From near to eternity: Spin-glass planting, tiling puzzles, and constraint-satisfaction problems.

@article{Hamze2018FromNT,
  title={From near to eternity: Spin-glass planting, tiling puzzles, and constraint-satisfaction problems.},
  author={Firas Hamze and Darryl C Jacob and Andrew J. Ochoa and Dilina Perera and Wenlong Wang and Helmut G. Katzgraber},
  journal={Physical review. E},
  year={2018},
  volume={97 4-1},
  pages={
          043303
        }
}
We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model defined on a cubic lattice, where subproblems, whose couplers are restricted to the two values {-1,+1}, are specified on unit cubes and are parametrized by their local degeneracy. The construction is shown to be equivalent to a type of three-dimensional… 
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References

SHOWING 1-10 OF 66 REFERENCES
On the computational complexity of Ising spin glass models
TLDR
In a spin glass with Ising spins, the problems of computing the magnetic partition function and finding a ground state are studied and are shown to belong to the class of NP-hard problems, both in the two-dimensional case within a magnetic field, and in the three-dimensional cases.
Probing for quantum speedup in spin-glass problems with planted solutions
TLDR
This work introduces a method to construct a set of frustrated Ising-model optimization problems with tunable hardness, and studies the performance of a D-Wave Two device with up to 503 qubits on these problems and compares it to a suite of classical algorithms.
Minor-embedding in adiabatic quantum computation: I. The parameter setting problem
  • V. Choi
  • Computer Science, Physics
    Quantum Inf. Process.
  • 2008
TLDR
The embedded Ising Hamiltonian for solving the maximum independent set (MIS) problem via adiabatic quantum computation (AQC) using an Ising spin-1/2 system is demonstrated.
Patch-planting spin-glass solution for benchmarking.
TLDR
An algorithm to generate spin-glass instances with planted solutions of arbitrary size and structure is introduced and the scaling of the typical computational complexity of these planted instances with various numbers of patches and patch sizes is investigated and compared to random instances.
Ground-state clusters of two-, three-, and four-dimensional +/-J Ising spin glasses.
  • A. Hartmann
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
TLDR
A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +/-J spin-glass models using the genetic cluster-exact approximation method, which allows even for large system sizes to identify clusters of ground states that are connected by chains of zero-energy flips of spins.
Efficient Cluster Algorithm for Spin Glasses in Any Space Dimension.
TLDR
This work presents a cluster algorithm for Ising spin glasses that works in any space dimension and speeds up thermalization by at least one order of magnitude at temperatures where thermalization is typically difficult.
Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly
TLDR
This work proposes to complement head-to-head scaling studies that compare quantum annealing machines to state-of-the-art classical codes with an approach that compares the performance of different algorithms and/or computing architectures on different classes of computationally hard tunable spin-glass instances.
Max 2-SAT with up to 108 qubits
We experimentally study the performance of a programmable quantum annealing processor, the D-Wave One (DW1) with up to 108 qubits, on maximum SAT problem with 2 variables per clause (MAX 2-SAT)
Effective optimization using sample persistence: A case study on quantum annealers and various Monte Carlo optimization methods
TLDR
A general-purpose, multistart algorithm for improving the performance of low-energy samplers used for solving optimization problems that iteratively fixes the value of a large portion of the variables to values that have a high probability of being optimal.
...
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