3,274 research outputs found
Microcanonical rates from ring-polymer molecular dynamics: Direct-shooting, stationary-phase, and maximum-entropy approaches
We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that simple application of the stationary-phase approximation (SPA) dramatically improves the performance of the microcanonical rates using RPMD, particularly in the low-energy region where tunneling dominates. Using the SPA as a Bayesian prior, numerically exact RPMD microcanonical rates are then obtained using maximum entropy inversion of the thermal reaction rates for both electronically adiabatic and non-adiabatic model systems. Finally, the direct-shooting method is revisited using the SPA-determined temperature for the internal ring-polymer modes, leading to a simple, direct-simulation method with improved accuracy in the tunneling regime. This work suggests a general strategy for the extraction of microcanonical dynamical quantities from RPMD (or other approximate thermal) simulations
Quantum machine learning: a classical perspective
Recently, increased computational power and data availability, as well as
algorithmic advances, have led machine learning techniques to impressive
results in regression, classification, data-generation and reinforcement
learning tasks. Despite these successes, the proximity to the physical limits
of chip fabrication alongside the increasing size of datasets are motivating a
growing number of researchers to explore the possibility of harnessing the
power of quantum computation to speed-up classical machine learning algorithms.
Here we review the literature in quantum machine learning and discuss
perspectives for a mixed readership of classical machine learning and quantum
computation experts. Particular emphasis will be placed on clarifying the
limitations of quantum algorithms, how they compare with their best classical
counterparts and why quantum resources are expected to provide advantages for
learning problems. Learning in the presence of noise and certain
computationally hard problems in machine learning are identified as promising
directions for the field. Practical questions, like how to upload classical
data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde
Analysing multiparticle quantum states
The analysis of multiparticle quantum states is a central problem in quantum
information processing. This task poses several challenges for experimenters
and theoreticians. We give an overview over current problems and possible
solutions concerning systematic errors of quantum devices, the reconstruction
of quantum states, and the analysis of correlations and complexity in
multiparticle density matrices.Comment: 20 pages, 4 figures, prepared for proceedings of the "Quantum
[Un]speakables II" conference (Vienna, 2014
Using Quantum Fluctuations to Regularize an Analytic Continuation Problem from Many-Body Physics
Extracting spectral information via inversion from Quantum Monte Carlo sampled data isa difficult task. There is a need to analytically continue noisy and often incomplete imaginary-time data into the full complex domain. A new approach is proposed that uses the quantum fluctuations of spin momenta to regularize the inversion. A one-dimensional Heisenberg chain in the presence of a transverse field is first encoded with synthetic data representing several classes of spectral functions and then run through a Density Matrix Renormalization Group algorithm to find its ground state. This solution corresponds to a probable, high quality solution to the inversion. Using optimization constraints and sampling techniques, forward model spectra are replicated by inversion that capture distinguishing characteristics that are often washed out in methods that favor smoothed out solutions
Microcanonical rates from ring-polymer molecular dynamics: Direct-shooting, stationary-phase, and maximum-entropy approaches
We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that simple application of the stationary-phase approximation (SPA) dramatically improves the performance of the microcanonical rates using RPMD, particularly in the low-energy region where tunneling dominates. Using the SPA as a Bayesian prior, numerically exact RPMD microcanonical rates are then obtained using maximum entropy inversion of the thermal reaction rates for both electronically adiabatic and non-adiabatic model systems. Finally, the direct-shooting method is revisited using the SPA-determined temperature for the internal ring-polymer modes, leading to a simple, direct-simulation method with improved accuracy in the tunneling regime. This work suggests a general strategy for the extraction of microcanonical dynamical quantities from RPMD (or other approximate thermal) simulations
Probabilistic performance estimators for computational chemistry methods: Systematic Improvement Probability and Ranking Probability Matrix. I. Theory
The comparison of benchmark error sets is an essential tool for the
evaluation of theories in computational chemistry. The standard ranking of
methods by their Mean Unsigned Error is unsatisfactory for several reasons
linked to the non-normality of the error distributions and the presence of
underlying trends. Complementary statistics have recently been proposed to
palliate such deficiencies, such as quantiles of the absolute errors
distribution or the mean prediction uncertainty. We introduce here a new score,
the systematic improvement probability (SIP), based on the direct system-wise
comparison of absolute errors. Independently of the chosen scoring rule, the
uncertainty of the statistics due to the incompleteness of the benchmark data
sets is also generally overlooked. However, this uncertainty is essential to
appreciate the robustness of rankings. In the present article, we develop two
indicators based on robust statistics to address this problem: P_{inv}, the
inversion probability between two values of a statistic, and \mathbf{P}_{r},
the ranking probability matrix. We demonstrate also the essential contribution
of the correlations between error sets in these scores comparisons
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