One of the main issues in liquid-state NMR QIP is the highly mixed
initial state. The methods for extracting pseudopure states are not
practical for more than 
(or so) nuclear spins. The problem is
that for these methods, the pseudopure state signal decreases
exponentially with the number of qubits prepared while the noise level
is constant. This exponential loss limits the ability to explore and
benchmark standard quantum algorithms even in the absence of
noise. There are in fact ways in which liquid-state NMR can be
usefully applied to many more qubits. The first and less practical is
to use computational cooling for a (unrealistically) large number of
spins to obtain less mixed initial states. Versions of this technique
have been studied and used in NMR to increase signal to
noise [39]. The second is to use the one-qubit model
of quantum computation instead of trying to realize pseudopure
states. For this purpose, liquid-state NMR is limited only by
relaxation noise and pulse control errors, not by the number of
qubits. Noise still limits the number of useful operations, but
non-trivial physics simulations are believed to be possible with less
than 100 qubits [40]. Remarkably, a one-qubit quantum
computer can efficiently obtain a significant amount of information
about the spectrum of a Hamiltonian that can be emulated on a quantum
computer [37,41,42].
Consequently, although QIP with molecules in liquid state cannot
realistically be used to implement standard quantum algorithms
involving more than about 
qubits, its capabilities have the
potential of exceeding the resource limitations of available classical
computers for some applications.