Simulating chemistry efficiently on fault-tolerant quantum computers

Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. Here we consider methods to make proposed chemical simulation algorithms computationally fast on fault-tolerant quantum computers in the circuit model. Fault tolerance constrains the choice of available gates, so that arbitrary gates required for a simulation algorithm must be constructed from sequences of fundamental operations. We examine techniques for constructing arbitrary gates which perform substantially faster than circuits based on the conventional Solovay-Kitaev algorithm [C.M. Dawson and M.A. Nielsen, \emph{Quantum Inf. Comput.}, \textbf{6}:81, 2006]. For a given approximation error $\epsilon$, arbitrary single-qubit gates can be produced fault-tolerantly and using a limited set of gates in time which is $O(\log \epsilon)$ or $O(\log \log \epsilon)$; with sufficient parallel preparation of ancillas, constant average depth is possible using a method we call programmable ancilla rotations. Moreover, we construct and analyze efficient implementations of first- and second-quantized simulation algorithms using the fault-tolerant arbitrary gates and other techniques, such as implementing various subroutines in constant time. A specific example we analyze is the ground-state energy calculation for Lithium hydride.Comment: 33 pages, 18 figure

Barriers and facilitators to adherence to group exercise in institutionalized older people living with dementia: a systematic review

Objectives Research suggests targeted exercise is important for people living with dementia, especially those living in residential care. The aim of this review was to collect and synthesize evidence on the known barriers and facilitators to adherence to group exercise of institutionalized older people living with dementia. Methods We searched all available electronic databases. Additionally, we searched trial registries (clinicaltrial.gov, and WHO ICTRP) for ongoing studies. We searched for and included papers from January 1990 until September 2017 in any language. We included randomized, non-randomized trials. Studies were not eligible if participants were either healthy older people or people suffering from dementia but not living in an institution. Studies were also excluded if they were not focused on barriers and facilitators to adherence to group exercise. Results Using narrative analysis, we identified the following themes for barriers: bio-medical reasons and mental wellbeing and physical ability, relationships dynamics, and socioeconomic reasons. The facilitators were grouped under the following thematic frames: bio-medical benefits and benefits related to physical ability, feelings and emotions and confidence improvements, therapist and group relationships dynamics and activity related reasons. Conclusions We conclude that institutionalized older people living with dementia, even those who are physically frail, incontinent and/or have mild dementia can demonstrate certain level of exercise adherence, and therefore can respond positively to exercise programs. Tailored, individually-adjusted and supported physical activity, led by a knowledgeable, engaging and well communicating therapist/facilitator improves the adherence to group exercise interventions of institutionalized older people living with dementia

System-Size Independence of Directed Flow Measured at the BNL Relativistic Heavy-Ion Collider

We measure directed flow (ν_1) for charged particles in Au+Au and Cu+Cu collisions at √S_(NN)=200 and 62.4 GeV, as a function of pseudorapidity (η), transverse momentum (p_t), and collision centrality, based on data from the STAR experiment. We find that the directed flow depends on the incident energy but, contrary to all available model implementations, not on the size of the colliding system at a given centrality. We extend the validity of the limiting fragmentation concept to ν_1 in different collision systems, and investigate possible explanations for the observed sign change in ν_1(p_t)

Spin alignment measurements of the K∗0(892)K^{*0}(892) and ϕ(1020)\phi(1020) vector mesons at RHIC

We present the first spin alignment measurements for the $K^{*0}(892)$ and $\phi(1020)$ vector mesons produced at mid-rapidity with transverse momenta up to 5 GeV/c at $\sqrt{s_{NN}}$ = 200 GeV at RHIC. The diagonal spin density matrix elements with respect to the reaction plane in Au+Au collisions are $\rho_{00}$ = 0.32 $\pm$ 0.04 (stat) $\pm$ 0.09 (syst) for the $K^{*0}$ ($0.8<p_T<5.0$ GeV/c) and $\rho_{00}$ = 0.34 $\pm$ 0.02 (stat) $\pm$ 0.03 (syst) for the $\phi$ ($0.4<p_T<5.0$ GeV/c), and are constant with transverse momentum and collision centrality. The data are consistent with the unpolarized expectation of 1/3 and thus no evidence is found for the transfer of the orbital angular momentum of the colliding system to the vector meson spins. Spin alignments for $K^{*0}$ and $\phi$ in Au+Au collisions were also measured with respect to the particle's production plane. The $\phi$ result, $\rho_{00}$ = 0.41 $\pm$ 0.02 (stat) $\pm$ 0.04 (syst), is consistent with that in p+p collisions, $\rho_{00}$ = 0.39 $\pm$ 0.03 (stat) $\pm$ 0.06 (syst), also measured in this work. The measurements thus constrain the possible size of polarization phenomena in the production dynamics of vector mesons.Comment: 7 pages, 4 figures. fig.1 updated; one more reference added, one typo corrected, published in PRC.77.06190

