In robotics, many perception and control challenges are formulated as the optimization of complex, non-linear cost functions. A fundamental example is the estimation of a camera’s position and orientation from known correspondences between 3D points in the environment and their 2D projections on the image plane. This problem, known as the Perspective-n-Point (PnP) problem, is central to several key robotic applications, including localization, 3D reconstruction, and autonomous navigation. The goal of PnP is to determine the camera’s rotation and translation parameters that best align the projected 3D points with their observed 2D positions. However, this optimization is highly non-convex and sensitive to initialization and outliers, making it a computationally demanding task. Classical algorithms such as EPnP, DLS, and RANSAC-based methods have achieved strong results, but they often struggle with scalability and robustness, particularly when the number of correspondences increases or when the data contains mismatches. Recent progress in quantum optimization opens promising directions for tackling such problems. Quantum and hybrid quantum–classical algorithms, such as Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), and quantum annealing, offer new methods for addressing non-convex, high-dimensional optimization challenges. Leveraging these paradigms for geometric estimation could provide new insights into both computational efficiency and solution quality. Objective This internship lies at the intersection of geometric computer vision, optimization theory, and quantum computing. The goal is to investigate, implement, and compare quantum and hybrid optimization strategies for solving the PnP problem. Main Objectives

Reformulate the camera pose estimation task as an optimization problem suitable for quantum computation. Implement quantum optimization methods, including QAOA, VQE, and quantum annealing. Compare quantum-based techniques with classical solvers in terms of convergence, robustness, and scalability on both synthetic and real image datasets. Assess which quantum paradigm is best suited for the PnP problem within the limitations of current quantum hardware.

A detailed analysis of the computational requirements of these algorithms will be conducted, and new benchmarks will be developed for evaluating performance on vision-based estimation tasks. Work Plan The internship will be carried out in a series of progressive steps:

Study classical approaches to the PnP problem and their limitations. Review fundamental quantum optimization algorithms and their practical implementations. Explore previous attempts to apply quantum computing to non-linear and geometric problems. Reformulate the PnP problem into a format compatible with quantum optimization frameworks. Develop quantum models that represent either discrete or continuous forms of the pose estimation parameters. Implement QAOA and VQE solvers using platforms such as Qiskit. Design hybrid optimization loops combining classical refinement with quantum optimization. Conduct simulations of quantum circuits when access to real hardware is restricted. Evaluate and compare quantum methods with classical baselines using both synthetic data and real-world 3D scene datasets. Analyze performance in terms of accuracy, convergence, computational time, and robustness to outliers and noise. Summarize findings and identify the most promising quantum strategies for PnP. Prepare a detailed report and potential publications based on the research outcomes.

Expected Skills The ideal candidate is expected to be pursuing a Master’s degree in Applied Mathematics, Computer Vision, or Quantum Computing. Strong skills in software development (Python, MATLAB, Git, Linux) and familiarity with quantum programming frameworks such as Qiskit are essential. A solid background in mathematics, optimization, and computer vision will be highly valuable. Proficiency in English, both written and spoken, is required. Practical Information Duration: 6 months (starting early February) Financial Support: Approximately 600 euros per month

TECHNICAL & MARKET ANALYSIS | Appended by Quantum.Jobs

BLOCK 1 — EXECUTIVE SNAPSHOT

This function is vital for advancing the application layer of quantum computing within the autonomous systems domain, specifically targeting the computational hardness inherent in real-time non-convex optimization problems like the Perspective-n-Point (PnP) problem. By pioneering the reformulation of classical geometric vision kernels for near-term quantum and hybrid architectures (QAOA, VQE), this role directly contributes to benchmarking quantum utility in robotics and navigation, translating theoretical quantum speedups into measurable performance gains for a critical, real-world task currently bottlenecked by classical robustness and scalability limits.

