Quantum Bayesian Networks

May 5, 2018

Quantum Edward, First Commit

Filed under: Uncategorized — rrtucci @ 5:43 am

Today, I uploaded to GitHub the first commit of my “Quantum Edward” software. This blog is among other things a scrapbook of my quantum computing adventures. In this blog post, I want to save a copy of the first README of Quantum Edward. The software is exploratory and therefore will change a lot in the future and its README will change to mirror the changes in the software. So this first README will have a sentimental and comic value for me in years to come. Here it goes:

# Quantum Edward

Quantum Edward at this point is just a small library of Python tools for
doing classical supervised learning on Quantum Neural Networks (QNNs).

An analytical model of the QNN is entered as input into QEdward and the training
is done on a classical computer, using training data already available (e.g.,
MNIST), and using the famous BBVI (Black Box Variational Inference) method
described in Reference 1 below.

The input analytical model of the QNN is given as a sequence of gate
operations for a gate model quantum computer. The hidden variables are
angles by which the qubits are rotated. The observed variables are the input
and output of the quantum circuit. Since it is already expressed in the qc’s
native language, once the QNN has been trained using QEdward, it can be
run immediately on a physical gate model qc such as the ones that IBM and
Google have already built. By running the QNN on a qc and doing
classification with it, we can compare the performance in classification
tasks of QNNs and classical artificial neural nets (ANNs).

Other workers have proposed training a QNN on an actual physical qc. But
current qc’s are still fairly quantum noisy. Training an analytical QNN on a
classical computer might yield better results than training it on a qc
because in the first strategy, the qc’s quantum noise does not degrade the
training.

The BBVI method is a mainstay of the “Edward” software library. Edward uses
Google’s TensorFlow lib to implement various inference methods (Monte Carlo
and Variational ones) for Classical Bayesian Networks and for Hierarchical
Models. H.M.s (pioneered by Andrew Gelman) are a subset of C.B. nets
(pioneered by Judea Pearl). Edward is now officially a part of TensorFlow,
and the original author of Edward, Dustin Tran, now works for Google. Before
Edward came along, TensorFlow could only do networks with deterministic
nodes. With the addition of Edward, TensorFlow now can do nets with both
deterministic and non-deterministic (probabilistic) nodes.

This first baby-step lib does not do distributed computing. The hope is that
it can be used as a kindergarten to learn about these techniques, and that
then the lessons learned can be used to write a library that does the same
thing, classical supervised learning on QNNs, but in a distributed fashion
using Edward/TensorFlow on the cloud.

The first version of Quantum Edward analyzes two QNN models called NbTrols
and NoNbTrols. These two models were chosen because they are interesting to
the author, but the author attempted to make the library general enough so
that it can accommodate other akin models in the future. The allowable
models are referred to as QNNs because they consist of ‘layers’,
as do classical ANNs (Artificial Neural Nets). TensorFlow can analyze
layered models (e.g., ANN) or more general DAG (directed acyclic graph)
models (e.g., Bayesian networks).

References
———-

1. R. Ranganath, S. Gerrish, D. M. Blei, “Black Box Variational
Inference”, https://arxiv.org/abs/1401.0118

2. https://en.wikipedia.org/wiki/Stochastic_approximation
discusses Robbins-Monro conditions

3. https://github.com/keyonvafa/logistic-reg-bbvi-blog/blob/master/log_reg_bbvi.py

4. http://edwardlib.org/

5. https://discourse.edwardlib.org/

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