Solving Set Cover with Pairs Problem using Quantum Annealing
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ABSTRACT
Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph preserves the structure of the original SCP instance and in particular, the embedding for general complete bipartite graphs and logical disjunctions may be of broader use than that the specific problem we deal with. No MeSH data available. |
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Mentions: Consider the SCP instance shown in Fig. 2a. With the mapping presented in Theorem 1, we arrive at an Ising instance ISING (h, J) where α = 1/4 in (10) and h, J are presented in Supplementary Material Details of the example SCP instance. The ground state subspace of the Hamiltonian in (2) with hi and Jij coefficients defined above, restricted to the si elements is spanned by . This corresponds to A = {f1, f4}, the solution to the SCP instance. Figure 2b illustrates the interaction graph of the spins in the Ising Hamiltonian that corresponds to the SCP instance. |
View Article: PubMed Central - PubMed
Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph preserves the structure of the original SCP instance and in particular, the embedding for general complete bipartite graphs and logical disjunctions may be of broader use than that the specific problem we deal with.
No MeSH data available.