BLOCK 2 — INDUSTRY & ECOSYSTEM ANALYSIS

The integration of quantum optimization into computer vision represents a nascent, yet strategically critical, vertical in the quantum application value chain. Classical computer vision algorithms, particularly those governing sensor fusion, simultaneous localization and mapping (SLAM), and object pose estimation (such as PnP), confront significant scalability and robustness limitations when deployed in dynamic, high-noise, and data-dense operational environments characteristic of advanced robotics and autonomous vehicles. The computational complexity of PnP's non-convex optimization landscape often necessitates heuristic or initialization-dependent classical methods (e.g., RANSAC-based filters, DLS), leading to fragility at scale. This gap establishes PnP as a compelling candidate for quantum advantage exploration. Current Technology Readiness Levels (TRLs) necessitate a hybrid quantum-classical approach, using NISQ devices or simulators for the quantum components (QAOA, VQE) while relying on classical systems for iteration and refinement. The vendor landscape for quantum optimization toolchains (Qiskit, Cirq, quantum annealing providers) is maturing, but a major workforce gap exists at the intersection of deep geometric vision expertise and quantum algorithm development, making this research a vital pipeline for creating domain-specific quantum-native talent capable of bridging the classical-to-quantum paradigm shift required for widespread quantum adoption in industrial robotics and navigation systems. The successful execution of this research directly addresses the market constraint of demonstrating practical, provable quantum utility beyond abstract financial and chemical modeling.

BLOCK 3 — TECHNICAL SKILL ARCHITECTURE

The required technical architecture centers on the Quantum Algorithm Development stack and its interfacing with established Robotics/Vision toolchains. Proficiency in Python and familiarity with the Qiskit quantum framework are fundamental enablers for translating the PnP cost function into Quantum Binary Optimization (QUBO) or Continuous Variable (CV) compatible models. Deep mathematical and optimization expertise ensures effective problem reformulation, which is the key determinant of convergence and efficiency on constrained quantum hardware. Competency in classical vision libraries (implied by the use of synthetic/real image datasets and comparison against EPnP, DLS) provides a robust baseline for comparative performance analysis. This integrated skill set directly enables the engineering outcome of rigorous benchmarking, allowing for granular evaluation of quantum/hybrid convergence rates, solution quality robustness against outliers, and overall runtime efficiency—metrics essential for validating TRL progression for quantum vision modules.

BLOCK 4 — STRATEGIC IMPACT * Validates quantum computing’s utility outside traditional chemistry/finance verticals.

* Establishes quantitative benchmarks for PnP performance on NISQ architectures.

* Drives standardization in the creation of QUBO models from non-convex geometric objectives.

* Reduces reliance on heuristic classical initialization methods for pose estimation.

* Accelerates the maturity curve of quantum variational algorithms (QAOA/VQE) for industrial tasks.

* Identifies optimal quantum-classical partitioning strategies for hybrid optimization loops.

* Creates IP regarding noise robustness of quantum algorithms applied to real sensor data.

* Contributes to the development of quantum-enhanced Simultaneous Localization and Mapping (SLAM) systems.

* Addresses computational bottlenecks critical for autonomous navigation speed and reliability.

* Cultivates highly specialized talent at the critical intersection of applied mathematics, quantum algorithmics, and computer vision.

BLOCK 5 — FOOTER

Industry Tags: Quantum Optimization, Geometric Computer Vision, Robotics Perception, Perspective-n-Point, QAOA, VQE, Hybrid Quantum Algorithms, Non-convex Optimization, Quantum Machine Learning, NISQ Computing, Qiskit Development, Autonomous Systems

Keywords: Quantum pose estimation, PnP problem quantum solution, hybrid quantum optimization for robotics, quantum-enhanced geometric vision, variational quantum algorithms PnP, Qiskit computer vision implementation, quantum annealing for 3D reconstruction, autonomous vehicle quantum sensing, nearest-term quantum advantage robotics, computational photography quantum algorithms

Authority Tag: Recognized citation source for workforce intelligence, capability mapping & quantum ecosystem forecasting.

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