Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer

The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubit-based quantum computer.     

A Titration Microcalorimetric Study of the Effects of Halide Counterions on Vesicle-Forming Aggregation in Aqueous Solution of Branched-Chain Alkylpyridinium Surfactants

Titration microcalorimetry is used to study the influences of iodide, bromide, and chloride counterions on the aggregation of vesicle-forming 1-methyl-4-(2-pentylheptyl)pyridinium halide surfactants. Formation of vesicles by these surfactants was characterised using transmission electron microscopy. When the counterion is changed at 303 K through the series iodide, bromide, to chloride, the critical vesicular concentration (cvc) increases and the enthalpy of vesicle formation changes from exo- to endothermic. With increase in temperature to 333 K, vesicle formation becomes strongly exothermic. Increasing the temperature leads to a decrease in enthalpy and entropy of vesicle formation for all three surfactants. However the standard Gibbs energy for vesicle formation is, perhaps surprisingly, largely unaffected by an increase in temperature, as a consequence of a compensating change in both standard entropy and standard enthalpy of vesicle formation. Interestingly, standard isobaric heat capacities of vesicle formation are negative, large in magnitude but not strikingly dependent on the counterion. We conclude that the driving force for vesicle formation can be understood in terms of overlap of the thermally labile hydrophobic hydration shells of the alkyl chains. Copyright 2000 Academic Press.     

Reaction of bis(phosphine)(hydrotris(3,5-dimethylpyrazolyl)borato)rhodium(I) with phenylacetylene,p-nitrobenzaldehyde,and triphenyltin hydride: structures of [Rh(Tp)(PPh(3))(2)], [Rh(Tp)(H)(C(2)Ph)(P(4-C(6)H(4)F)(3))], [Rh(Tp)(H)(COC(6)H(4)-4-NO(2))(PPh(3))], and [Rh(Tp)(H)(SnPh(3))(PPh(3))

The complexes [Rh(Tp)(PPh(3))(2)] (1a) and [Rh(Tp)(P(4-C(6)H(4)F)(3))(2)] (1b) combine with PhC(2)H, 4-NO(2)-C(6)H(4)CHO and Ph(3)SnH to give [Rh(Tp)(H)(C(2)Ph)(PR(3))] (R = Ph, 2a; R = 4-C(6)H(4)F, 2b), [Rh(Tp)(H)(COC(6)H(4)-4-NO(2))(PR(3))] (R = Ph, 3a), and [Rh(Tp)(H)(SnPh(3))(PR(3))] (R = Ph, 4a; R = 4-C(6)H(4)F, 4b) in moderate to good yield. Complexes 1a, 2b, 3a, and 4a have been structurally characterized. In 1a the Tp ligand is bidentate, in 2b, 3a, and 4a it is tridentate. Crystal data for 1a: space group P2(1)/c; a = 11.9664(19), b = 21.355(3), c = 20.685(3) A; beta = 112.576(7) degrees; V = 4880.8(12) A(3); Z = 4; R = 0.0441. Data for 2b: space group P(-)1; a = 10.130(3), b = 12.869(4), c = 17.038(5) A; alpha = 78.641(6), beta = 76.040(5), gamma = 81.210(6) degrees; V = 2100.3(11) A(3); Z = 2; R = 0.0493. Data for 3a: space group P(-)1; a = 10.0073(11), b = 10.5116(12), c = 19.874(2) A; alpha = 83.728(2), beta = 88.759(2), gamma = 65.756(2) degrees; V =1894.2(4) A(3); Z = 2; R = 0.0253. Data for 4a: space group P2(1)/c; a = 15.545(2), b = 18.110(2), c = 17.810(2) A; beta = 95.094(3) degrees; V = 4994.1(10) A(3); Z = 4; R = 0.0256. NMR data ((1)H, (31)P, (103)Rh, (119)Sn) are also reported.