Construction of non-convex polynomial loss functions for training a binary classifier with quantum annealing

Abstract

Quantum annealing is a heuristic quantum algorithm which exploits quantum resources to minimize an objective function embedded as the energy levels of a programmable physical system. To take advantage of a potential quantum advantage, one needs to be able to map the problem of interest to the native hardware with reasonably low overhead. Because experimental considerations constrain our objective function to take the form of a low degree PUBO (polynomial unconstrained binary optimization), we employ non-convex loss functions which are polynomial functions of the margin. We show that these loss functions are robust to label noise and provide a clear advantage over convex methods. These loss functions may also be useful for classical approaches as they compile to regularized risk expressions which can be evaluated in constant time with respect to the number of training examples.

arXiv comment15 pages, 6 figures

References in corpus (9)

• Quantum Annealing in the Transverse Ising Model
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Quantum annealing with more than one hundred qubits
• Theory of Quantum Annealing of an Ising Spin Glass
• Noise Tolerance under Risk Minimization
• Quantum Simulations of Classical Annealing Processes
• Quantum Speedup by Quantum Annealing
• On Quadratization of Pseudo-Boolean Functions
• Robust Classification with Adiabatic Quantum Optimization

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• Machine learning \& artificial intelligence in the quantum domain