Measurements of ϕ\phi meson production in relativistic heavy-ion collisions at RHIC

We present results for the measurement of $\phi$ meson production via its charged kaon decay channel $\phi \to K^+K^-$ in Au+Au collisions at $\sqrt{s_{_{NN}}}=62.4$, 130, and 200 GeV, and in $p+p$ and $d$+Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV from the STAR experiment at the BNL Relativistic Heavy Ion Collider (RHIC). The midrapidity ($|y|<0.5$) $\phi$ meson transverse momentum ($p_{T}$) spectra in central Au+Au collisions are found to be well described by a single exponential distribution. On the other hand, the $p_{T}$ spectra from $p+p$, $d$+Au and peripheral Au+Au collisions show power-law tails at intermediate and high $p_{T}$ and are described better by Levy distributions. The constant $\phi/K^-$ yield ratio vs beam species, collision centrality and colliding energy is in contradiction with expectations from models having kaon coalescence as the dominant mechanism for $\phi$ production at RHIC. The $\Omega/\phi$ yield ratio as a function of $p_{T}$ is consistent with a model based on the recombination of thermal $s$ quarks up to $p_{T}\sim 4$ GeV/$c$, but disagrees at higher transverse momenta. The measured nuclear modification factor, $R_{dAu}$, for the $\phi$ meson increases above unity at intermediate $p_{T}$, similar to that for pions and protons, while $R_{AA}$ is suppressed due to the energy loss effect in central Au+Au collisions. Number of constituent quark scaling of both $R_{cp}$ and $v_{2}$ for the $\phi$ meson with respect to other hadrons in Au+Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV at intermediate $p_{T}$ is observed. These observations support quark coalescence as being the dominant mechanism of hadronization in the intermediate $p_{T}$ region at RHIC.Comment: 22 pages, 21 figures, 4 table

Enhanced strange baryon production in Au+Au collisions compared to p+p at sqrts = 200 GeV

We report on the observed differences in production rates of strange and multi-strange baryons in Au+Au collisions at sqrts = 200 GeV compared to pp interactions at the same energy. The strange baryon yields in Au+Au collisions, then scaled down by the number of participating nucleons, are enhanced relative to those measured in pp reactions. The enhancement observed increases with the strangeness content of the baryon, and increases for all strange baryons with collision centrality. The enhancement is qualitatively similar to that observed at lower collision energy sqrts =17.3 GeV. The previous observations are for the bulk production, while at intermediate pT, 1 < pT< 4 GeV/c, the strange baryons even exceed binary scaling from pp yields.Comment: 7 pages, 4 figures. Printed in PR

Growth of Long Range Forward-Backward Multiplicity Correlations with Centrality in Au+Au Collisions at sNN\sqrt{s_{NN}} = 200 GeV

Forward-backward multiplicity correlation strengths have been measured with the STAR detector for Au+Au and $\textit{p+p}$ collisions at $\sqrt{s_{NN}}$ = 200 GeV. Strong short and long range correlations (LRC) are seen in central Au+Au collisions. The magnitude of these correlations decrease with decreasing centrality until only short range correlations are observed in peripheral Au+Au collisions. Both the Dual Parton Model (DPM) and the Color Glass Condensate (CGC) predict the existence of the long range correlations. In the DPM the fluctuation in the number of elementary (parton) inelastic collisions produces the LRC. In the CGC longitudinal color flux tubes generate the LRC. The data is in qualitative agreement with the predictions from the DPM and indicates the presence of multiple parton interactions.Comment: 6 pages, 3 figures The abstract has been slightly modifie

Hadronic resonance production in dd+Au collisions at sNN\sqrt{s_{_{NN}}} = 200 GeV at RHIC

We present the first measurements of the $\rho(770)^0$, $K^*$(892), $\Delta$(1232)$^{++}$, $\Sigma$(1385), and $\Lambda$(1520) resonances in $d$+Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV, reconstructed via their hadronic decay channels using the STAR detector at RHIC. The masses and widths of these resonances are studied as a function of transverse momentum ($p_T$). We observe that the resonance spectra follow a generalized scaling law with the transverse mass ($m_T$). The $$of resonances in minimum bias collisions is compared to the$$ of $\pi$, $K$, and $\bar{p}$. The $\rho^0/\pi^-$, $K^*/K^-$, $\Delta^{++}/p$, $\Sigma(1385)/\Lambda$, and $\Lambda(1520)/\Lambda$ ratios in $d$+Au collisions are compared to the measurements in minimum bias $p+p$ interactions, where we observe that both measurements are comparable. The nuclear modification factors ($R_{dAu}$) of the $\rho^0$, $K^*$, and $\Sigma^*$ scale with the number of binary collisions ($N_{bin}$) for $p_T >$ 1.2 GeV/$c$.Comment: STAR Collaboration. Submitted to PR