Parameter Efficiency of Variational Quantum Circuits in Image Classification: The Role of Circuit Depth

Abstract

The practical value of quantum machine learning must be derived from efficiency rather than scale, as current NISQ processors support only small, shallow circuits. This paper evaluated whether variational quantum circuits (VQCs) can reduce the trainable parameter count in an image classification scenario while preserving accuracy. Experimentation compared quantum classifier heads to parameter-matched classical heads on an identical set of frozen features drawn from the Fashion-MNIST dataset by a CNN. 9 configurations of a quantum circuit crossed 4, 6, and 8 qubits with 1, 2, and 4 entangling layers, each matched to a multilayer perceptron with an approximately equal parameter count. The linear probes served as a floor baseline for all 105 runs across 5 random seed values. 7 out of 9 quantum-based configurations met the mean test accuracy of no more than 1 percentage point below its matched classical head, enforced by the pre-specified criterion. The 2 failures were single-layer circuits, with each falling roughly 8 points below its matched classical head and 12 points below the circuit-free linear probe; in total, 6 configs with 2+ layers passed, with the smallest at 74 trainable parameters. The general trend noticed was that accuracy increased progressively with depth. The 4-layer circuits exceeded the linear probe at every qubit count and produced the highest accuracy at 6 and 8 qubits. The simulation ran noiselessly; VQCs preserved accuracy at the matched parameter budget when depth was given, showcasing depth rather than qubit count gating performance.