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In this paper we develop a quantum optimization algorithm and use it to solvethe bundle adjustment problem with a simulated quantum computer. Bundleadjustment is the process of optimizing camera poses and sensor properties tobest reconstruct the three-dimensional structure and viewing parameters. Thisproblem is often solved using some implementation of the Levenberg--Marquardtalgorithm. In this case we implement a quantum algorithm for solving the linearsystem of normal equations that calculates the optimization step inLevenberg--Marquardt. This procedure is the current bottleneck in thealgorithmic complexity of bundle adjustment. The proposed quantum algorithmdramatically reduces the complexity of this operation with respect to thenumber of points.  We investigate 9 configurations of a toy-model for bundle adjustment, limitedto 10 points and 2 cameras. This optimization problem is solved both by usingthe sparse Levenberg-Marquardt algorithm and our quantum implementation. Theresulting solutions are presented, showing an improved rate of convergence,together with an analysis of the theoretical speed up and the probability ofrunning the algorithm successfully on a current quantum computer.  The presented quantum algorithm is a seminal implementation of using quantumcomputing algorithms in order to solve complex optimization problems incomputer vision, in particular bundle adjustment, which offers several avenuesof further investigations.

Quantum Levenberg--Marquardt Algorithm for optimization in Bundle Adjustment