  Quantum computing is expected to transform a range of computational tasks
beyond the reach of classical algorithms. In this work, we examine the
application of variational quantum algorithms (VQAs) for unsupervised image
segmentation to partition images into separate semantic regions. Specifically,
we formulate the task as a graph cut optimization problem and employ two
established qubit-efficient VQAs, which we refer to as Parametric Gate Encoding
(PGE) and Ancilla Basis Encoding (ABE), to find the optimal segmentation mask.
In addition, we propose Adaptive Cost Encoding (ACE), a new approach that
leverages the same circuit architecture as ABE but adopts a problem-dependent
cost function. We benchmark PGE, ABE and ACE on synthetically generated images,
focusing on quality and trainability. ACE shows consistently faster convergence
in training the parameterized quantum circuits in comparison to PGE and ABE.
Furthermore, we provide a theoretical analysis of the scalability of these
approaches against the Quantum Approximate Optimization Algorithm (QAOA),
showing a significant cutback in the quantum resources, especially in the
number of qubits that logarithmically depends on the number of pixels. The
results validate the strengths of ACE, while concurrently highlighting its
inherent limitations and challenges. This paves way for further research in
quantum-enhanced computer vision.
