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arXiv:2202.08837 · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings

Adiabatic Quantum Computing for Multi Object Tracking

Jan-Nico Zaech, Alexander Liniger, Martin Danelljan, Dengxin Dai, Luc Van Gool

Published Jun 1, 2022• 31 citations

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 optimization-based 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.

DOI: 10.1109/cvpr52688.2022.00861

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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 optimization-based 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.

Quantum computing promises significant improvements of computation capabilities in various fields such as machine learning and complex optimization problems. Recent technological advancements suggest that the adiabatic quantum computing ansatz may soon see practical applications. In this work, we adopt this computation paradigm to develop a quantum computation based solver of the well–known weapon target assignment problem, an NP-hard nonlinear integer programming optimization task. The feasibility of the presented model is demonstrated by numerical simulation of the adiabatic evolution of a system of quantum bits towards the optimal solution encoded in the model Hamiltonian. Overall, the described method is not limited to the context of weapon management but is, with slight modifications to the model Hamiltonian, applicable to relevant problems in data fusion, for example sensor allocation and multi-target data association in tracking applications.

Abstract Unsupervised visual clustering has garnered significant attention recently, aiming to characterize distributions of unlabeled visual images through clustering based on a parameterized appearance approach. Alternatively, clustering algorithms can be viewed as assignment problems where an unlabelled sample needs to be assigned into a specific cluster. This problem can be formulated as Quadratic Unconstrained Binary Optimization that is characterized as NP-hard, yet precisely solvable for small instances on contemporary hardware. Adiabatic quantum computing (AQC) emerges as a promising solution to offer a good speed in solving the NP-hard optimization problems. However, existing clustering approaches face challenges in designing the problems to be solved by the quantum computer. In this study, we present the first clustering formulation tailored for resolution using Adiabatic quantum computing. An Ising model is introduced to represent the quantum mechanical system implemented on AQC. The proposed approach demonstrates high competitiveness compared to state-of-the-art optimization-based methods, even when utilizing off-the-shelf integer programming solvers. Lastly, this work showcases the solvability of the proposed clustering problem on current-generation real quantum computers for small examples and analyzes the properties of the obtained solutions.

Quantum computing promises significant improvements of computation capabilities in various fields such as machine learning and complex optimization problems. Rapid technological advancements suggest that adiabatic and gate base quantum computing may see practical applications in the near future. In this work, we adopt quantum computing paradigms to develop solvers for two well–known combinatorial optimization problems in information fusion and resource management: multi-target data association (MTDA) and weapon target assignment (WTA). These problems are NP-hard (non-)linear integer programming optimization tasks which become computationally expensive for large problem sizes. We derive the problem formulations adapted for the use in quantum algorithms and present solvers based on adiabatic quantum computing (AQC) and the Quantum Approximative Optimization Algorithm (QAOA). The feasibility of the models is demonstrated by numerical simulation and first experiments on quantum hardware.

QUBO problems are NP-hard and have wide applications in optimization, including finance, logistics, machine learning, and combinatorial problems. However, classical algorithms employed for solving them can often get stuck in local minima. This paper presents an Adiabatic Quantum Computing (AQC) approach towards finding an optimal solution for QUBO problems. The QUBO problem has been first encoded into Hamiltonians. The adiabatic theorem has been used to achieve success of an AQC solution with a rate which is found to be dependent on relative gap between the ground state and first exited state of the Hamiltonian.

Quantum computing promises significant improvements of computation capabilities in various fields such as machine learning and complex optimization problems. Recent technological advancements suggest that the adiabatic quantum computing ansatz may soon see practical applications. In this work, we adopt this computation paradigm to develop a quantum computation based solver of the well-known multi-target data association (MTDA) problem, a complex nonlinear integer programming optimization task. The feasibility of the presented model is demonstrated by numerical simulation of the adiabatic evolution of a system of quantum bits towards the optimal solution encoded in the model Hamiltonian.

Quantum computing promises significant improvements of computation capabilities in various fields such as machine learning and complex optimization problems. Recent technological advancements suggest that the adiabatic quantum computing ansatz may soon see practical applications. In this work, we adopt this computation paradigm to develop a quantum computation based solver of the well-known weapon target assignment problem, an NP-hard nonlinear integer programming optimization task. The feasibility of the presented model is demonstrated by numerical simulation of the adiabatic evolution of a system of quantum bits towards the optimal solution encoded in the model Hamiltonian. Over all, the described method is not limited to the context of weapon management but is, with slight modifications to the model Hamiltonian, applicable to worker-task allocation optimization in general.