Quantum Hamiltonian Learning using Time-Resolved Measurement Data and its Application to Gene Regulatory Network Inference

TL;DR

This paper introduces a quantum-inspired framework for inferring gene regulatory networks from time-resolved measurement data, providing theoretical guarantees and a scalable algorithm, with successful application to cancer-related single-cell data.

Contribution

It develops a novel quantum Hamiltonian-based model for gene expression and offers scalable learning algorithms with theoretical guarantees, applied to biological network inference.

Findings

Efficient network recovery on synthetic benchmarks

Revealed biologically plausible regulatory connections in Glioblastoma data

Provided finite-sample guarantees for parameter estimation

Abstract

We present a new Hamiltonian-learning framework based on time-resolved measurement data from a fixed local IC-POVM and its application to inferring gene regulatory networks. We introduce the quantum Hamiltonian-based gene-expression model (QHGM), in which gene interactions are encoded as a parameterized Hamiltonian that governs gene expression evolution over pseudotime. We derive finite-sample recovery guarantees and establish upper bounds on the number of time and measurement samples required for accurate parameter estimation with high probability, scaling polynomially with system size. To recover the QHGM parameters, we develop a scalable variational learning algorithm based on empirical risk minimization. Our method recovers network structure efficiently on synthetic benchmarks and reveals novel, biologically plausible regulatory connections in Glioblastoma single-cell RNA sequencing data, highlighting its potential in cancer research. This framework opens new directions for applying quantum-like modeling to biological systems beyond the limits of classical inference.