Macao Polytechnic Team Detects Angular Order in Complex Images

Zheng Xing of the Macao Polytechnic University and colleagues have identified signatures encoded within Fourier phase, which are easily corrupted by local cellular rotation. Quantum-inspired data processing offers new avenues for complex signal characterisation, but practical tools for directly extracting gauge-invariant angular correlations without explicit phase reconstruction remain scarce. They introduce Quantum Phase Bicoherence (QPBC) spectroscopy, a new quantum-interferometric framework for capturing gauge-invariant angular order.

The method embeds image angular sectors into a nine-qubit entangled state and probes three-body bicoherence via an ancilla, yielding 16 interpretable readout channels. They validate their framework on three independent public datasets.

Quantum spectroscopy reveals enhanced biological texture discrimination via angular-phase order A 300 per cent improvement in the resolution of angular-phase order has been achieved by researchers at Macao Polytechnic University and colleagues, consistently discriminating biological phenotypes across multiple imaging datasets where conventional Fourier-phase statistics previously failed. This breakthrough unlocks the ability to quantitatively measure previously inaccessible biological textures, establishing interpretable quantum morphometry and overcoming a fundamental limitation of classical image analysis which discards important Fourier phase information. The team’s Quantum Phase Bicoherence (QPBC) spectroscopy embeds image data into a nine-qubit entangled state, enabling the extraction of gauge-invariant angular order without explicit phase reconstruction, a process impossible with real-valued image pipelines.

Validation of Quantum Phase Bicoherence (QPBC) spectroscopy across fluorescence, bright-field, and histopathology imaging revealed a consistent physical principle. Aligning images to a principal axis consistently converged the most effective frequency for probing to a value of (0, 1) across all datasets. This convergence stems from the inherent directional sensitivity of Fourier bases and the dominant orientation of textures within biological samples.

Further experiments demonstrated that adjusting the probing frequency functions as a switch, enabling or disabling the ability to distinguish between different biological cell types, with each output channel representing a specific angular probing range. The team established that QPBC accesses three-body bicoherence signatures, classically unmeasurable due to limitations in capturing angular correlations. Conventional phase analysis tools only extract low-order statistical features. ## Quantum Phase Bicoherence reveals universal texture observables across multi-modal cellular images Scientists are utilising multi-modal imaging datasets covering fluorescence (BBBC021), bright-field (BBBC041) and histopathology (PathMNIST).

Quantum Phase Bicoherence (QPBC) consistently resolves angular-phase order and discriminates distinct biological phenotypes with high statistical significance. After principal-axis alignment, the optimal probing frequency universally converges, driven by Fourier directional sensitivity. Negative-control experiments fully eliminate discriminative capacity, demonstrating frequency tuning acts as an on-off switch.

Cross-dataset benchmarks confirm QPBC outperforms conventional Fourier-phase statistics, where inherent inversion symmetry serves as a built-in pipeline self-check. This delivers a universal, classically unachievable quantitative texture observable, establishes interpretable quantum morphometry, and broadens the set of tools for quantum-inspired analysis applicable to diverse multi-modal microscopic measurements. Understanding biological organisation across spatial scales, from the nanometre-scale alignment of cytoskeletal filaments to the millimetre-scale architecture of tumour microenvironments, is a central challenge in modern biology.

This organisation is inherently directional; microtubules radiate from centrosomes, collagen fibres align along stress axes, and erythrocyte membranes deform along preferred orientations during parasite invasion. Quantifying this directional order from microscopy images is therefore essential for drug discovery, disease diagnosis, and fundamental cell biology. However, extracting structural order parameters directly from image textures remains difficult, as measured pixel intensities confound the true biological structure with imaging artefacts, cell-to-cell pose variation, and the inherent randomness of photon detection.

Quantitative analysis of biological images is central to modern drug discovery, digital pathology, and functional genomics. Standard computational pipelines extract hundreds of morphological and textural features from single-cell images, converting each cell into a high-dimensional numerical vector that is subsequently used to infer biological states or drug mechanisms. The Cell Painting assay has become a widely adopted image-based profiling platform, revealing cellular responses to genetic and chemical perturbations at scale.

Deep learning Methods have further advanced the field by learning task-specific representations directly from pixel intensities, achieving state-of-the-art performance in compound classification and mechanism prediction. Graph neural networks and transformer architectures are pushing molecular property prediction to new levels of accuracy. All current approaches, whether based on hand-crafted features or learned representations, share a fundamental limitation: they operate exclusively on real-valued intensities or their real-valued transforms, discarding the Fourier phase information encoded in the spatial frequency domain.

This is not an engineering oversight but a physical necessity; the absolute Fourier phase of a single cell is randomised by its in-plane rotation, rendering it meaningless as a phenotypic descriptor. Classical texture features such as Local Binary Patterns, Gray-Level Co-occurrence Matrices, and Gabor filters all collapse complex Fourier coefficients into real-valued magnitudes, explicitly discarding the phase component that carries information about filament orientation and structural continuity. Even equivariant deep learning architectures, which achieve rotation invariance by aggregating over orientation channels, discard the relative phase relationships between different angular sectors of the same cell.

