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arXiv:2209.00615 · Sensor Data Fusion: Trends, Solutions, Applications (SDF)

Multiple Target Tracking and Filtering Using Bayesian Diabatic Quantum Annealing

Timothy M. McCormick, Zipporah Klain, Ian Herbert, Anthony M. Charles, Robert Blair Angle, Bryan R. Osborn, Roy L. Streit

Published Oct 12, 2022• 2 citations
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Abstract

In this paper, we present a hybrid quantum/classical algorithm to solve an NP-hard combinatorial problem called the multiple target data association (MTDA) and tracking problem. We use diabatic quantum annealing (DQA) to enumerate the low energy, or high probability, feasible assignments, and we use a classical computer to find the Bayesian expected mean track estimate by summing over these assignments. We demonstrate our hybrid quantum/classical approach on a simple example. This may be the first demonstration of a Bayesian hybrid quantum-classical multiple target tracking filter. We contrast our DQA method with the adiabatic quantum computing (AQC) approach to MTDA. We give a theoretical overview of DQA and characterize some of the technical limitations of using quantum annealers in this novel diabatic modality.

DOI
10.1109/sdf55338.2022.9931948

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In this paper, we present a hybrid quantum/classical algorithm to solve an NP-hard combinatorial problem called the multiple target data association (MTDA) and tracking problem. We use diabatic quantum annealing (DQA) to enumerate the low energy, or high probability, feasible assignments, and we use a classical computer to find the Bayesian expected mean track estimate by summing over these assignments. We demonstrate our hybrid quantum/classical approach on a simple example. This may be the first demonstration of a Bayesian hybrid quantum-classical multiple target tracking filter. We contrast our DQA method with the adiabatic quantum computing (AQC) approach to MTDA. We give a theoretical overview of DQA and characterize some of the technical limitations of using quantum annealers in this novel diabatic modality.
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.
Recent work at Fraunhofer FKIE shows that More-field's method for multiple target data association can in theory be solved on an adiabatic quantum computer. The present paper validates the theory and examines the significant limitations of currently available adiabatic quantum computers for solving the data association problem. The limitations of such architectures are both theoretical and practical in nature, and both are discussed. The data association problem is formulated as a quadratic unconstrained binary optimization (QUBO) problem; consequently, much of the discussion is relevant to other applications which are, or can be, posed as QUBO problems.
We propose a quantum algorithm for the filtering step in Bayesian state estimation, based on adiabatic quantum computing (AQC).The approach embeds the likelihood function into the energy landscape of an Ising Hamiltonian, enabling the posterior distribution to emerge through quantum annealing.Unlike existing gate-based methods, our formulation avoids complex conditional operations and scales more naturally with the size of the state space.Numerical simulations confirm that the resulting distributions closely match the correct posterior, even with approximate parameter settings.This demonstrates the feasibility of AQC as a tool for probabilistic inference in high-dimensional filtering problems.
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 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.
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum computing, quantum annealing (QA), has been proposed to solve these problems by encoding optimization problems into physical energy landscapes and solving them by quantum tunnelling systematically through exploration of solution space. This is a critical review that summarizes the current applications of quantum annealing to combinatorial optimization and includes a theoretical background, hardware designs, algorithm implementation strategies, encoding and embedding schemes, protocols to benchmark quantum annealing, areas of implementation, and links with the quantum algorithms implementation with gate-based hardware and classical solvers. We develop a unified framework, relating adiabatic quantum dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to modern flux-qubit annealers (Chimera, Pegasus, Zephyr topologies), and emergent architectures (Lechner-Hauke-Zoller systems, Rydberg atom platforms), and hybrids of quantum and classical computation. Through our analysis, we find that overhead in embedding and encoding is the largest determinant of the scalability and performance (this is not just the number of qubits). Minor embeddings also usually have a physical qubit count per logical variable of between 5 and 12 qubits, which limits effective problem capacity by 80-92% and, due to chain-breaking errors, compromises the quality of solutions.