Using nuclear magnetic resonance techniques with a solution of chloroform molecules we implement Grover's search algorithm for a system with four states. By performing a tomographic reconstruction of the density matrix during the computation good agreement is seen between theory and experiment. This provides the first complete experimental demonstration of loading an initial state into a quantum computer, performing a computation requiring fewer steps than on a classical computer, and then reading out the final state. [S0031-9007(98)05850-5]

We show that quantum computation is possible with mixed states instead of pure states as inputs. This is performed by embedding within the mixed state a subspace that transforms like a pure state and that can be identified by labelling based on logical (spin), temporal, or spatial degrees of freedom. This permits quantum computation to be realized with bulk ensembles far from the ground state. Experimental results are presented for quantum gates and circuits implemented with liquid nuclear magnetic resonance techniques and verified by quantum state tomography.

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The catalytic desulfurization of some organosulfur compounds has been proposed to proceed through an intermediate containing a metal-sulfur multiple bond which reacts with H 2 . 1-5 However, the activation of H 2 by a terminal MdS bond has not been observed in a discrete homogenous system. 6 In this communication, we report the synthesis of the terminal decamethyltitanocene sulfido complex Cp* 2 Ti(S)py (1, py ) pyridine) and its reactivity toward H-H and H-Si bonds. We also report the synthesis of the corresponding disulfide complex Cp* 2 Ti-(S 2 ) (2) and describe its reactivity toward dihydrogen.The decamethyltitanocene ethylene complex Cp* 2 Ti-(CH 2 CH 2 ) 7 (3) is a useful starting material for the synthesis of titanocene oxo, 8 imido, 9 and diazoalkane 10 complexes. This compound is also an excellent synthon for 1. Addition of a suspension of S 8 ( 1 / 8 equiv) to a toluene solution of 3 and py (5 equiv) results in an immediate color change from green to red. Subsequent reduction of the solvent volume, addition of pentane, and cooling to -40°C produce red crystals of 1 in 76% yield. Alternatively, 1 can be synthesized by addition of H 2 S (1 equiv) to a cold solution of 3 and py in THF, although in this case the product is isolated in much lower (ca. 30%) yields. The structure of 1 has been determined by X-ray diffraction; an ORTEP diagram is shown in Figure 1. The Ti-S bond length of 2.217(1) Å is longer than that found for other terminal titanium sulfido bonds 11-13 and is slightly longer than the value predicted for [Cp 2 TiS] using ab initio methods. 14,15 The geometry about the titanium center is very similar to that found in the analogous oxo compound, 8 although the Ti-N bond length is slightly longer (2.245(3) vs 2.215(4) Å) and the E-Ti-N bond angle is slightly wider (93.91(7)°vs 90.8(1)°) in the sulfido complex. At room temperature, the 300 MHz 1 H NMR spectrum shows a sharp Cp* resonance and two broadened peaks assigned to the meta and para pyridine proton resonances; the ortho proton resonances are broadened into the baseline. The broad pyridine resonances indicate that the pyridine ligand is dissociating reversibly from the metal center on the NMR time scale.Placing a degassed toluene-d 8 solution of 1 under H 2 (1 atm) results in a color change from red to yellow. The room temperature 300 MHz 1 H NMR spectrum of the yellow solution shows only a new Cp* resonance and peaks assignable to free py. Attempts to isolate the reaction product by removal of solvent from the yellow solution have resulted only in recovery of 1, indicating that the reaction is readily reversible. 16,17 However, cooling the solution to 273 K results in the decoalescence of resonances assignable to free py, free H 2 , and the hydride and hydrosulfido protons of Cp* 2 Ti(SH)H (4) (Scheme 1). 18 The 2D EXSY 1 H NMR spectrum 19 of this solution at 253 K ( Figure 2) shows that exchange is occurring between the H 2 , hydride, and hydrosulfido protons. Interestingly, the cross peaks between the hydride and hydrosulfido resona...

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.