Mean-Field Solution of the Weak-Strong Cluster Problem for Quantum Annealing with Stoquastic and Non-Stoquastic Catalysts

Abstract

We study the weak-strong cluster problem for quantum annealing in its mean-field version as proposed by Albash [Phys. Rev. A 99 (2019) 042334] who showed by numerical diagonalization that non-stoquastic $XX$ interactions (non-stoquastic catalysts) remove the problematic first-order phase transition. We solve the problem exactly in the thermodynamic limit by analytical methods and show that the removal of the first-order transition is successfully achieved either by stoquastic or non-stoquastic $XX$ interactions depending on whether the $XX$ interactions are introduced within the weak cluster, within the strong cluster, or between them. We also investigate the case where the interactions between the two clusters are sparse, i.e. not of the mean-field all-to-all type. The results again depend on where to introduce the $XX$ interactions. We further analyze how inhomogeneous driving of the transverse field affects the performance of the system without $XX$ interactions and find that inhomogeneity in the transverse field removes the first-order transition if appropriately implemented.

arXiv comment25 pages, 11 figures. v2: modified colormap of 3D figures, corrected typos, and changed format to one-column layout

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Cited by in corpus (8)

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• Improving Schrödinger Equation Implementations with Gray Code for Adiabatic Quantum Computers
• Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model
• Reduction of the energy-gap scaling by coherent catalysis in models of quantum annealing
• Effect of Quantum Statistics on Computational Power of Atomic Quantum Annealers
• Convergence condition of simulated quantum annealing with a non-stoquastic catalyst