Quantum annealing with trigger Hamiltonians: Application to 2-satisfiability and nonstoquastic problems

Mehta, Vrinda; Jin, Fengping; Raedt, Hans De; Michielsen, Kristel

doi:10.1103/physreva.104.032421

Cited by 10 publications

(20 citation statements)

References 39 publications

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“…The class of 2SAT problems analyzed in this paper has already been studied extensively through computer simulated quantum annealing and by means of D-Wave quantum annealers [14,15]. The general conclusion is that, in spite of the small number (N ≤ 20) of variables, the 2SAT class contains instances which are very difficult to solve by simulated annealing [11] and Frontiers in Physics frontiersin.org quantum annealing [14,15]. For completeness, in Figure 6 we present data for the success probabilities for the set of N ≤ 20 problems, also used to study the Hamming distance and level spacing distributions.…”

Section: Quantum Annealing Experimentsmentioning

confidence: 99%

On the hardness of quadratic unconstrained binary optimization problems

et al. 2022

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We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments with the D-Wave Advantage 5.1 quantum annealer, solving many instances of up to 170-variable, quadratic unconstrained binary optimization problems. Our results demonstrate that the exponents characterizing the success probability of a D-Wave annealer to solve a quadratic unconstrained binary optimization correlate very well with the predictions based on the Hamming distance distributions computed for small problem instances.

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Section: Quantum Annealing Experimentsmentioning

confidence: 99%

On the hardness of quadratic unconstrained binary optimization problems

et al. 2022

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show abstract

Section: Quantum Annealing Experimentsmentioning

confidence: 99%

On the hardness of quadratic unconstrained binary optimization problems

Mehta¹,

Jin²,

Michielsen³

et al. 2022

Preprint

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We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments with the D-Wave Advantage 5.1 quantum annealer, solving many instances of up to 170-variable, quadratic unconstrained binary optimization problems. Our results demonstrate that the exponents characterizing the success probability of a D-Wave annealer to solve a QUBO correlate very well with the predictions based on the Hamming distance distributions computed for small problem instances.

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“…To overcome this zero energy gap difficulty we sought alternative models and one such way recommended was the addition of an extra term to Hamiltonian. Those are referred to as trigger terms or steering terms [30,31] and the form we will be using is…”

Section: Anisotropic Couplingmentioning

confidence: 99%

Effects of Graph Network Connections on The Efficiency of Quantum Annealing

Ege¹,

Müstecaplıoğlu²

2021

Preprint

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Graph structure of quantum spin networks plays an important role in the applications of quantum annealing. In this work, we compare the performance results of four basic graph structures. Generally, the interaction model choice for quantum annealing is Ising but we test Hamilton XY and antisymmetric anisotropic models as well. Major findings include that Ising model interactions are the most persistent with the change of graph structure. Heisenberg XY model suffers from performance losses with highly connected square graphs which can be attributed to large entropy built-up. Whereas anisotropic model is impractical with square type graphs as energy gap calculations approach zero during annealing. Furthermore, inhomogeneous couplings and their effects on different models and graph structures show a trade-off between coupling strength and performance especially in the case of the anisotropic model.

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Quantum annealing with trigger Hamiltonians: Application to 2-satisfiability and nonstoquastic problems

Cited by 10 publications

References 39 publications

On the hardness of quadratic unconstrained binary optimization problems

On the hardness of quadratic unconstrained binary optimization problems

On the hardness of quadratic unconstrained binary optimization problems

Effects of Graph Network Connections on The Efficiency of Quantum Annealing

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