[Paper Review] Adiabatic Quantum Computing for Multi Object Tracking

Jan-Nico Zaech, Alexander Liniger+3 more|arXiv (Cornell University)|Feb 17, 2022

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper presents the first adiabatic quantum computing (AQC) formulation for Multi-Object Tracking (MOT), mapping the assignment problem to a Quadratic Unconstrained Binary Optimization (QUBO) problem solvable via quantum annealing. It achieves competitive MOTA scores (49.9%) on MOT15 and demonstrates feasibility on real D-Wave hardware for small-scale tracking instances with optimized Lagrangian multipliers.

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.

Motivation & Objective

• To address the NP-hard discrete optimization challenge in Multi-Object Tracking (MOT) using adiabatic quantum computing (AQC).
• To design a QUBO formulation for MOT that is compatible with current AQC hardware, particularly D-Wave systems.
• To improve solution probability on noisy quantum hardware by optimizing Lagrangian multipliers using few problem measurements.
• To demonstrate that real-world MOT problems can be solved on current-generation quantum computers, even at small scales.
• To establish a quantum-compatible MOT framework that scales linearly with detections, tracks, and timesteps.

Proposed method

• Formulates the MOT data association problem as a QUBO problem, representing it as an Ising spin glass Hamiltonian suitable for AQC.
• Uses a Lagrangian relaxation approach to handle constraints, with multipliers tuned via few measurements to increase solution probability.
• Employs quantum annealing on D-Wave Advantage hardware with 1600 µs annealing time and 500 measurements per subproblem.
• Splits long sequences into 5-frame segments for tractable problem size, solving each subproblem independently on the quantum processor.
• Validates classical performance using GUROBI and compares results with state-of-the-art methods like ApLift.
• Analyzes energy levels and solution probabilities across different noise levels and offset parameters to assess robustness.

Experimental results

Research questions

• RQ1 Can a quantum computing formulation of MOT be designed that is compatible with current adiabatic quantum hardware?
• RQ2 How does the solution probability of quantum annealing compare to classical solvers for small-scale MOT problems?
• RQ3 To what extent can Lagrangian multipliers be optimized using minimal measurements to improve solution fidelity on noisy quantum devices?
• RQ4 What is the performance of the proposed AQC-based MOT method on real-world datasets like MOT15 and PETS09-S2L1?
• RQ5 Can current quantum hardware solve real-world MOT instances with occlusions, and how do energy levels correlate with solution quality?

Key findings

• The proposed AQC-based MOT formulation achieves a MOTA score of 49.9% on the MOT15 dataset, performing within 1.2% of the state-of-the-art ApLift method.
• Under leave-one-out cross-validation on the MOT15 training set, the method improves by 0.2% in MOTA over ApLift, indicating robustness to higher detection density.
• On the PETS09-S2L1 sequence, the method successfully tracks three objects through two occlusions using D-Wave Advantage hardware, with solution probabilities of 0.8% even without offset tuning.
• For subproblems with occlusions (e.g., frames 5 and 10), solution probability drops due to degenerate low-energy states, but remains measurable at 3.5% with optimized Lagrangian multipliers.
• The method shows that solution probability can be significantly enhanced using only a few problem measurements to tune Lagrangian multipliers, even under noise.
• Energy level analysis confirms that optimal solutions are consistently found at the lowest energy states, validating the quantum annealing approach for MOT.