At the current rate of progress, in about two decades the scaling of VLSI is
going to simultaneously hit many physical limits: a transistor will be one
atom wide, a memory cell will have just one electron per bit (and the cost of
the fab plant will be the GNP of the planet). If computers are to work any
faster, progress is going to have to come from a radically different
direction.
Quantum computation is an exciting prospect, because a quantum computer (if it
could be built) would be exponentially faster than a classical computer on
some problems. For example, a quantum computer could find prime factors in
polynomial time instead of the exponential time required by a classical
computer, thereby breaking conventional cryptographic codes.
The problem with building a quantum computer is that the quantum bits (called
qubits) simultaneously need to be protected from the environment so that they
retain their quantum phase, but they need to be coupled to the environment so
that initial conditions can be loaded, the calculation applied, and the
results read out. Because of these apparently contradictory constraints, it's
taken a heroic experimental effort to make just a 2 bit quantum computer. This
has been done in systems such as trapped ions, or cavity quantum
electrodynamics, that carefully isolate the qubits and cool them to their
ground state.
Neil Gershenfeld and Isaac Chuang have developed an entirely new approach to
quantum computation that promises to solve many of these problems. Instead of
carefully isolating a small number of qubits, we use a large thermal ensemble
(such as a cup of coffee). Such a system has ~10^23 degrees of freedom; by
applying RF pulses that excite nuclear magnetic resonances, we can create a
tiny deviation from equilibrium that acts just like a much smaller number of
pure qubits.
The nuclear spin is beautifully isolated from the environment; its spin
coherence can last for thousands of seconds. By representing the effective
computational qubits in such an ensemble, we get these very long coherence
times permitting thousands of logical operations before coherence is lost.
Further, because the bits are represented in an ensemble, it is possible to
continuously read out the quantum state (somthing that is of course impossible
for individual quantum degrees of freedom). Best of all, the most important
part of the experimental apparatus is built by nature in the form of ordinary
molecules.
Implementing such a quantum computer requires the mature techniques of
multiple pulse spin resonance. Using existing NMR spectrometers it will be
straightforward to reach about 10 qubits, enough to demonstrate for the first
time quantum superfast algorithms and quantum error correction, and to prepare
a range of unusual quantum states that have never been realized before (such
as the Greenberger-Horne-Zeilinger states that maximally violate Bell's
Theorem). The required instrumentation even promises to scale down to the
desktop, so that everyone could have a quantum co-processor.
Here is the first
paper on bulk spin resonance quantum computation (N. Gershenfeld and I.
Chuang, Science, 275, pp. 350-356, 1997).
More recent experimental and theoretical papers are available at the Physics
and Media Group's
publications page,
here is one of the first news articles
(The Economist, pp. 91-92, February 22, 1997),
Go to Chuang's archive on quantum
computation
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and here is a talk about it. 
Useful NMRQC resources