A solvable model of quantum random optimization problems

TL;DR

This paper investigates a quantum optimization model with a transverse field, revealing a complex energy landscape with phase transitions that could significantly impact quantum algorithm performance.

Contribution

It introduces a solvable quantum model of optimization problems, analyzing its spectral properties and phase transitions, which are novel insights into quantum complexity landscapes.

Findings

Complex low-energy spectrum with abrupt condensation transition

Continuum of level crossings as a function of transverse field

Implications for quantum algorithms in solving optimization problems

Abstract

We study the quantum version of a simplified model of optimization problems, where quantum fluctuations are introduced by a transverse field acting on the qubits. We find a complex low-energy spectrum of the quantum Hamiltonian, characterized by an abrupt condensation transition and a continuum of level crossings as a function of the transverse field. We expect this complex structure to have deep consequences on the behavior of quantum algorithms attempting to find solutions to these problems.