Quantum Speedup by Quantum Annealing

TL;DR

This paper demonstrates that quantum annealing can exponentially outperform classical algorithms in solving the glued-trees problem by using an efficient schedule despite small energy gaps, advancing quantum speedup understanding.

Contribution

It introduces an annealing schedule that achieves exponential speedup in solving an oracular problem without suffering from the sign problem, even with exponentially small energy gaps.

Findings

Quantum annealing solves the glued-trees problem exponentially faster than classical methods.

The proposed schedule remains efficient despite exponentially small energy gaps.

Generalizations suggest initial-state randomization can mitigate slowdowns in adiabatic quantum computing.

Abstract

We study the glued-trees problem of Childs et. al. in the adiabatic model of quantum computing and provide an annealing schedule to solve an oracular problem exponentially faster than classically possible. The Hamiltonians involved in the quantum annealing do not suffer from the so-called sign problem. Unlike the typical scenario, our schedule is efficient even though the minimum energy gap of the Hamiltonians is exponentially small in the problem size. We discuss generalizations based on initial-state randomization to avoid some slowdowns in adiabatic quantum computing due to small gaps.