Adiabatic Quantum Computing for Multi Object Tracking

Abstract

Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. The association step naturally leads to discrete optimization problems. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. Adiabatic quantum computing (AQC) offers a solution for this, as it has the potential to provide a considerable speedup on a range of NP-hard optimization problems in the near future. However, current MOT formulations are unsuitable for quantum computing due to their scaling properties. In this work, we therefore propose the first MOT formulation designed to be solved with AQC. We employ an Ising model that represents the quantum mechanical system implemented on the AQC. We show that our approach is competitive compared with state-of-the-art optimizationbased approaches, even when using of-the-shelf integer programming solvers. Finally, we demonstrate that our MOT problem is already solvable on the current generation of real quantum computers for small examples, and analyze the properties of the measured solutions.

Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization

“…Some of the proposed algorithms require additional constraints formulated as weighted linear terms (Lagrange multipliers) [72,9,79]. Such conditions rectify the original unconstrained objective and preserve the QUBO form consumable by modern QA.…”

“…inserted, row-wise) to inject soft-permutation constraints into QUBO. This required tuning of a parameter λ ∈ R, whose large values are found to cause problems [9,72,79]. As a heuristic, [72] suggested a spectral-gap 7 analysis to bound the regularization coefficient λ.…”

“…Albeit restricted, experimental realisations of QA, such as DWave [26], can solve non-convex, quadratic unconstrained binary optimization (QUBO) problems, without resorting to continuous relaxations. This premise of AQC and QA has led to the emergence of quantum computer vision (QCV), where researchers started to port existing computer vision problems into forms amenable to quantum computation [42,55,38,72,79,9].…”

“…For example, estimating correspondences require solving QBOs for permutations and not for arbitrary binary vectors. To this end, the state of the art QCV methods either use a regularization with cherry picked coefficients [9] or resort to heuristics for auto-controlling the impact of the constraints [72,79]. Unfortunately, none of these approaches are optimal and jeopardize the solution quality guarantees of quantum computers.…”