| Date | 13th, Jul 2021 |
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Recently, functional quantum computers became available for the research community. They enable researchers to investigate the application of quantum computing on various computer vision tasks.
A recent study looks into combinatorial graph matching, a fundamental problem of visual computing.
Photograph of a chip constructed by D-Wave Systems Inc., designed to operate as a 128-qubit superconducting adiabatic quantum optimization processor, mounted in a sample holder. Image credit: D-Wave Systems Inc., License: Creative Commons Attribution 3.0 via Wikiwand
The researchers show how a quadratic assignment problem, an NP-hard problem, which is an essential part of matching problems, can be efficiently solved with quantum annealing for small problem instances. It opens the way for multiple problem types in 3D computer vision.
The numerical verification in simulations and on a real adiabatic quantum computer was performed. It is shown that the proposed approach effectively increases the success rate of solving combinatorial optimization problems with permutation matrix constraints.
Matching problems on 3D shapes and images are challenging as they are frequently formulated as combinatorial quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. In this work, we address such problems with emerging quantum computing technology and propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. We investigate several ways to inject permutation matrix constraints in a quadratic unconstrained binary optimization problem which can be mapped to quantum hardware. We focus on obtaining a sufficient spectral gap, which further increases the probability to measure optimal solutions and valid permutation matrices in a single run. We perform our experiments on the quantum computer D-Wave 2000Q (2^11 qubits, adiabatic). Despite the observed discrepancy between simulated adiabatic quantum computing and execution on real quantum hardware, our reformulation of permutation matrix constraints increases the robustness of the numerical computations over other penalty approaches in our experiments. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures, which opens up multiple new directions for solving matching problems in 3D computer vision and graphics.
Research paper: Seelbach Benkner, M., Golyanik, V., Theobalt, C., and Moeller, M., “Adiabatic Quantum Graph Matching with Permutation Matrix Constraints”, 2021. Link: https://arxiv.org/abs/2107.04032
Link to the project page: https://gvv.mpi-inf.mpg.de/projects/QGM/
