Degeneracy Engineering for Classical and Quantum Annealing: A Case Study of Sparse Linear Regression in Collider Physics

TL;DR

This paper introduces degeneracy engineering to improve classical and quantum annealing for solving sparse linear regression problems, demonstrating significant performance gains in collider physics applications.

Contribution

It proposes a novel degeneracy engineering technique to enhance annealing algorithms, applied to $ ext{l}_0$-norm regularization reformulated as QUBO for collider physics.

Findings

Degeneracy engineering increases ground state degeneracy and improves annealing performance.

QUBO formulation of $ ext{l}_0$-norm regularization enables annealing implementation.

Application to collider physics energy flow polynomials shows substantial performance improvements.

Abstract

Classical and quantum annealing are computing paradigms that have been proposed to solve a wide range of optimization problems. In this paper, we aim to enhance the performance of annealing algorithms by introducing the technique of degeneracy engineering, through which the relative degeneracy of the ground state is increased by modifying a subset of terms in the objective Hamiltonian. We illustrate this novel approach by applying it to the example of $\ell_0$-norm regularization for sparse linear regression, which is in general an NP-hard optimization problem. Specifically, we show how to cast $\ell_0$-norm regularization as a quadratic unconstrained binary optimization (QUBO) problem, suitable for implementation on annealing platforms. As a case study, we apply this QUBO formulation to energy flow polynomials in high-energy collider physics, finding that degeneracy engineering substantially improves the annealing performance. Our results motivate the application of degeneracy engineering to a variety of regularized optimization problems.