748,256 research outputs found
Staying adiabatic with unknown energy gap
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
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 . 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 , which is approximated by an
iPEPS with the original . 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 . 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 . We test the algorithm simulating Lindbladian evolution and
unitary evolution after a sudden quench of transverse field in the 2D
quantum Ising model. Furthermore, we simulate thermal states of this model and
estimate the critical temperature with good accuracy: for and
for the more challenging case of close to the quantum
critical point at .Comment: published version, presentation improve
Speeding up Thermalisation via Open Quantum System Variational Optimisation
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 . 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
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
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
. 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
times the original one. The new iPEPS does not make optimal use of its enlarged
bond dimension , hence in principle it can be represented accurately by a
more compact ansatz, favourably with the original . 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
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
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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