Quantum computing is a vast and fascinating interdisciplinary project of the
21st century. Research and development in this monumental enterprise involve
just about every field of science and engineering. In this volume, we focus on
two important disciplines–mathematics and physics. The choice is made with
good reasons:
(1) Mathematics and mathematicians have played major roles in the development
of quantum computation. In the middle 1990’s Peter Shor’s
quantum factoring algorithm generated tremendous enthusiasm for the
push to build the quantum computer. Shor’s algorithm was the first example
showing that, in principle, quantum computers could out-perform
classical digital computers on problems of significance. This opened
wide the field for discovery of new quantum algorithms. This search
has gone on in tandem with the search for new principles and techniques
that will make the new computers practical and actual. Mathematics
participates in this process at all levels.
(2) Physicists and engineers are the principal players in the design and evolution
of the quantum computer. The technological aspect of building a
scalable quantum computer within a reasonable time horizon is crucial
for the field to remain viable. Recent advances in hardware development
are extremely encouraging. Such quantum technology is the material
cornerstone of quantum computing. The impact of this research goes
well beyond quantum computing, reaching nanotechnology, chemical
physics, condensed matter physics and the fundamental nature of matter
at the quantum mechanical level.