# Training a Binary Classifier with the Quantum Adiabatic Algorithm

@article{Neven2008TrainingAB, title={Training a Binary Classifier with the Quantum Adiabatic Algorithm}, author={Hartmut Neven and Vasil S. Denchev and Geordie Rose and William G. Macready}, journal={arXiv: Quantum Physics}, year={2008} }

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 minimize 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…

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## References

SHOWING 1-10 OF 14 REFERENCES

A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

- Physics, Computer ScienceScience
- 2001

For the small examples that the authors could simulate, the quantum adiabatic algorithm worked well, providing evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.

Quantum Computation by Adiabatic Evolution

- Physics
- 2000

We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that…

Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem

- BusinessEur. J. Oper. Res.
- 2001

Multistart Tabu Search Strategies for the Unconstrained Binary Quadratic Optimization Problem

- Computer ScienceAnn. Oper. Res.
- 2004

Five rather different multistart tabu search strategies for the unconstrained binary quadratic optimization problem are described and experimentally compared: a random restart procedure, an application of a deterministic heuristic to specially constructed subproblems, anApplication of a randomized procedure to the full problem, a constructive procedure usingtabu search adaptive memory, and an approach based on solving perturbed problems.

Solving quadratic (0,1)-problems by semidefinite programs and cutting planes

- Mathematics
- 1998

We present computational experiments for solving quadratic (0, 1) problems. Our approach combines a semidefinite relaxation with a cutting plane technique, and is applied in a Branch and Bound…

A Short Introduction to Boosting

- Computer Science
- 1999

This short overview paper introduces the boosting algorithm AdaBoost, and explains the underlying theory of boosting, including an explanation of why boosting often does not suffer from overfitting as well as boosting’s relationship to support-vector machines.

Use of the Zero-Norm with Linear Models and Kernel Methods

- EngineeringJ. Mach. Learn. Res.
- 2003

A blow-molded thermoplastic can has front and side walls and a nozzle integral therewith. The nozzle leads into a quarter-moon-shaped, force-absorbing protuberance in the wall of the can directed…

GML AdaBoost Matlab toolbox 0.3. MSU Graphics & Media Lab

- GML AdaBoost Matlab toolbox 0.3. MSU Graphics & Media Lab
- 2006