such as an almost complete
Lundbeck Foundation Theoretical Center for Quantum System Research, Department
of Physics and Astronomy, University of Aarhus, 8000 Arhus C, Denmark. E-mail:
Department of Physics, University of Windsor, Windsor, Ontario, Canada N9B 3P4.
To whom correspondence should be addressed.
1570-0755/08/0200-0033/0 © 2008 Springer Science+Business Media, LLC