http://www.bibsonomy.org/burst/user/statphys23/adiabaticBibSonomy BuRST Feed for /user/statphys23/adiabatic2008-07-26T04:33:09+02:00http://www.bibsonomy.org/bibtex/22799f575fbfde3908942f29d37871cf9/statphys23statphys232007-06-20T10:16:09+02:00topic-8 quantum adiabatic disordered spin systems statphys23 computation annealing <span style="color:#555555;">G.E. <a href="http://www.bibsonomy.org/author/Santoro">Santoro</a> and T. <a href="http://www.bibsonomy.org/author/Caneva">Caneva</a> and R. <a href="http://www.bibsonomy.org/author/Fazio">Fazio</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyQuantum annealing of a random Ising chain2007topic-8 quantum adiabatic disordered spin systems statphys23 computation annealing We present results concerning the application of a Quantum Annealing (QA) strategy (alias Adiabatic Quantum Computation) to the determination of the trivial classical ground state of the one-dimensional random Ising ferromagnet $-\sum_i J_i \sigma^z_i \sigma^z_{i+1}$. The QA approach consists in adding to the classical Hamiltonian a source of time-dependent quantum fluctuations, for instance a transverse field term $-\Gamma(t)\sum_i \sigma^x_i$, transforming the classical ground state search into a time-dependent Schroedinger dynamics where the quantum fluctuations are switched off. The one-dimensional case is particularly useful because, due to the quadratic nature of the problem in terms of Wigner-Jordan fermions, one can follow the time-dependent Scroedinger dynamics in an essentially exact way, even for large chain sizes. We show that the presence, in the quantum Hamiltonian, of an infinite randomness critical point --- separating the large-$\Gamma$ paramagnetic phase from the small-$\Gamma$ ferromagnetic one, and analyzed in detail by D.S. Fisher in PRB {\bf 51}, 6411 (1995) --- makes the Schroedinger dynamics intrinsically slow in attaining the correct classical ferromagnetic state: indeed, the residual energy $E_{res}$ after annealing decreases as an inverse power of the {\em logarithm} of the annealing time $\tau$ \[ E_{res}(\tau) \propto \frac{1}{\log^{\zeta}{(\gamma \tau)}} \] in a way that is qualitatively not different (although quantitatively better, because of a larger $\zeta$) from what classical simulated annealing would do (see D.A. Huse and D.S. Fisher, PRL {\bf 57}, 2203 (1986)). We believe that this represents a paradigmatic illustration of how a computationally simple problem can become highly non-trivial for a quantum dynamical approach whenever disorder plays a role.http://www.bibsonomy.org/bibtex/203d506efc28e5d8a5c4f1a3ecc9e0145/statphys23statphys232007-06-20T10:16:09+02:00phase spin quantum passage transitions dynamics topic-8 noise adiabatic models statphys23 <span style="color:#555555;">A. <a href="http://www.bibsonomy.org/author/Fubini">Fubini</a> and G. <a href="http://www.bibsonomy.org/author/Falci">Falci</a> and A. <a href="http://www.bibsonomy.org/author/Osterloh">Osterloh</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyRobustness of adiabatic passage through a quantum critical point2007phase spin quantum passage transitions dynamics topic-8 noise adiabatic models statphys23 We analyze the crossing of a quantum critical point based on exact results for the transverse XY model. In dependence of the change rate of the driving field, the evolution of the ground state is studied while the transverse magnetic field is tuned through the critical point with a linear ramping. The excitation probability is obtained exactly and is compared to previous studies and to the Landau-Zener formula, a long time solution for non-adiabatic transitions in two-level systems. The exact time dependence of the excitations density in the system allows to identify the adiabatic and diabatic regions during the sweep and to study the m esoscopic fluctuations of the excitations. The effect of white noise is investigated, where the critical point transmutes into a non-hermitian ``degenerate region''. Besides an overall increase of the excitations during and at the end of the sweep, the most destructive effect of the noise is the decay of the state purity that is enhanced by the passage through the degenerate region.http://www.bibsonomy.org/bibtex/29a1f754ef258fc212024541403989803/statphys23statphys232007-06-20T10:16:09+02:00adiabatic theorem problem algorithm quantum annealing topic-11 statphys23 optimization <span style="color:#555555;">S. <a href="http://www.bibsonomy.org/author/Morita">Morita</a> and H. <a href="http://www.bibsonomy.org/author/Nishimori">Nishimori</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyAnnealing Schedules for Quantum Annealing2007adiabatic theorem problem algorithm quantum annealing topic-11 statphys23 optimization Quantum annealing (QA) attracts much attention as a novel algorithm for optimization problems. This method is based on the adiabatic theorem of quantum mechanics. The non-trivial target state is expected to be obtained from the trivial initial state after the adiabatic evolution. However, too rapid change of the Hamiltonian causes the non-adiavatic transition, and then QA misses the desired solution. Therefore an important problem is how quickly to change the Hamiltonian. We prove, using the adiabatic theorem, that a power decay of the transverse field is sufficient to guarantee the convergence of QA for the transverse field Ising model. The power is in inverse proportion to the system size. This annealing schedule is in agreement with the previous known result, which were obtained via stochastic approaches. It is remarkable that this annealing rate is faster than that for a well-known classical algorithm, simulated annealing. In addition, we propose faster annealing schedules for QA with finite evolution time. It is known that an error rate of the adiabatic evolution is inversely proportional to the square of the annealing time when the Hamiltonian depends linearly on time. We show that the upper bound of the first-order term of the error rate is determined only by the information at the initial and final times. Our new annealing schedules drop this term, thus bring a faster rate of the error decrease.