954 research outputs found
Semantics for a Quantum Programming Language by Operator Algebras
This paper presents a novel semantics for a quantum programming language by
operator algebras, which are known to give a formulation for quantum theory
that is alternative to the one by Hilbert spaces. We show that the opposite
category of the category of W*-algebras and normal completely positive
subunital maps is an elementary quantum flow chart category in the sense of
Selinger. As a consequence, it gives a denotational semantics for Selinger's
first-order functional quantum programming language QPL. The use of operator
algebras allows us to accommodate infinite structures and to handle classical
and quantum computations in a unified way.Comment: In Proceedings QPL 2014, arXiv:1412.810
Disintegration and Bayesian Inversion via String Diagrams
The notions of disintegration and Bayesian inversion are fundamental in
conditional probability theory. They produce channels, as conditional
probabilities, from a joint state, or from an already given channel (in
opposite direction). These notions exist in the literature, in concrete
situations, but are presented here in abstract graphical formulations. The
resulting abstract descriptions are used for proving basic results in
conditional probability theory. The existence of disintegration and Bayesian
inversion is discussed for discrete probability, and also for measure-theoretic
probability --- via standard Borel spaces and via likelihoods. Finally, the
usefulness of disintegration and Bayesian inversion is illustrated in several
examples.Comment: Accepted for publication in Mathematical Structures in Computer
Scienc
The EfProb Library for Probabilistic Calculations
EfProb is an abbreviation of Effectus Probability. It is the name of
a library for probability calculations in Python. EfProb offers a
uniform language for discrete, continuous and quantum probability.
For each of these three cases, the basic ingredients of the language
are states, predicates, and channels. Probabilities are typically
calculated as validities of predicates in states. States can be
updated (conditioned) with predicates. Channels can be used for state
transformation and for predicate transformation. This short paper
gives an overview of the use of EfProb
Control-Data Separation and Logical Condition Propagation for Efficient Inference on Probabilistic Programs
We introduce a novel sampling algorithm for Bayesian inference on imperative
probabilistic programs. It features a hierarchical architecture that separates
control flows from data: the top-level samples a control flow, and the bottom
level samples data values along the control flow picked by the top level. This
separation allows us to plug various language-based analysis techniques in
probabilistic program sampling; specifically, we use logical backward
propagation of observations for sampling efficiency. We implemented our
algorithm on top of Anglican. The experimental results demonstrate our
algorithm's efficiency, especially for programs with while loops and rare
observations.Comment: 11 pages with appendice
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