Effect of Quantum Statistics on Computational Power of Atomic Quantum Annealers

Abstract

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.

7 pages, 6 figures

References in corpus (20)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Probing many-body dynamics on a 51-atom quantum simulator
• Tools for quantum simulation with ultracold atoms in optical lattices
• Many-Body Localization in a Quasiperiodic System
• Mathematical Foundation of Quantum Annealing
• Bounds for the adiabatic approximation with applications to quantum computation
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Simple Glass Models and their Quantum Annealing
• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• Quench Dynamics of a Fermi Gas with Strong Non-Local Interactions
• State-dependent, addressable subwavelength lattices with cold atoms
• Shortcuts to adiabaticity for quantum annealing
• Programmable Quantum Annealing Architectures with Ising Quantum Wires
• Quantum annealing with ultracold atoms in a multimode optical resonator
• Two-parameter counter-diabatic driving in quantum annealing
• Optimal quantum annealing: A variational shortcut to adiabaticity approach
• Effect of particle statistics in strongly correlated two-dimensional Hubbard models
• De-Signing Hamiltonians for Quantum Adiabatic Optimization
• Mean-Field Solution of the Weak-Strong Cluster Problem for Quantum Annealing with Stoquastic and Non-Stoquastic Catalysts
• Phase transitions in the frustrated Ising ladder with stoquastic and nonstoquastic catalysts