An important part of doing artificial intelligence is doing inferences. Heretofore, a CB net has been sampled with a classical computer to do inferences. A cool alternative is to embed a CB net within a QB net in such a way that by sampling the QB net on a quantum computer, one obtains the same sample distribution that one obtains when one samples the CB net on a classical computer.
August 27, 2008
Bayesian networks shed much light into Quantum Information Theory. For example, they led to the discovery of Squashed Entanglement.
Every quantum circuit diagram can be converted into an equivalent (though not unique) QB net. Likewise, every QB net can be converted into an equivalent (though not unique) quantum circuit diagram. Thus, QB nets can be very useful in quantum computation. They can be used as a high level (i.e., not necessarily bit-level, although it can be) graphical language for writing quantum computer programs. These programs could be just simulations of quantum processes like Teleportation (see examples that come with Quantum Fog). Alternatively, they can be implementations of algorithms like Shor’s.
In the previous post, I discussed conventional Bayesian networks. If one assigns a unitary matrix (or also a “marginalizer”) instead of a probability matrix to each node of a DAG, one obtains a quantum version of Bayesian nets that I like to call “quantum Bayesian networks” (QB nets). I like to call the ordinary version of Bayesian nets, “classical Bayesian networks” (CB nets). I’ve written various ArXiv papers about QB nets. Also, I have written a Mac application called Quantum Fog, that implements QB nets.
A Bayesian network consists of a DAG (directed acyclic graph, i.e. a network) together with a conditional probability matrix assigned to each node of the net. One can represent any probability distribution P(x1,x2….) as a Bayesian net, where each variable x1,x2… corresponds to a different node of the graph. Bayesian nets are used to pose and solve inference problems graphically. Bayesian nets generalize Bayes rule, which corresponds to the case of a two node net. A fun way to start learning about Bayesian nets is to download one of the many free or trial-version software applications that implement Bayesian nets, and to go through its tutorial. At the end of this article, you will find a list of such software. Enjoy!