Quantum Circuit Simulation of Compartmental Drug Dynamics: Leveraging Variational Algorithms for Nonlinear Mixed-Effects Population Pharmacokinetics
This work introduces a quantum computing approach to population pharmacokinetic modeling, potentially improving statistical fit for drug development, but it is an incremental application of existing variational algorithms to a specific domain.
The authors reformulate a compartmental PK/PD model as an open quantum system, implementing it with quantum circuits on 12 qubits. On Phase 1 clinical data, the quantum model achieves improved log-likelihood values and faster iteration convergence compared to classical methods, though total runtime increases due to simulation overhead.
Population pharmacokinetic/pharmacodynamic (PK/PD) modeling traditionally relies on classical ordinary differential equations to simulate drug dynamics. In this work, we reformulate a compartmental PK/PD model as an open quantum system and implement it using quantum circuits developed in PennyLane. Four pharmacological compartments (central, peripheral, effect-site, and response) are encoded using twelve qubits, with inter-compartmental transitions represented through controlled quantum operations that emulate stochastic dynamics. The framework is evaluated on Phase 1 clinical data using a quantum-enhanced stochastic approximation expectation-maximization (SAEM) approach. Compared with the classical implementation, the quantum model achieves substantially improved log-likelihood values, indicating stronger statistical fit while preserving identical parameter estimates, thereby validating numerical consistency and model interpretability. The quantum-based optimization converges faster in terms of iterations, although total runtime is increased due to current simulation overhead. The study demonstrates stable large-scale simulation performance and establishes a hybrid quantum-classical approach that maintains biological fidelity while improving statistical modeling capacity. The dataset and problem statement originate from the Quantum Innovation Challenge 2025, and additional details are provided via the associated link.