Why telling a quantum image model to ignore rotation can help

Imagine sorting pictures of galaxies by shape. A galaxy’s classification should not change just because the image is rotated. But a machine-learning system shown only a few examples may treat each orientation as a separate pattern, or latch onto an accidental clue that happens to predict the label in its training data.

That is the problem Giuseppe D’Ambruoso and colleagues investigate in a study of quantum neural networks, or QNNs: trainable quantum circuits used to classify data. Their central question is whether requiring a model to ignore certain image transformations improves its predictions, rather than some other difference in circuit design explaining the result.

A controlled comparison

The researchers focused on the eight symmetries of a square: rotations by 90-degree steps and reflections, collectively called the dihedral group D4. For their chosen tasks, the label was intended to stay the same under those transformations. A model that is invariant gives the same output for an image and its rotated or reflected versions.

They compared four eight-qubit models. The models shared their image encoding, circuit layout and number of trainable parameters; the circuit variants also had equivalent dynamical Lie algebras, a mathematical description of the operations their gates can generate. The design separated two questions: whether the circuit itself respected the symmetry, and whether the model’s final prediction was invariant. One model became invariant by averaging predictions over transformed copies of an image, a process called group twirling.

The team tested four binary classification tasks: handwritten 4s versus 5s, a synthetic cross-versus-square task, face-on versus edge-on galaxies, and elongated versus other deformed red blood cells. In the main experiments, models trained on 40 images per task—or 20 for the synthetic task—and were evaluated across 15 training seeds. The circuits were simulated exactly, without measurement shot noise. The researchers also tested artificial shortcuts and simulated a noise model intended to represent a superconducting quantum processor.

What the tests found

Across all four tasks, the invariant models had smaller gaps between performance on training examples and on new images. They also had higher test accuracy than the non-invariant models in the study’s main comparisons. The authors report that the advantage was especially apparent with fewer training images and diminished as training sets grew.

A useful control helps explain why. When the researchers used upright handwritten digits, orientation was fixed and could itself help classification. The non-invariant model then overfit less than it did when digits appeared in random poses—and could outperform the invariant model on upright images. When that model was tested on rotated digits, its accuracy fell. In other words, ignoring orientation can help when orientation is irrelevant, but it can discard useful information when the task makes orientation meaningful.

The shortcut tests made the distinction concrete. Researchers added a small, class-dependent corner watermark to training images. Non-invariant models learned to use it: when the watermark was moved, their performance often fell close to chance, and on real-image tasks they were also near chance when the watermark was removed. Invariant models could not distinguish the watermark’s orientation, and generally performed better without it than the non-invariant models. There was an important exception: on Galaxy10, removing the watermark also lowered the invariant models’ accuracy. The paper attributes this to the watermark’s contribution to the encoded image, which shifted model outputs even though the models could not identify its position. The invariant models were not immune to every shortcut: all models learned a different artificial cue that was itself invariant under the tested rotations and reflections.

The results also distinguish a symmetric circuit from a symmetric prediction rule. An equivariant circuit paired with a non-invariant readout overfit much like the non-invariant models. What mattered most in these experiments was whether the whole model was invariant. The two ways of achieving invariance did not always have the same accuracy, and averaging required multiple circuit evaluations per image.

What remains uncertain

These findings are evidence about particular simulated models and tasks, not a demonstration that quantum computers outperform classical ones. The noise tests were also simulations: they suggest the pattern can persist under the modeled errors, but do not establish performance on a real device. The study used small image inputs and selected classification tasks; its authors identify larger symmetry groups, different encodings and deeper circuits as areas needing further investigation. They also report that some deeper circuits failed to train reliably.

The lesson is conditional rather than universal: a model’s built-in assumptions can help when they match the task, by ruling out patterns it should not rely on. If those assumptions are wrong, the same constraint can hurt. This work is an arXiv preprint, so its claims should be treated as provisional pending peer review and independent replication. The authors say they released code and results, which may help others check and extend the comparisons.