Geometric deep learning has extended this paradigm to non-Euclidean domains such as graphs and manifolds, yet the fundamental limitation persists: all operations are performed on real-valued inputs, and the phase of the Fourier transform remains unexploited. Phase relationships have long been used to probe structural order, from the bispectrum in nonlinear signal processing to phase coherence in quantum optics, but their application to the angular texture of single cells remains unexplored. Parallel progress in quantum-enabled biosignal processing demonstrates the growing interest in mapping biological information onto quantum-mechanical representations.

Quantum algorithms have been developed to tackle biomolecular modelling tasks such as lattice-model protein folding, while specialised quantum-state-encoding schemes provide practical pathways to represent biological molecular data within quantum-hardware frameworks. Broader community roadmaps further highlight quantum-thermodynamic and quantum-representation challenges for complex many-body biological systems. Nevertheless, existing quantum-oriented biological-data efforts predominantly target molecular-scale simulation; few frameworks are designed to extract gauge-invariant angular-order texture observables directly from multi-modal microscopic imaging inputs.

Quantum systems natively store and process complex amplitudes, offering a natural substrate for encoding Fourier-phase information. Recent advances in noisy intermediate-scale quantum (NISQ) algorithms have demonstrated that shallow quantum circuits can perform classically intractable feature encoding and interferencebased measurement, enabling quantum-enhanced feature spaces, quantum kernel Methods, and variational algorithms for classification. Quantum sensing protocols have demonstrated exquisite sensitivity to classically inaccessible quantities, from magnetic fields and gravitational waves to nanoscale temperature and magnetic resonance in living cells.

These advances place quantum-enhanced biological measurement within experimental reach, motivating the search for new quantum observables that directly report on biomedically relevant structural properties. However, applying quantum interference to extract biologically meaningful order parameters from microscopy images has remained unexplored. While absolute phases are meaningless under global image rotation, relative phase relationships among distinct angular sectors of a cell remain strictly gauge-invariant.

Such rotation-independent phase combinations constitute intrinsic physical order parameters that faithfully characterise structural texture, especially for anisotropic filamentous architectures such as cytoskeletal networks. A continuous microtubule filament propagating from sector a to sector c must structurally traverse the intermediate sector b. Notably, this composite phase observable is fully gauge-invariant; global rotation introduces identical phase offsets across all angular sectors and leaves the phase combination unchanged. It therefore provides a physically rigorous, rotation-invariant signature for quantifying structural coherence in ordered biological textures.

Extracting such pure phase coupling without explicit individual-phase reconstruction represents an open technical challenge for classical real-valued image pipelines, which inevitably break gauge invariance during feature extraction. By contrast, quantum interference mechanisms naturally support invariant nonlinear phase composition, offering a principled route toward gauge-consistent texture characterisation. Here we introduce Quantum Phase Bicoherence (QPBC) spectroscopy, a frequency-tunable quantum-inspired interferometric framework that directly extracts gauge-invariant angular phase coupling from multi-modal imaging data without explicit phase reconstruction.

We validate the universality and strong performance of the proposed quantum paradigm across three biologically independent imaging modalities, including fluorescence microscopy, bright-field blood smear imaging, and histopathology slides. We further demonstrate that frequency tuning behaves as a quantum-like discriminative switch for biological phenotyping, where each output channel corresponds to a physically interpretable angular probing corridor.

We term this consistent, physically grounded framework quantum morphometry, establishing a new quantum-inspired analytical tool for complex multi-modal biological measurements. The central challenge that QPBC addresses is to measure the gauge-invariant angular phase coherence of a biological texture without estimating individual Fourier phases.

As argued in the Introduction, this task is physically impossible for classical image analysis. QPBC overcomes this by translating complex-valued spatial frequency information from angular image sectors into a multi-qubit entangled state, manipulating quantum phases through controlled interference, and reading out the three-body bicoherence via a single-ancilla probe. Stage 1: Angular sectorisation and frequency-domain encoding.

For each sector Θj, the local image patch is extracted, zero-padded to at least 4×4 pixels, and the two-dimensional discrete Fourier transform is computed.

Amplitudes are normalised per cell to; phases are used directly. Consequently, by selecting different spatial frequencies, one can systematically probe different angular corridors of the image, a principle we term frequency-selective angular gating.

Stage 2: Quantum Phase Bicoherence (QPBC) spectroscopy and gauge-invariant angular order. Classical image analysis discards structurally meaningful orientation signatures within Fourier phase, susceptible to local cellular rotation. QPBC spectroscopy embeds image angular sectors into a nine-qubit entangled state and probes three-body bicoherence via an ancilla, yielding 16 interpretable readout channels.

Validation using fluorescence, bright-field, and histopathology datasets demonstrates QPBC resolves angular-phase order and discriminates biological phenotypes with statistical significance. One ancilla qubit is prepared in |+⟩= H|0⟩. ## Quantifying image texture using a novel quantum-inspired spectroscopic technique The team’s new Quantum Phase Bicoherence spectroscopy offers a powerful method for deciphering complex image textures, potentially revolutionising fields reliant on detailed structural analysis such as materials science and disease diagnosis. However, the current implementation relies on simulating quantum processes on conventional computers.

The research demonstrated Quantum Phase Bicoherence (QPBC) spectroscopy successfully resolves angular-phase order within images. QPBC outperformed conventional Fourier-phase statistics, and the study confirmed a tunable frequency acts as a switch for detecting angular patterns. The authors simulated these quantum processes on conventional computers, suggesting a path for further development of the technique.