Efficiency of structured adiabatic quantum computation

TL;DR

This paper demonstrates that a structured approach to Adiabatic Quantum Computation can efficiently solve most satisfiability problems, with resources growing subexponentially for fixed success probabilities, especially near phase transitions.

Contribution

It introduces a multi-step algorithm for structured AQC that efficiently solves satisfiability problems, supported by statistical analysis up to 140 qubits.

Findings

Subexponential growth of resources for fixed success probability

Effective solution of satisfiability problems near phase transitions

Validation with large-scale simulations up to 140 qubits

Abstract

We show enough evidence that a structured version of Adiabatic Quantum Computation (AQC) is efficient for most satisfiability problems. More precisely, when the success probability is fixed beforehand, the computational resources grow subexponentially in the number of qubits. Our study focuses on random satisfiability and exact cover problems, developing a multi-step algorithm that solves clauses one by one. Relating the computational cost to classical properties of the problem, we collect significant statistics with up to N=140 qubits, around the phase transitions, which is where the hardest problems appear.