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.     

On strongly stable normal operators in Krein spaces

For bounded normal operators in Krein spaces we give a necessary and sufficient condition for strong stability. The same result for unitary operators was obtained by M.G.Krein [1] (see also [2]). For selfadjoint operators we refer to the papers of P.Jonas, H.Langer [3] and H.Langer [4].     

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.     

Rhodium-103 NMR of [Rh(X)(PPh3)3] [X = Cl, N3, NCO, NCS, N(CN)2, NCBPh3, CNBPh3, CN] and derivatives containing CO, isocyanide, pyridine, H2 and O2. Ligand, solvent and temperature effects

Rhodium-103 chemical shifts are reported for 62 compounds, namely [Rh(X)(PPh3)3] [X = Cl, N3, NCO, NCS, N(CN)2, NCBPh3, CNBPh3, CN] and derivatives formed by replacement of a phosphine by CO, xylyl isocyanide (XNC) and pyridine and/or by oxidative addition of H2 or O2 to give trans-[Rh(X)(PPh3)2(CO)] (delta in the range -816 to -368 ppm) trans-[Rh(X)(PPh3)2(XNC)] (delta -817 to -250 ppm), cis-[Rh(X)(PPh3)2(py)] (the trans isomer is formed with X = CN, CNBPh3) (delta -233 to 170 ppm), [Rh(X)(H)2(PPh3)3] (delta -611 to 119), trans-[Rh(X)(H)2(PPh3)2(py)] (delta -30 to 566 ppm), [Rh(X)(O2)(PPh3)3] (delta 1393 to 3273 ppm) and cis-[Rh(X)(O2)(PPh3)2(py)] (delta 1949 to 3374 ppm). For the majority of these compounds data were obtained from solutions in chloroform and in toluene at temperatures of 247 and 300 K; for [Rh(X)(PPh3)3] (delta -562 to -4 ppm) data are reported at a number of temperatures in the range 195-300 K for solutions in chloroform, toluene and dichloromethane and at 300 K for solutions in DMSO. The expected trend to lower delta(103Rh) with decreasing temperature (vibrational shielding) is observed for the dichloromethane data, but data from solutions {of [Rh(X)(PPh3)3]} in chloroform and toluene show a number of features which diverge from this pattern, i.e. shifts to higher delta are found to accompany a decrease in temperature, most noticeably where X = CN and Cl [on changing the solvent from dichloromethane to chloroform changes in delta(103Rh) of up to 172 ppm are observed]. These results are interpreted in terms of a hydrogen-bonded interaction with the solvent that is enhanced by the presence of a polarizable ligand (CN, Cl). With a ligand (O2CCF3) that is only weakly polarizable the solvent dependence of delta(103Rh) is minimal.     

Thermal and solvent effects on the NMR and UV parameters of some bioreductive drugs

15N NMR chemical shifts and n-->pi* electronic transition energy for metronidazole (1) has been calculated and compared with experimental data. A detailed computational study of 1 is presented, with special attention to the performance of various theoretical methods for reproducing spectroscopic parameters in solution. The most sophisticated approach involves density functional based on the Car-Parrinello molecular dynamics simulations of 1 in aqueous solution (BP86 level) and averaging chemical shifts and deltaE(n-->pi*) over snapshots from the trajectory. In the NMR and UV calculations for these snapshots (performed at the B3LYP level), a small number of discrete water molecules are retained, and the remaining bulk solution effects are included via a polarizable continuum model (PCM). A good agreement with experiment is also obtained using static geometry optimization and NMR computation of pristine 1 employing a PCM approach. Further theoretical predictions are also reported for 17O NMR and deltaE(n-->pi*) of three hydroxycinnamic acid derivatives, which suggest that it is essential to incorporate the dynamics and solvent effects for NMR and UV calculations in the condensed phase.     

Synthesis of (-)-calicoferol B

The first total synthesis of (-)-calicoferol B (III) is described. The cyclozirconation product I, prepared in enantiomerically pure form, was converted into the CD ring chiron II. This was coupled with the aromatic A-ring, and then the side chain was constructed with control of relative and absolute configuration to complete the total synthesis of III. The first total synthesis of (-)-calicoferol B (1) is described. The cyclozirconation product 8, prepared in enantiomerically pure form, was converted into the CD ring chiron 6. This was coupled with the aromatic A-ring, and then the side chain was constructed with control of relative and absolute configuration to complete the total synthesis of 1.     

Reactions of metal ions with dithizone in molten naphthalene

A comparative study has been made of the reactions of metal ions with dithizone in the two media, chloroform and molten naphthalene. The absorption spectra of several metal dithizonates, prepared in molten naphthalene, were recorded and were found to be the same as those of the dithizonates obtained by extraction of metal ions from aqueous solution with chloroform dithizone.     

Predicting future duration from present age: A critical assessment

Using a temporal version of the Copernican principle, Gott has proposed a statistical predictor of future longevity based on present age (Gott III, J. R., 1993, Nature, 363, 315) and applied the predictor to a variety of examples, including the longevity of the human species. Although Gott's proposal contains a grain of truth, it does not have the universal predictive power that he attributes to it.     

Generalized limits for single-parameter quantum estimation

We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multisystem interactions. For a Hamiltonian with k-system parameter-sensitive terms, the quantum limit scales as 1/Nk, where N is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter-independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.