Quantum Annealing with Trigger Hamiltonians: Application to 2-SAT and Nonstoquastic Problems

Abstract

We study the performance of quantum annealing for two sets of problems, namely, 2-satisfiability (2-SAT) problems represented by Ising-type Hamiltonians, and nonstoquastic problems which are obtained by adding extra couplings to the 2-SAT problem Hamiltonians. In addition, we add to the transverse Ising-type Hamiltonian used for quantum annealing a third term, the trigger Hamiltonian with ferromagnetic or antiferromagnetic couplings, which vanishes at the beginning and end of the annealing process. We also analyze some problem instances using the energy spectrum, average energy or overlap of the state during the evolution with the instantaneous low lying eigenstates of the Hamiltonian, and identify some non-adiabatic mechanisms which can enhance the performance of quantum annealing.

arXiv comment16 pages, 17 figures

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• Guided quantum walk
• Quantum annealing for hard 2-SAT problems : Distribution and scaling of minimum energy gap and success probability
• On the hardness of quadratic unconstrained binary optimization problems
• Unraveling Reverse Annealing: A Study of D-Wave Quantum Annealers
• Performance of quantum annealing for 2-SAT problems with multiple satisfying assignments
• Ising Hamiltonians for Constrained Combinatorial Optimization Problems and the Metropolis-Hastings Warm-Starting Algorithm
• Posiform Planting: Generating QUBO Instances for Benchmarking
• Fighting Exponentially Small Gaps by Counterdiabatic Driving
• Effects of Graph Network Connections on The Efficiency of Quantum Annealing
• Variational Quantum Algorithm for Constrained Combinatorial Optimization Problems