Quantum annealing speedup of embedded problems via suppression of Griffiths singularities

Abstract

Optimal parameter setting for applications problems embedded into hardware graphs is key to practical quantum annealers (QA). Embedding chains typically crop up as harmful Griffiths phases, but can be used as a resource as we show here: to balance out singularities in the logical problem changing its universality class. Smart choice of embedding parameters reduces annealing times for random Ising chain from $O(exp[c\sqrt{N}])$ to $O(N^2)$. Dramatic reduction in time-to-solution for QA is confirmed by numerics, for which we developed a custom integrator to overcome convergence issues.

11 pages [5 pages (3 figs) main text+references; 5 pages (2 figs) appendix; 1 page code listing]

References in corpus (5)

• Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Quantum annealing correction for random Ising problems
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Minimizing minor embedding energy: an application in quantum annealing

Cited by in corpus (5)

• Quantum Annealing: An Overview
• Assessing and Advancing the Potential of Quantum Computing: A NASA Case Study
• Reducing defect production in random transverse-field Ising chains by inhomogeneous driving fields
• Exact bounds on the energy gap of transverse-field Ising chains by mapping to random walks
• Exact bounds for dynamical critical exponents of transverse-field Ising chains with a correlated disorder