Quantum Information Processing, Vol. 4, No. 2, June 2005 (© 2005)
Ergodic Quantum Computing
Dominik Janzing and Pawel Wocjan
Received July 22, 2004; accepted February 25, 2005
We propose a (theoretical) model for quantum computation where the result can
be read out from the time average of the Hamiltonian dynamics of a 2-dimensional
crystal on a cylinder. The Hamiltonian is a spatially local interaction among
Wigner–Seitz cells containing six qubits. The quantum circuit that is simulated
is speciﬁed by the initialization of program qubits. As in Margolus’ Hamiltonian
cellular automaton (implementing classical circuits), a propagating wave in a
clock register controls asynchronously the application of the gates. However, in
our approach all required initializations are basis states. After a while the syn-
chronizing wave is essentially spread around the whole crystal. The circuit is
designed such that the result is available with probability about 1/4 despite of the
completely undeﬁned computation step. This model reduces quantum computing to
preparing basis states for some qubits, waiting, and measuring in the computa-
tional basis. Even though it may be unlikely to ﬁnd our speciﬁc Hamiltonian in
real solids, it is possible that also more natural interactions allow ergodic quantum
KEY WORDS: Quantum cellular automata; thermodynamics of computation;
Hamiltonian of a quantum computer; solid state quantum computing.
The question which control operations are necessary to achieve univer-
sal quantum computing is essential for quantum computing research.
The standard model of quantum computation requires (1) preparation
of basis states, (2) implementation of single and two-qubit gates, and
(3) single-qubit measurements in the computational basis. Meanwhile there
are many proposals that reduce or modify the set of necessary control
operations (see e.g. Refs. 1–5). Common to all those models is that the
program is encoded in a sequence of control operations.
IAKS Prof. Beth, Arbeitsgruppe Quantum Computing, Universit
at Karlsruhe, Am Fasanen-
garten 5, 76 131 Karlsruhe, Germany. E-mail: email@example.com, firstname.lastname@example.org
1570-0755/05/0600-0129/0 © 2005 Springer Science+Business Media, Inc.