Quantum Network-Based Prediction of Cancer Driver Genes

TL;DR

This paper tackles cancer driver-gene identification by leveraging a quantum graph-learning approach. It introduces Quantum Multi-Order Moment Embedding (QMME), which encodes local graph statistics—specifically the first four origin moments of immediate and two-hop neighborhood mutation scores—into amplitude-encoded quantum states via oracle-based state preparation. Classification is performed with a swap-test quantum kernel that assesses the similarity between test and labeled node embeddings, enabling end-to-end quantum inference without classical optimization. In simulations on a real cancer PPI network, QMME achieves a 12.6-percentage-point recall gain over a classical baseline and shows polylogarithmic resource scaling, supporting the potential for quantum graph learning to accelerate biological discovery and network-based cancer gene prediction.

Abstract

Identification of cancer driver genes is fundamental for the development of targeted therapeutic interventions. The integration of mutational profiles with protein-protein interaction (PPI) networks offers a promising avenue for their detection [ 1, 2], but scaling to large network datasets is computationally demanding. Quantum computing offers compact representations and potential complexity reductions. Motivated by the classical method of Gumpinger et al. [3], in this work we introduce a supervised quantum framework that combines mutation scores with network topology via a novel state preparation scheme, Quantum Multi-order Moment Embedding (QMME). QMME encodes low-order statistical moments over the mutation scores of a node's immediate and second-order neighbors, and encodes this information into quantum states. These are used as inputs to a kernel-based quantum binary classifier that discriminates known driver genes from others. Simulations on an empirical PPI network demonstrate competitive performance, with a 12.6% recall gain over a classical baseline. The pipeline performs explicit quantum state preparation and requires no classical training, enabling an efficient, nearly end-to-end quantum workflow. A brief complexity analysis suggests the approach could achieve a quantum speedup in network-based cancer gene prediction. This work underscores the potential of supervised quantum graph learning frameworks to advance biological discovery.

Figures (5)

• Figure 1: Cancer driver genes prediction.(a) PPI network where genes are colored by class. (b) Classical machine learning approaches: a model is trained on the labeled dataset and then used to classify the test data. (c) Novel quantum approach: QMME (left) produces quantum embeddings, yielding the labeled state $\ket{\psi_l}$ and test state $\ket{\psi_t}$. The labeled state serves as a reference to classify the test state on-the-go via a swap-test (right).
• Figure 2: Circuit of the feature oracle $O_X$, built from controlled rotations $F_X$.(a) Gate representation of $O_X$. (b) Detailed view: a two-qubit control register $\ket{i}$ determines how many of the four ancilla qubits undergo $F_X$ rotations (00 → first qubit, 01 → first two, 10 → first three, 11 → all four). A $d'$-qubit register is used internally but omitted for clarity.
• Figure 3: Quantum Multi-order Moment Embedding (QMME) protocol.(a) Gate view of the unitary operator $U_\mathcal{G}$, which maps $\ket{v} \ket{0}^{\otimes \mathfrak{m}} \mapsto \ket{v} \ket{\boldsymbol{\psi}_v}$, amplitude-encoding low-order statistical moments of node $v$'s neighborhood. Here, $\ket{v}$ encodes the node index $v \in V$, and the $\mathfrak{m}$-qubit data register is initialized to zero. (b) Input PPI network $\mathcal{G} = (V, E, \boldsymbol{x})$ with node features $\boldsymbol{x}$ representing mutation scores. Immediate neighbors of $v$ are shown in purple, second-hop neighbors in orange. These provide the data for the embedding $\ket{\boldsymbol{\psi}_v} \in \mathbb{R}^{2^{\mathfrak{m}}}$. (c) The moment-feature embedding $\boldsymbol m_v$, based on the moments $\varphi(\cdot)$ over $v$'s neighborhood, is encoded as the quantum state $\ket{\boldsymbol{\psi}_v}$. (d) Circuit-level implementation of the gate $U_\mathcal{G}$. The $\mathfrak{m}$-qubit register is composed of subregisters for immediate and second-hop ($\ell_1$,$\ell_2$) neighbors, a control qubit $c$, a two-qubit register $i$ indexing the $i$-th moment, and a five-qubit ancilla register $a$. The circuit accesses the PPI network in (b) via the quantum oracles in \ref{['eq:input-model-oracles']}.
• Figure 4:
• Figure 5: Experimental setup for QMME and classical embedding comparison and performance evaluation.(a) The dataset consists of 6 850 genes, of which 590 (in orange) are known cancer driver genes 10.1093/nar/gky1015. The remaining 6 260 genes have unknown labels, as they are not part of the CGC dataset. (b) Embeddings for each gene $v$ are obtained via two methods: the Quantum Multi-order Moment Embedding (QMME) protocol, and the Moment Propagation (MoPro) embedding with hyperparameter $t=1$gumpinger2020prediction. The QMME approach is implemented via algebraic computations on classical software. (c) In each random split, 80% of the positive genes are selected and combined with an equal number of unlabeled genes (assigned a negative class label) to form the labeled training set $V_l$. The remaining genes form the test set $V_t$, whose labels are used only for evaluation. For both embedding methods, kernel matrices are computed and the expectation values in \ref{['eq:expectation-values']} are evaluated on all test genes. This process is repeated across 50 random splits, and performance metrics are averaged.