Hybrid Quantum-Classical Architecture for Single-Cell Gene Expression Prediction

In order to generate cellular function maps, we have a large reliance on predicting how genetic modifications shift gene activity. Although high-throughput screens are available, the huge number of possibilities slows down scaling. Our present frameworks offer insight, but they still aren't the most ideal when working with complex biological intricacies.

This project is a hybrid quantum-classical architecture to predict single-cell gene expression profiles following gene perturbations. First, inside a frozen classical State Transition (STATE) transformer core, we embedded parameterized quantum circuits (PQCs), as trainable nonlinear transformations in our system. Then, we had the system encode basal gene expression and perturbation features into a shared latent representation, mapped using linear projection to our quantum circuit parameters.

The quantum part itself used layers of adjustable single-qubit rotations and entanglement gates. From there, the Pauli-Z expectation values were then compacted into usable encoding, which a final linear layer decoded into gene expression predictions. The optimization process was mainly focused on the quantum parameters and decoder, while keeping the classical backbone frozen.

The hybrid design worked for enhancing the classical encoder with the additional nonlinear processing. It allowed for organization while bringing together localized and correlated quantum states to predict expression for hidden perturbations.

The research shows that adaptable quantum circuits are able to work as nonlinear operators in biological foundation frameworks. Our hybrid strategy shows a very real route of this very application of quantum learning techniques for the dimensionality complexities inherent to genes.

To isolate the effects of genetic modifications, the model prototype was designed using a "Delta Prediction" architecture. Instead of predicting the entire gene expression profile from scratch, the model was engineered to predict only the perturbation shift.

Frozen Classical Encoding: Single-cell gene expression profiles (18,080 genes) and perturbation features (5,120-dimensional ESM2 embeddings) are fed into a pre-trained STATE transformer. The transformer's weights are kept entirely frozen, reducing the data into a dense, 672-dimensional shared latent representation without losing previously learned biological rules.

Quantum Projection & Data Re-uploading: A linear projection layer reduces the 672-dimensional vector into rotation angles suitable for an 8-qubit quantum processor. The classical inputs are re-embedded at every variational layer using Angle Embedding, increasing expressivity by acting as a multi-frequency Fourier series.

Entanglement & Multi-Basis Measurement: The circuit utilizes adjustable single-qubit rotations (RX, RY, RZ) and CNOT gates in a ring topology for entanglement. Crucially, the quantum state is measured across three bases (Pauli-X, Pauli-Y, and Pauli-Z), expanding the output to 24 expectation values (3 X 8 qubits).

Decoding & Skip Connection: A linear decoder maps the quantum output to the 18,080-dimensional perturbation delta. A skip connection mathematically adds the original basal (control) cell data back to this predicted delta to generate the final cellular state.

Testing Conditions: During evaluation, instead of using a single mean control profile, the algorithm samples 200 distinct, individual control cells. This engineered variance mimics natural biology and provides the statistical rigor required for accurate Wilcoxon rank-sum testing.

The hybrid prototype successfully showed state-of-the-art ability to identify differentially expressed genes across 51 diverse genetic perturbations.

Primary Endpoint Achieved: The architecture achieved a highly competitive Differential Expression Score (DES) of 0.8532 (Scaled: 0.8455).

Engineering Efficiency: By relying on the delta-prediction skip connection, 100% of the trainable parameters (9.29 million) were focused purely on the genetic shift, completely bypassing the computational waste of reconstructing the underlying cell.

The model excelled at identifying which genes changed, we used Principal Component Analysis (PCA) was conducted to interpret the limitations of the current prototype.

Secondary Metrics: The model achieved a Perturbation Discrimination Score (PDS) of 0.5076 and a Mean Absolute Error (MAE) of 0.1433.

The Quantum Bottleneck: PCA determined that the first 4 principal components captured 25.8% of the data's variance, resulting in a highly restricted effective dimensionality of only 2.58.

Interpretation: Because the 672-dimensional biological latent space was compressed into just an 8-qubit space, the model exhibited "mode collapse," resulting in a between-perturbation similarity of 0.9993. The prototype predicted highly accurate, but ultimately uniform, shifts for different targets.

The current prototype achieved a strong DES of 0.8532, but PDS and MAE metrics indicate room for improvement. The following phases outline the systematic plan to enhance model performance toward competitive standings.