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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.
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore conjectured to be i
The system of electrons trapped in vacuum above the liquid helium surface displays the highest mobilities known in condensed matter physics. We provide a brief summary of the experimental and theoretical results obtained for this system. We then show
This paper describes recent progress using nuclear magnetic resonance (NMR) as a platform for implementing quantum information processing (QIP) tasks. The basic ideas of NMR QIP are detailed, examining the successes and limitations of liquid and soli
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental stud
This paper describes a general method for manipulation of nuclear spins in zero magnetic field. In the absence of magnetic fields, the spins lose the individual information on chemical shifts and inequivalent spins can only be distinguished by nuclea