Adiabatic Quantum Graph Matching with Permutation Matrix Constraints

Lately, purposeful quantum computers turned out there for the investigation neighborhood. They allow researchers to investigate the application of quantum computing on several computer system eyesight duties.

A modern examine looks into combinatorial graph matching, a essential difficulty of visible computing.

The researchers clearly show how a quadratic assignment difficulty, an NP-tough difficulty, which is an important component of matching issues, can be competently solved with quantum annealing for smaller difficulty situations. It opens the way for many difficulty styles in 3D computer system eyesight.

The numerical verification in simulations and on a genuine adiabatic quantum computer system was done. It is demonstrated that the proposed technique effectively increases the success price of fixing combinatorial optimization issues with permutation matrix constraints.

Matching issues on 3D shapes and images are demanding as they are routinely formulated as combinatorial quadratic assignment issues (QAPs) with permutation matrix constraints, which are NP-tough. In this get the job done, we tackle such issues with emerging quantum computing technological innovation and suggest many reformulations of QAPs as unconstrained issues suited for successful execution on quantum components. We investigate many ways to inject permutation matrix constraints in a quadratic unconstrained binary optimization difficulty which can be mapped to quantum components. We target on getting a enough spectral hole, which even more increases the likelihood to evaluate optimum answers and legitimate permutation matrices in a one operate. We perform our experiments on the quantum computer system D-Wave 2000Q (two^eleven qubits, adiabatic). Irrespective of the noticed discrepancy between simulated adiabatic quantum computing and execution on genuine quantum components, our reformulation of permutation matrix constraints increases the robustness of the numerical computations more than other penalty approaches in our experiments. The proposed algorithm has the possible to scale to better dimensions on long run quantum computing architectures, which opens up many new directions for fixing matching issues in 3D computer system eyesight and graphics.

Analysis paper: Seelbach Benkner, M., Golyanik, V., Theobalt, C., and Moeller, M., “Adiabatic Quantum Graph Matching with Permutation Matrix Constraints”, 2021. Connection: https://arxiv.org/abs/2107.04032

Connection to the challenge web site: https://gvv.mpi-inf.mpg.de/jobs/QGM/

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