Rigorous convergence condition for quantum annealing

Abstract

We derive a generic bound on the rate of decrease of transverse field for quantum annealing to converge to the ground state of a generic Ising model when quantum annealing is formulated as an infinite-time process. Our theorem is based on a rigorous upper bound on the excitation probability in the infinite-time limit and is a mathematically rigorous counterpart of a previously known result derived only from the leading-order term of the asymptotic expansion of adiabatic condition. Since our theorem gives a sufficient condition of convergence for a generic transverse-field Ising model, any specific problem may allow a better, faster, control of the coefficient.

arXiv comment11 pages

References in corpus (6)

• Quantum Annealing in the Transverse Ising Model
• Adiabatic Quantum Computing
• Perspectives of quantum annealing: Methods and implementations
• Mathematical Foundation of Quantum Annealing
• Bounds for the adiabatic approximation with applications to quantum computation
• A Quantum Approach to Classical Statistical Mechanics

Cited by in corpus (3)

• First-quantized adiabatic time evolution for the ground state of a many-electron system and the optimal nuclear configuration
• Convergence condition of simulated quantum annealing for closed and open systems
• Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy