Dynamics of simulated quantum annealing in random Ising chains
| Autor: | Lorenzo Privitera, Luca Arceci, Glen Bigan Mbeng, Giuseppe E. Santoro |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Electronic
Optical and Magnetic Materials Condensed Matter Physics Physics Ising chain Transverse field Monte Carlo method Quantum annealing 01 natural sciences Power law Settore FIS/03 - Fisica della Materia 010305 fluids & plasmas 0103 physical sciences Electronic Ising model Optical and Magnetic Materials Monte carlo dynamics 010306 general physics Scaling Mathematical physics |
| Zdroj: | Physical Review B 99 (2019). doi:10.1103/PhysRevB.99.064201 info:cnr-pdr/source/autori:Mbeng G.B.; Privitera L.; Arceci L.; Santoro G.E./titolo:Dynamics of simulated quantum annealing in random Ising chains/doi:10.1103%2FPhysRevB.99.064201/rivista:Physical Review B/anno:2019/pagina_da:/pagina_a:/intervallo_pagine:/volume:99 |
| DOI: | 10.1103/PhysRevB.99.064201 |
| Popis: | Simulated quantum annealing (SQA) is a classical computational strategy that emulates a quantum annealing (QA) dynamics through a path-integral Monte Carlo whose parameters are changed during the simulation. Here we apply SQA to the one-dimensional transverse field Ising chain, where previous works have shown that, in the presence of disorder, a coherent QA provides a quadratic speedup with respect to classical simulated annealing, with a density of Kibble-Zurek defects decaying as ${\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{QA}}\ensuremath{\sim}{({log}_{10}\ensuremath{\tau})}^{\ensuremath{-}2}$ as opposed to ${\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{SA}}\ensuremath{\sim}{({log}_{10}\ensuremath{\tau})}^{\ensuremath{-}1}, \ensuremath{\tau}$ being the total annealing time, while for the ordered case both give the same power law ${\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{QA}}\ensuremath{\approx}{\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{SA}}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$. We show that the dynamics of SQA, while correctly capturing the Kibble-Zurek scaling ${\ensuremath{\tau}}^{\ensuremath{-}1/2}$ for the ordered case, is unable to reproduce the QA dynamics in the disordered case at intermediate $\ensuremath{\tau}$. We analyze and discuss several issues related to the choice of the Monte Carlo moves (local or global in space), the time-continuum limit needed to eliminate the Trotter-discretization error, and the long autocorrelation times shown by a local-in-space Monte Carlo dynamics for large disordered samples. |
| Databáze: | OpenAIRE |
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