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A Numerical Solution for Wootters Correlation
Abdul Hissami, Alberto Pretel, and E. Tamura
Pontificia Universidad Javeriana - Cali
Calle 18 118-250, Santiago de Cali, Colombia
{abdulh,apretel,tek}@javerianacali.edu.co
Abstract.
This paper describes QDsim, a parallel application designed
to compute the quantum concurrence by calculating the Wootters cor-
relation of a quantum system. The system is based on a two-level two
quantum dots inside a resonant cavity. A Beowulf-like cluster was used
for running QDsim. The application was developed using open, portable
and scalable software and can be controlled via a GUI client from a
remote terminal over either the Internet or a local network. A serial
version and three parallel models (shared memory, distributed memory
and hybrid -distributed/shared memory) using two different partitioning
schemes were implemented to assess their performance. Results showed
that the hybrid model approach using domain decomposition achieves
the highest performance (12
.
2
X
speedup in front of the sequential ver-
sion) followed by the distributed memory model (6
.
6
X
speedup). In both
cases, the numerical error is within 1
×
10
−
4
, which is accurate enough
for estimating the correlation trend.
Keywords:
Quantum Computing, Wootters Correlation, Density Ma-
trix, Parallel Algorithms, Parallel Models, Cluster Computing.
1 Introduction
Quantum Computing is a revolutionary field of Physics whose goal is increase
enormously the computing performance by using quantum mechanics laws to
create very small-scale processing units (a few atoms in size) thus surpassing the
limits of classic computing. This field studies different topics on the classic infor-
mation theory and its processing, e.g., quantum algorithms, quantum teleporta-
tion, quantum codes and error detection, and realization of quantum computers.
The latter topic investigates new forms of processing and information storage
at the nano scale. A variety of future candidate technologies for implementation
are currently being explored [1]; for example, superconductor quantum com-
puter, trapped-ion quantum computer, solid state Nuclear Magnetic Resonance
(NMR), Kane Quantum computers and Quantum Dot computers.
Nowadays, Quantum Dot computers are a promising technology for the real-
ization of quantum computers. Unfortunately, a Quantum Dot (QD) is not able
to retain its state for a long time. Consequently, the information is destroyed [1].
