Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Towards a syntactic characterization of PTAS
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Journal of the ACM (JACM)
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Approximation algorithms
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
Polynomial-Time Approximation Algorithms for Ising Model (Extended Abstract)
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
How Powerful is Adiabatic Quantum Computation?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The Power of Quantum Systems on a Line
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
The complexity of quantum spin systems on a two-dimensional square lattice
Quantum Information & Computation
Minor-embedding in adiabatic quantum computation: I. The parameter setting problem
Quantum Information Processing
The UGC Hardness Threshold of the Lp Grothendieck Problem
Mathematics of Operations Research
Spinto: high-performance energy minimization in spin glasses
Proceedings of the Conference on Design, Automation and Test in Europe
Product-state approximations to quantum ground states
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We describe a classical approximation algorithm for evaluating the ground state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of spins and exponentially with 1/∈, where ∈ is the worst-case relative error. This result contrasts the well known fact that exact computation of the ground state energy for the two-dimensional Ising spin glass model is NP-hard. We also present a classical approximation algorithm for the quantum Local Hamiltonian Problem or Quantum Ising Spin Glass problem on a planar graph with bounded degree which is known to be a QMA-complete problem. Using a different technique we find a classical approximation algorithm for the quantum Ising spin glass problem on the simplest planar graph with unbounded degree, the star graph.