  Liquid crystals offer several advantages as solvents for molecules used for
nuclear magnetic resonance quantum computing (NMRQC). The dipolar coupling
between nuclear spins manifest in the NMR spectra of molecules oriented by a
liquid crystal permits a significant increase in clock frequency, while short
spin-lattice relaxation times permit fast recycling of algorithms, and save
time in calibration and signal-enhancement experiments. Furthermore, the use of
liquid crystal solvents offers scalability in the form of an expanded library
of spin-bearing molecules suitable for NMRQC. These ideas are demonstrated with
the successful execution of a 2-qubit Grover search using a molecule
($^{13}$C$^{1}$HCl$_3$) oriented in a liquid crystal and a clock speed eight
times greater than in an isotropic solvent. Perhaps more importantly, five
times as many logic operations can be executed within the coherence time using
the liquid crystal solvent.
