  In this paper we develop a quantum optimization algorithm and use it to solve
the bundle adjustment problem with a simulated quantum computer. Bundle
adjustment is the process of optimizing camera poses and sensor properties to
best reconstruct the three-dimensional structure and viewing parameters. This
problem is often solved using some implementation of the Levenberg--Marquardt
algorithm. In this case we implement a quantum algorithm for solving the linear
system of normal equations that calculates the optimization step in
Levenberg--Marquardt. This procedure is the current bottleneck in the
algorithmic complexity of bundle adjustment. The proposed quantum algorithm
dramatically reduces the complexity of this operation with respect to the
number of points.
  We investigate 9 configurations of a toy-model for bundle adjustment, limited
to 10 points and 2 cameras. This optimization problem is solved both by using
the sparse Levenberg-Marquardt algorithm and our quantum implementation. The
resulting solutions are presented, showing an improved rate of convergence,
together with an analysis of the theoretical speed up and the probability of
running the algorithm successfully on a current quantum computer.
  The presented quantum algorithm is a seminal implementation of using quantum
computing algorithms in order to solve complex optimization problems in
computer vision, in particular bundle adjustment, which offers several avenues
of further investigations.
