Adiabatic Quantum Graph Matching with Permutation Matrix Constraints

Victoria D. Doty

Not long ago, functional quantum desktops turned out there for the analysis community. They enable researchers to investigate the application of quantum computing on many computer vision jobs.

A new study looks into combinatorial graph matching, a elementary dilemma of visual computing.

Photograph of a chip manufactured by D-Wave Systems Inc., designed to work as a 128-qubit superconducting adiabatic quantum optimization processor, mounted in a sample holder. Impression credit rating: D-Wave Systems Inc., License: Artistic Commons Attribution 3. via Wikiwand

The researchers clearly show how a quadratic assignment dilemma, an NP-challenging dilemma, which is an necessary portion of matching issues, can be effectively solved with quantum annealing for small dilemma cases. It opens the way for several dilemma sorts in 3D computer vision.

The numerical verification in simulations and on a genuine adiabatic quantum computer was carried out. It is demonstrated that the proposed method proficiently increases the accomplishment fee of solving combinatorial optimization issues with permutation matrix constraints.

Matching issues on 3D designs and photos are demanding as they are frequently formulated as combinatorial quadratic assignment issues (QAPs) with permutation matrix constraints, which are NP-challenging. In this perform, we address these issues with emerging quantum computing technological innovation and propose a number of reformulations of QAPs as unconstrained issues ideal for economical execution on quantum hardware. We investigate a number of ways to inject permutation matrix constraints in a quadratic unconstrained binary optimization dilemma which can be mapped to quantum hardware. We concentrate on getting a adequate spectral hole, which further increases the probability to evaluate best alternatives and valid permutation matrices in a solitary operate. We complete our experiments on the quantum computer D-Wave 2000Q (two^eleven qubits, adiabatic). Despite the observed discrepancy amongst simulated adiabatic quantum computing and execution on genuine quantum hardware, our reformulation of permutation matrix constraints increases the robustness of the numerical computations about other penalty approaches in our experiments. The proposed algorithm has the potential to scale to larger proportions on long term quantum computing architectures, which opens up several new directions for solving matching issues in 3D computer vision and graphics.

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

Hyperlink to the job web site: https://gvv.mpi-inf.mpg.de/initiatives/QGM/


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