Qubitless Quantum Logic
Richard B. Kassman,
Gennady P. Berman,
Vladimir I. Tsifrinovich,
and Gustavo V. Lo
Received February 12, 2002; accepted February 17, 2003
We discuss the implementation of quantum logic in a system of strongly interacting
particles. The implementation is qubitless since ‘‘logical qubits’’ do not correspond
to any well-deﬁned physical substates. As an illustration, we present the results of
simulations of the quantum controlled-NOT gate and Shor’s algorithm for a chain of
spin-1/2 particles with Heisenberg coupling. Our proposal extends quantum
information processing theory to systems with permanent strong coupling between
the two-state subsystems.
KEY WORDS: Qubits; quantum logic; quantum information; Heisenberg
coupling; Shor’s algorithm.
PACS: 03.67.Lx; 03.65.Ta.
Current quantum computation and quantum information processing theory
is based on the manipulation of two-state subsystems known as physical
(The physical qubits need not be identical to the binary digits
used for encoding information, which are called logical qubits). One begins
with a system of weakly interacting or noninteracting physical qubits and, in
order to implement quantum logic gates, one either applies short pulses of
an external ﬁeld or ‘‘turns on’’ strong coupling between the qubits for short
Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico
Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street,
Urbana, Illinois 61801.
IDS Department, Polytechnic University, Six Metrotech Center, Brooklyn, New York 11201.
Departamento de Fı
sica, Universidad de Guadalajara, Corregidora 500, SR 44420,
Guadalajara, Jalisco, Mexico.
To whom correspondence should be addressed. E-mail: firstname.lastname@example.org
Quantum Information Processing, Vol. 1, No. 6, December 2002 (# 2003)
1570-0755/02/1200–0425/0 # 2003 Plenum Publishing Corporation