Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet

Abstract

We study the performance of quantum annealing for the simple $p$-body infinite-range ferromagnetic Ising model. In particular, we generalize the transverse antiferromagnetic interactions proposed by Seki and Nishimori as a quantum driver to many-body transverse interactions to understand if the two-body interactions are essential to allow the system to avoid troublesome first-order quantum phase transitions. We conclude that the general many-body interactions are effective to let the system evolve only through second-order transitions as long as a few minor conditions are satisfied. It is also discussed whether the overlap of the ground-state wave function of the new driver term with the target ground state is an essential factor for the success.

24 pages, 8 figures

References in corpus (7)

• Quantum annealing with antiferromagnetic fluctuations
• Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• Simple Glass Models and their Quantum Annealing
• On quantum mean-field models and their quantum annealing
• Quantum phase transitions in fully connected spin models: an entanglement perspective
• Quantum annealing of the random-field Ising model by transverse ferromagnetic interactions

Cited by in corpus (12)

• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stochastic Hamiltonians
• Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field
• Reverse quantum annealing of the $p$-spin model with relaxation
• Improving quantum annealing of the ferromagnetic $p$-spin model through pausing
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Two-parameter counter-diabatic driving in quantum annealing
• Comparative Study of the Performance of Quantum Annealing and Simulated Annealing
• Direct comparison of quantum and simulated annealing on a fully-connected Ising ferromagnet
• Mean-Field Solution of the Weak-Strong Cluster Problem for Quantum Annealing with Stoquastic and Non-Stoquastic Catalysts
• Exact expression of the energy gap at first-order quantum phase transitions of a non-stoquastic Hamiltonian
• Quantum Phase Transition in Fully-Connected Quantum Wajnflasz-Pick Model