On the hardness of quadratic unconstrained binary optimization problems

Mehta, Vrinda; Jin, Fengping; Michielsen, K.; Raedt, Hans De

doi:10.3389/fphy.2022.956882

Cited by 4 publications

(4 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The previous researches have illustrated that only by containing the configurations in the training datasets that are close to the ground state, measured by Hamming distance, to train the neural networks, may we obtain the ground state after training [4][5][6][7]. Therefore, we design this regularizer to explore the relationship between the Hamming distance and the success rates of finding the ground state for different network architectures combined with VAN.…”

Section: The Hamming Distance Regularizermentioning

confidence: 99%

“…Unlike the results on the WPE, the success rates are pretty high because it is easier to find the ground state of the SK model than the WPE with the same system size (when the WPE with α = 0.2). The difference in the success rates between the WPE and the SK model may be caused by their diverse distribution of the Hamming distance between excited states and the ground state [6,7]. Also, when the value of z is large, the VAN framework based on GNN has the highest success rates, indicating that it has the strongest generalization capabilities.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Only when there is a large overlap between the initial state and the ground state can the algorithms obtain the ground state. Therefore, whether the ground state can be found by heuristic algorithms depends heavily on the Hamming distance between the initial state and the ground state [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A method for quantifying the generalization capabilities of generative models for solving Ising models

Ma,

Gao

2024

Mach. Learn.: Sci. Technol.

View full text Add to dashboard Cite

For Ising models with complex energy landscapes, whether the ground state can be found by neural networks depends heavily on the Hamming distance between the training datasets and the ground state. Despite the fact that various recently proposed generative models have shown good performance in solving Ising models, there is no adequate discussion on how to quantify their generalization capabilities. Here we design a Hamming distance regularizer in the framework of a class of generative models, variational autoregressive networks (VAN), to quantify the generalization capabilities of various network architectures combined with VAN. The regularizer can control the size of the overlaps between the ground state and the training datasets generated by networks, which, together with the success rates of finding the ground state, form a quantitative metric to quantify their generalization capabilities. We conduct numerical experiments on several prototypical network architectures combined with VAN, including feed-forward neural networks, recurrent neural networks, and graph neural networks, to quantify their generalization capabilities when solving Ising models. Moreover, considering the fact that the quantification of the generalization capabilities of networks on small-scale problems can be used to predict their relative performance on large-scale problems, our method is of great significance for assisting in the Neural Architecture Search field of searching for the optimal network architectures when solving large-scale Ising models.

show abstract

Section: The Hamming Distance Regularizermentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

See 1 more Smart Citation

A method for quantifying the generalization capabilities of generative models for solving Ising models

Ma,

Gao

2024

Mach. Learn.: Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…However, it is very well possible that many states in the first excited sector have a large Hamming distance to the ground state and between themselves. In fact, there are many indications that a large Hamming distance between the ground state and the first excited state(s) is common for hard instances [6,63]. The order of the perturbation theory is then accordingly large and the convergence difficult to analyze.…”

Section: A Sherrington-kirkpatrick Modelmentioning

confidence: 99%

Diabatic quantum and classical annealing of the Sherrington-Kirkpatrick model

Rakcheev

Läuchli

2023

Phys. Rev. A

View full text Add to dashboard Cite

Guided quantum walk

Schulz,

Willsch,

Michielsen

2024

Phys. Rev. Research

View full text Add to dashboard Cite

We utilize the theory of local amplitude transfer (LAT) to gain insights into quantum walks (QWs) and quantum annealing (QA) beyond the adiabatic theorem. By representing the eigenspace of the problem Hamiltonian as a hypercube graph, we demonstrate that probability amplitude traverses the search space through a series of local Rabi oscillations. We argue that the amplitude movement can be systematically guided towards the ground state using a time-dependent hopping rate based solely on the problem's energy spectrum. Building upon these insights, we extend the concept of multistage QW by introducing the guided quantum walk (GQW) as a bridge between QW-like and QA-like procedures. We assess the performance of the GQW on exact cover, traveling salesperson, and garden optimization problems with 9 to 30 qubits. Our results provide evidence for the existence of optimal annealing schedules, beyond the requirement of adiabatic time evolutions. These schedules might be capable of solving large-scale combinatorial optimization problems within evolution times that scale linearly in the problem size. Published by the American Physical Society 2024

show abstract

On the hardness of quadratic unconstrained binary optimization problems

Cited by 4 publications

References 12 publications

A method for quantifying the generalization capabilities of generative models for solving Ising models

A method for quantifying the generalization capabilities of generative models for solving Ising models

Diabatic quantum and classical annealing of the Sherrington-Kirkpatrick model

Guided quantum walk

Contact Info

Product

Resources

About