Geometric vs. Dynamical Gates in Quantum Computing Implementations Using Zeeman and Heisenberg Hamiltonians

Quantum computing in terms of geometric phases, i.e. Berry or Aharonov-Anandan phases, is fault-tolerant to a certain degree. We examine its implementation based on Zeeman coupling with a rotating field and isotropic Heisenberg interaction, which describe NMR and can also be realized in quantum dots and cold atoms. Using a novel physical representation of the qubit basis states, we construct $\pi/8$ and Hadamard gates based on Berry and Aharonov-Anandan phases. For two interacting qubits in a rotating field, we find that it is always impossible to construct a two-qubit gate based on Berry phases, or based on Aharonov-Anandan phases when the gyromagnetic ratios of the two qubits are equal. In implementing a universal set of quantum gates, one may combine geometric $\pi/8$ and Hadamard gates and dynamical $\sqrt{\rm SWAP}$ gate.Comment: published version, 5 page

Trace and antitrace maps for aperiodic sequences, their extensions and applications

We study aperiodic systems based on substitution rules by means of a transfer-matrix approach. In addition to the well-known trace map, we investigate the so-called `antitrace' map, which is the corresponding map for the difference of the off-diagonal elements of the 2x2 transfer matrix. The antitrace maps are obtained for various binary, ternary and quaternary aperiodic sequences, such as the Fibonacci, Thue-Morse, period-doubling, Rudin-Shapiro sequences, and certain generalizations. For arbitrary substitution rules, we show that not only trace maps, but also antitrace maps exist. The dimension of the our antitrace map is r(r+1)/2, where r denotes the number of basic letters in the aperiodic sequence. Analogous maps for specific matrix elements of the transfer matrix can also be constructed, but the maps for the off-diagonal elements and for the difference of the diagonal elements coincide with the antitrace map. Thus, from the trace and antitrace map, we can determine any physical quantity related to the global transfer matrix of the system. As examples, we employ these dynamical maps to compute the transmission coefficients for optical multilayers, harmonic chains, and electronic systems.Comment: 13 pages, REVTeX, now also includes applications to electronic systems, some references adde

Measurement of the chi_{c2} Polarization in psi(2S) to gamma chi_{c2}

The polarization of the chi_{c2} produced in psi(2S) decays into gamma chi_{c2} is measured using a sample of 14*10^6 psi(2S) events collected by BESII at the BEPC. A fit to the chi_{c2} production and decay angular distributions in psi(2S) to gamma chi_{c2}, chi_{c2} to pi pi and KK yields values x=A_1/A_0=2.08+/-0.44 and y=A_2/A_0=3.03 +/-0.66, with a correlation rho=0.92 between them, where A_{0,1,2} are the chi_{c2} helicity amplitudes. The measurement agrees with a pure E1 transition, and M2 and E3 contributions do not differ significantly from zero.Comment: 6 pages, 4 figures, 1 tabl

\psi(2S) Decays into \J plus Two Photons

Using \gamma \gamma J/\psi, J/\psi \ra e^+ e^- and $\mu^+ \mu^-$ events from a sample of $14.0\times 10^6$ \psip decays collected with the BESII detector, the branching fractions for \psip\ra \pi^0\J, \eta\J, and \psi(2S)\ar\gamma\chi_{c1},\gamma\chi_{c2}\ar\gamma\gamma\jpsi are measured to be B(\psip\ra \pi^0\J) = (1.43\pm0.14\pm0.13)\times 10^{-3}, B(\psip\ra \eta\J) = (2.98\pm0.09\pm0.23)%, B(\psi(2S)\ar\gamma\chi_{c1}\ar\gamma\gamma\jpsi) = (2.81\pm0.05\pm 0.23)%, and B(\psi(2S)\ar\gamma\chi_{c2}\ar\gamma\gamma\jpsi) = (1.62\pm0.04\pm 0.12)%.Comment: 7 pages, 6 figures. submitted to Phys. Rev.

Measurement of the branching fractions of psi(2S) -> 3(pi+pi-) and J/psi -> 2(pi+pi-)

Using data samples collected at sqrt(s) = 3.686GeV and 3.650GeV by the BESII detector at the BEPC, the branching fraction of psi(2S) -> 3(pi+pi-) is measured to be [4.83 +- 0.38(stat) +- 0.69(syst)] x 10^-4, and the relative branching fraction of J/psi -> 2(pi+pi-) to that of J/psi -> mu+mu- is measured to be [5.86 +- 0.19(stat) +- 0.39(syst)]% via psi(2S) -> (pi+pi-)J/psi, J/psi -> 2(pi+pi-). The electromagnetic form factor of 3(pi+pi-) is determined to be 0.21 +- 0.02 and 0.20 +- 0.01 at sqrt(s) = 3.686GeV and 3.650GeV, respectively.Comment: 17pages, 7 figures, submitted to Phys. Rev.

Measurement of the final states ωπ0\omega \pi^0, ρη\rho \eta, and ρη′\rho \eta^{'} from \psip electromagnetic decays and \ee annihilations

Cross sections and form factors for \ee \to \wpi, $\rho\eta$, and \rho\etap at center of mass energies of 3.650, 3.686, and 3.773 GeV are measured using data samples collected with the BESII detector at the BEPC. Also, the branching fractions of \psi(2S) \rar \wpi, $\rho\eta$, and \rho\etap are determined to be $(1.87^{+0.68}_{-0.62}\pm0.28)\times 10^{-5}$, $(1.78^{+0.67}_{-0.62}\pm0.17)\times 10^{-5}$, and $(1.87^{+1.64}_{-1.11}\pm0.33)\times10^{-5}$, respectively.Comment: 8 pages, 4 figures, 4 table

Measurements of J/psi decays into phi pi^0, phi eta, and phi eta^prime

Based on 5.8x10^7 J/psi events detected in BESII, the branching fractions of J/psi--> phi eta and phi eta^prime are measured for different eta and eta^prime decay modes. The results are significantly higher than previous measurements. An upper limit on B(J/psi--> phi pi^0) is also obtained.Comment: 9 pages, 10 figure

Measurements of ψ(2S)\psi(2S) decays into Vector- Tensor final states

Decays of the $\psi(2S)$ into vector plus tensor meson final states have been studied with 14 million $\psi(2S)$ events collected with the BESII detector. Branching fractions of \psi(2S) \rt \omega f_{2}(1270), $\rho a_2(1320)$, $K^*(892)^0\bar{K}^*_2(1430)^0+c.c.$ and $\phi f_2^{\prime}(1525)$ are determined. They improve upon previous BESI results and confirm the violation of the "12%" rule for $\psi(2S)$ decays to VT channels with higher precision.Comment: 7 pages, 7 figures and 2 table

Observation of p pbar pi^0 and p pbar eta in psi' decays

The processes psi'-->p pbar pi^0 and psi'-->p pbar eta are studied using a sample of 14 million psi' decays collected with the Beijing Spectrometer at the Beijing Electron-Positron Collider. The branching fraction of psi'-->p pbar pi^0 is measured with improved precision as (13.2\pm 1.0\pm 1.5)\times 10^{-5}, and psi'-->p pbar eta is observed for the first time with a branching fraction of (5.8\pm 1.1\pm 0.7)\times 10^{-5}, where the first errors are statistical and the second ones are systematic.Comment: 15 pages, 8 figures and 3 table