5,364 research outputs found
How to best sample a periodic probability distribution, or on the accuracy of Hamiltonian finding strategies
Projective measurements of a single two-level quantum mechanical system (a
qubit) evolving under a time-independent Hamiltonian produce a probability
distribution that is periodic in the evolution time. The period of this
distribution is an important parameter in the Hamiltonian. Here, we explore how
to design experiments so as to minimize error in the estimation of this
parameter. While it has been shown that useful results may be obtained by
minimizing the risk incurred by each experiment, such an approach is
computationally intractable in general. Here, we motivate and derive heuristic
strategies for experiment design that enjoy the same exponential scaling as
fully optimized strategies. We then discuss generalizations to the case of
finite relaxation times, T_2 < \infty.Comment: 7 pages, 2 figures, 3 appendices; Quantum Information Processing,
Online First, 20 April 201
Sampling algorithms for validation of supervised learning models for Ising-like systems
In this paper, we build and explore supervised learning models of
ferromagnetic system behavior, using Monte-Carlo sampling of the spin
configuration space generated by the 2D Ising model. Given the enormous size of
the space of all possible Ising model realizations, the question arises as to
how to choose a reasonable number of samples that will form physically
meaningful and non-intersecting training and testing datasets. Here, we propose
a sampling technique called ID-MH that uses the Metropolis-Hastings algorithm
creating Markov process across energy levels within the predefined
configuration subspace. We show that application of this method retains phase
transitions in both training and testing datasets and serves the purpose of
validation of a machine learning algorithm. For larger lattice dimensions,
ID-MH is not feasible as it requires knowledge of the complete configuration
space. As such, we develop a new "block-ID" sampling strategy: it decomposes
the given structure into square blocks with lattice dimension no greater than 5
and uses ID-MH sampling of candidate blocks. Further comparison of the
performance of commonly used machine learning methods such as random forests,
decision trees, k nearest neighbors and artificial neural networks shows that
the PCA-based Decision Tree regressor is the most accurate predictor of
magnetizations of the Ising model. For energies, however, the accuracy of
prediction is not satisfactory, highlighting the need to consider more
algorithmically complex methods (e.g., deep learning).Comment: 43 pages and 16 figure
The Coupled Electron-Ion Monte Carlo Method
In these Lecture Notes we review the principles of the Coupled Electron-Ion
Monte Carlo methods and discuss some recent results on metallic hydrogen.Comment: 38 pages, 6 figures, Lecture notes for the International School of
Solid State Physics, 34th course: "Computer Simulation in Condensed Matter:
from Materials to Chemical Biology", 20 July-1 August 2005 Erice (Italy). To
appear in Lecture Notes in Physics (2006
Quantum Hamiltonian Learning Using Imperfect Quantum Resources
Identifying an accurate model for the dynamics of a quantum system is a
vexing problem that underlies a range of problems in experimental physics and
quantum information theory. Recently, a method called quantum Hamiltonian
learning has been proposed by the present authors that uses quantum simulation
as a resource for modeling an unknown quantum system. This approach can, under
certain circumstances, allow such models to be efficiently identified. A major
caveat of that work is the assumption of that all elements of the protocol are
noise-free. Here, we show that quantum Hamiltonian learning can tolerate
substantial amounts of depolarizing noise and show numerical evidence that it
can tolerate noise drawn from other realistic models. We further provide
evidence that the learning algorithm will find a model that is maximally close
to the true model in cases where the hypothetical model lacks terms present in
the true model. Finally, we also provide numerical evidence that the algorithm
works for non-commuting models. This work illustrates that quantum Hamiltonian
learning can be performed using realistic resources and suggests that even
imperfect quantum resources may be valuable for characterizing quantum systems.Comment: 16 pages 11 Figure
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