Limits...
Solving Set Cover with Pairs Problem using Quantum Annealing

View Article: PubMed Central - PubMed

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.


Related in: MedlinePlus

Embedding the interaction graph of the example physical system in Fig. 2b onto F(4, 4, 4).Note that the structure of Fig. 2 is preserved on the Chimera graph.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5037405&req=5

f7: Embedding the interaction graph of the example physical system in Fig. 2b onto F(4, 4, 4).Note that the structure of Fig. 2 is preserved on the Chimera graph.

Mentions: Proof. Our embedding combines ideas from Lemma 1 and 2. We modify the mapping ϕp,q constructed in Lemma 1 to produce a new mapping θp,q that produces more spacing between the embedded nodes (see for example and in Fig. 7):


Solving Set Cover with Pairs Problem using Quantum Annealing
Embedding the interaction graph of the example physical system in Fig. 2b onto F(4, 4, 4).Note that the structure of Fig. 2 is preserved on the Chimera graph.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037405&req=5

f7: Embedding the interaction graph of the example physical system in Fig. 2b onto F(4, 4, 4).Note that the structure of Fig. 2 is preserved on the Chimera graph.
Mentions: Proof. Our embedding combines ideas from Lemma 1 and 2. We modify the mapping ϕp,q constructed in Lemma 1 to produce a new mapping θp,q that produces more spacing between the embedded nodes (see for example and in Fig. 7):

View Article: PubMed Central - PubMed

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.


Related in: MedlinePlus