748,256 research outputs found

    Staying adiabatic with unknown energy gap

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    We introduce an algorithm to perform an optimal adiabatic evolution that operates without an apriori knowledge of the system spectrum. By probing the system gap locally, the algorithm maximizes the evolution speed, thus minimizing the total evolution time. We test the algorithm on the Landau-Zener transition and then apply it on the quantum adiabatic computation of 3-SAT: The result is compatible with an exponential speed-up for up to twenty qubits with respect to classical algorithms. We finally study a possible algorithm improvement by combining it with the quantum Zeno effect.Comment: 4 pages, 4 figure

    Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm

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    An infinite projected entangled pair state (iPEPS) is a tensor network ansatz to represent a quantum state on an infinite 2D lattice whose accuracy is controlled by the bond dimension DD. Its real, Lindbladian or imaginary time evolution can be split into small time steps. Every time step generates a new iPEPS with an enlarged bond dimension D>DD' > D, which is approximated by an iPEPS with the original DD. In Phys. Rev. B 98, 045110 (2018) an algorithm was introduced to optimize the approximate iPEPS by maximizing directly its fidelity to the one with the enlarged bond dimension DD'. In this work we implement a more efficient optimization employing a local estimator of the fidelity. For imaginary time evolution of a thermal state's purification, we also consider using unitary disentangling gates acting on ancillas to reduce the required DD. We test the algorithm simulating Lindbladian evolution and unitary evolution after a sudden quench of transverse field hxh_x in the 2D quantum Ising model. Furthermore, we simulate thermal states of this model and estimate the critical temperature with good accuracy: 0.1%0.1\% for hx=2.5h_x=2.5 and 0.5%0.5\% for the more challenging case of hx=2.9h_x=2.9 close to the quantum critical point at hx=3.04438(2)h_x=3.04438(2).Comment: published version, presentation improve

    Speeding up Thermalisation via Open Quantum System Variational Optimisation

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    Optimizing open quantum system evolution is an important step on the way to achieving quantum computing and quantum thermodynamic tasks. In this article, we approach optimisation via variational principles and derive an open quantum system variational algorithm explicitly for Lindblad evolution in Liouville space. As an example of such control over open system evolution, we control the thermalisation of a qubit attached to a thermal Lindbladian bath with a damping rate γ\gamma. Since thermalisation is an asymptotic process and the variational algorithm we consider is for fixed time, we present a way to discuss the potential speedup of thermalisation that can be expected from such variational algorithms.Comment: 10 pages, 4 figures, comments welcom

    A Hybrid N-body--Coagulation Code for Planet Formation

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    We describe a hybrid algorithm to calculate the formation of planets from an initial ensemble of planetesimals. The algorithm uses a coagulation code to treat the growth of planetesimals into oligarchs and explicit N-body calculations to follow the evolution of oligarchs into planets. To validate the N-body portion of the algorithm, we use a battery of tests in planetary dynamics. Several complete calculations of terrestrial planet formation with the hybrid code yield good agreement with previously published calculations. These results demonstrate that the hybrid code provides an accurate treatment of the evolution of planetesimals into planets.Comment: Astronomical Journal, accepted; 33 pages + 11 figure

    Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles

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    A typical quantum state obeying the area law for entanglement on an infinite 2D lattice can be represented by a tensor network ansatz -- known as an infinite projected entangled pair state (iPEPS) -- with a finite bond dimension DD. Its real/imaginary time evolution can be split into small time steps. An application of a time step generates a new iPEPS with a bond dimension kk times the original one. The new iPEPS does not make optimal use of its enlarged bond dimension kDkD, hence in principle it can be represented accurately by a more compact ansatz, favourably with the original DD. In this work we show how the more compact iPEPS can be optimized variationally to maximize its overlap with the new iPEPS. To compute the overlap we use the corner transfer matrix renormalization group (CTMRG). By simulating sudden quench of the transverse field in the 2D quantum Ising model with the proposed algorithm, we provide a proof of principle that real time evolution can be simulated with iPEPS. A similar proof is provided in the same model for imaginary time evolution of purification of its thermal states.Comment: 9 pages, 10 figures, replaced with the published versio

    Low-frequency expansion for probability amplitudes: An alternative approach to certain intramolecular dynamics problems

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    We present an algorithm to determine the averaged time evolution of the probability amplitude for a nonstationary state in a quantum mechanical system. The algorithm is based on a low‐frequency expansion of the probability amplitude and is related to the generalized moment expansion method which has been applied successfully to the description of dynamic correlation functions in stochastic systems. It is shown that the proposed algorithm gives excellent results for the description of quantum beats in the time evolution of the occupation probability for a nonstationary state in model systems. The relation of the algorithm to other theoretical approaches and the relevance for the description of intramolecular energy transfer processes is discussed

    Star formation and chemical evolution in SPH simulations: a statistical approach

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    In Smoothed Particles Hydrodynamics (SPH) codes with a large number of particles, star formation as well as gas and metal restitution from dying stars can be treated statistically. This approach allows to include detailed chemical evolution and gas re-ejection with minor computational effort. Here we report on a new statistical algorithm for star formation and chemical evolution, especially conceived for SPH simulations with large numbers of particles, and for parallel SPH codes. For the sake of illustration, we present also two astrophysical simulations obtained with this algorithm, implemented into the Tree-SPH code by Lia & Carraro (2000). In the first one, we follow the formation of an individual disc-like galaxy, predict the final structure and metallicity evolution, and test resolution effects. In the second one we simulate the formation and evolution of a cluster of galaxies, to demonstrate the capabilities of the algorithm in investigating the chemo-dynamical evolution of galaxies and of the intergalactic medium in a cosmological context.Comment: 17 pages, 20 figures, accepted for publication on MNRA
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