  Quantum particle statistics fundamentally controls the way particles
interact, and plays an essential role in determining the properties of the
system at low temperature. Here we study how the quantum statistics affects the
computational power of quantum annealing. We propose an annealing Hamiltonian
describing quantum particles moving on a square lattice and compare the
computational performance of the atomic quantum annealers between two
statistically-different components: spinless fermions and hard-core bosons. In
addition, we take an Ising quantum annealer driven by traditional
transverse-field quantum fluctuations as a baseline. The potential of our
quantum annealers to solve combinatorial optimization problems is demonstrated
on random 3-regular graph partitioning. We find that the bosonic quantum
annealer outperforms the fermionic case. The superior performance of the
bosonic quantum annealer is attributed to larger excitation gaps and the
consequent smoother adiabatic transformation of its instantaneous quantum
ground states. Along our annealing schedule, the bosonic quantum annealer is
less affected by the glass order and explores the Hilbert space more
efficiently. Our theoretical finding could shed light on constructing atomic
quantum annealers using Rydberg atoms in optical lattices.
