Solving systems of Boolean multivariate equations with quantum annealing

Abstract

Polynomial systems over the binary field have important applications, especially in symmetric and asymmetric cryptanalysis, multivariate-based post-quantum cryptography, coding theory, and computer algebra. In this work, we study the quantum annealing model for solving Boolean systems of multivariate equations of degree 2, usually referred to as the Multivariate Quadratic problem. We present different methodologies to embed the problem into a Hamiltonian that can be solved by available quantum annealing platforms. In particular, we provide three embedding options, and we highlight their differences in terms of quantum resources. Moreover, we design a machine-agnostic algorithm that adopts an iterative approach to better solve the problem Hamiltonian by repeatedly reducing the search space. Finally, we use D-Wave devices to successfully implement our methodologies on several instances of the Multivariate Quadratic problem.

10 pages, 2 figures, 2 tables, code available on Github link in paper

References in corpus (4)

• Non-perturbative k-body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins
• Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions
• Pegasus: The second connectivity graph for large-scale quantum annealing hardware
• Fast Quantum Algorithm for Solving Multivariate Quadratic Equations

Cited by in corpus (1)

• Basic Elements for Simulations of Standard Model Physics with Quantum Annealers: Multigrid and Clock States