Quantum Information Processing, Vol. 4, No. 4, October 2005 (© 2005)
Implementation Schemes for the Factorized Quantum
Lattice-Gas Algorithm for the One Dimensional
Diffusion Equation Using Persistent-Current Qubits
David M. Berns
and T. P. Orlando
Received January 14, 2005; accepted May 4, 2005
We present two experimental schemes that can be used to implement the Factor-
ized Quantum Lattice-Gas Algorithm for the 1D Diffusion Equation with Persis-
tent-Current (PC) Qubits. One scheme involves biasing the PC Qubit at multiple
ﬂux bias points throughout the course of the algorithm. An implementation analo-
gous to that done in Nuclear Magnetic Resonance (NMR) Quantum Computing
is also developed. Errors due to a few key approximations utilized are discussed
and differences between the PC Qubit and NMR systems are highlighted.
KEY WORDS: Quantum Lattice-Gas; ﬂux qubit; diffusion; quantum
PACS: 03.67.Lx; 85.25.Cp.
Most algorithms designed for quantum computers will not best their clas-
sical counterparts until they are implemented with thousands of qubits.
For example, the factoring of binary numbers with a quantum computer is
estimated to be faster than a classical computer only when the length of
the number is greater than about 500 digits.
Accounting for error cor-
would bring the size of the needed quantum computer
to be in the thousands of qubits. In contrast, the Factorized Quantum
Lattice-Gas Algorithm (FQLGA)
for ﬂuid dynamics simulation, even
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Department of Electrical Engineering and Computer Science, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA.
To whom correpondence should be addressed. E-mail: dmb@MIT.edu
1570-0755/05/1000-0265/0 © 2005 Springer Science+Business Media, Inc.