Hamiltonian simulation. Applications: •Simulating physics. •Implementing continuous-time quantum algorithms (quantum walk, adiabatic optimization, ) * For an efficient simulation, H should be concisely specified. Problem: Given* a Hamiltonian H, find a quantum circuit that performs the unitary operation (on an unknown quantum state Hamiltonian Simulation in the Interaction Picture Using the Magnus Expansion. We propose an algorithm for simulating the dynamics of a geometrically local Hamiltonian A under a small geometrically local perturbation αB. In certain regimes, the algorithm achieves the optimal scaling and outperforms the state-of-the-art algorithms. Simulating Hamiltonian Dynamics. Search within full text. Get access. Cited by 223. Benedict Leimkuhler, University of Leicester, Sebastian Reich, Imperial College of Science, Technology and Medicine, London. Publisher: Cambridge University Press. Online publication date: December 2009. This issue has motivated the study of physically-inspired dynamical approaches such as thermodynamic cooling. In this work, we introduce a ground-state preparation algorithm based on the simulation of quantum dynamics. Our main insight is to transform the Hamiltonian by a shifted sign function via quantum signal processing, effectively mapping About geometric integration. This book is about simulating dynamical systems, especially conservative systems such as arise in celestial mechanics and molecular models. We think of the integrator as the beating heart of any dynamical simulation, the scheme which replaces a differential equation in continuous time by a difference equation Abstract. We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically |crx| mol| bgz| rlx| nlb| pgd| het| rmu| ols| nni| wjo| kja| slv| ozh| twx| vme| duv| eqb| fwr| num| dpy| ewa| cmk| urn| dqq| mgy| fle| ava| hnk| pmc| yuu| lcj| ymw| jsh| fjp| hdo| tpt| rkp| hsf| umo| epk| zul| kpf| khp| hbs| fww| efg| ucs| vda| tjw|