Qubit-efficient Variational Quantum Algorithms for Image Segmentation

TL;DR

This paper tackles the challenge of performing image segmentation on near-term quantum hardware by formulating segmentation as a graph-cut QUBO and introducing qubit-efficient variational quantum algorithms. It presents three encoding schemes—Parametric Gate Encoding (PGE), Ancilla Basis Encoding (ABE), and Adaptive Cost Encoding (ACE)—to reduce qubit requirements from linear in the number of pixels to logarithmic, with ACE offering a problem-specific cost that aligns circuit optimization with the true min-cut objective. The authors provide a theoretical scalability analysis showing significant resource savings relative to QAOA, and empirical evidence on synthetic grid images demonstrating faster and more consistent training for ACE, along with strong performance even at small scales. Collectively, the work advances quantum-assisted computer vision by enabling scalable image segmentation on NISQ devices and motivates further research into task-tailored cost functions and optimization strategies. The results indicate a viable pathway to leverage quantum resources for complex vision tasks while highlighting challenges in measurement overhead and optimizer design that warrant future exploration.

Abstract

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.

Figures (4)

• Figure 1: The figure depicts an architecture for segmenting an image. Generating a graph representation of the image, the distinct semantic regions in the image are identified by finding the minimum cut in the graph that can be formulated as Quadratic Unconstrained Binary Optimization (QUBO). The QUBO problem is subsequently solved using a VQA by optimizing the circuit parameters that incidentally explore an exponentially large solution space to locate the global optimum, which can be decoded as the segmentation mask.
• Figure 2: Transformation of a $2\times 2$ pixel image into a grid graph, where edge weights indicate pixel similarity. The red dashed line depicts the edges that are cut to partition the graph.
• Figure 3: Circuit schematic of ABE/ACE for finding the segmentation mask of the example image in Fig. \ref{['fig: example']}. illustrating the encoding of the solution of a QUBO problem of size $4$ into a quantum state facilitated by 3 qubits: $q_1, q_2$ are the register qubits and $q_3$ is the ancilla qubit. The circuit initialization employs Hadamard gates to induce superposition across all qubits, followed by two layers of hardware-efficient ansatz with entanglement and rotation gates parameterized by $\vec{\Theta}$. Executing and measuring the circuit obtains a probability distribution over the basis states. For the basis states whose register qubits are the same encodes the value of the binary variable. For example, with the register qubit basis states $|\phi_1\rangle_r = |00\rangle$, we obtain the value $x_{v_1} = 1$ as the probability of the ancilla qubit in state $|1\rangle > |0\rangle$ (Eq. \ref{['eqn: minimal decoding']}).
• Figure 4: The figure illustrates the performance of PGE, ABE and ACE for finding the minimum cut on grid graphs of size $2 \times 2$ and $4 \times 4$ with the layers in the ansatz of the quantum circuit ranging from $1$ to $5$ in terms of the solution quality and the efficiency of the optimization process. The plots show the average and standard deviation of the relative errors in the obtained solution's cost as a measure of quality and the number of iterations to quantify the trainability using COBYLA, Powell, and SLSQP optimizers.