Training a Binary Classifier with the Quantum Adiabatic Algorithm

author: Hartmut Neven, Google, Inc.
published: Dec. 20, 2008,   recorded: December 2008,   views: 3312
Categories

Slides

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.
  Delicious Bibliography

Description

This paper describes how to make the problem of binary classification amenable to quantum computing. A formulation is employed in which the binary classifier is constructed as a thresholded linear superposition of a set of weak classifiers. The weights in the superposition are optimized in a learning process that strives to min- imize the training error as well as the number of weak classifiers used. No efficient solution to this problem is known. To bring it into a format that allows the applica- tion of adiabatic quantum computing (AQC), we first show that the bit-precision with which the weights need to be represented only grows logarithmically with the ratio of the number of training examples to the number of weak classifiers. This allows to effectively formulate the training process as a binary optimization prob- lem. Solving it with heuristic solvers such as tabu search, we find that the resulting classifier outperforms a widely used state-of-the-art method, AdaBoost, on a va- riety of benchmark problems. Moreover, we discovered the interesting fact that bit-constrained learning machines often exhibit lower generalization error rates. Changing the loss function that measures the training error from 0-1 loss to least squares maps the training to quadratic unconstrained binary optimization. This corresponds to the format required by D-Wave’s implementation of AQC. Simu- lations with heuristic solvers again yield results better than those obtained with boosting approaches. Since the resulting quadratic binary program is NP-hard, additional gains can be expected from applying the actual quantum processor.

See Also:

Download slides icon Download slides: opt08_neven_tabcwt_01.pdf (624.5 KB)


Help icon Streaming Video Help

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Reviews and comments:

Comment1 xaml, December 14, 2009 at 5:59 p.m.:

Ze 'excited state' schrinks ze more "th" is pronaunsd "z".

Write your own review or comment:

make sure you have javascript enabled or clear this field: