Quantum Circuit Simulation of Compartmental Drug Dynamics: Leveraging Variational Algorithms for Nonlinear Mixed-Effects Population Pharmacokinetics

TL;DR

This paper introduces a quantum circuit approach to simulate compartmental drug dynamics, achieving improved statistical fit and faster convergence in pharmacokinetic modeling using variational algorithms.

Contribution

It reformulates classical PK/PD models as open quantum systems and implements them with quantum circuits, demonstrating enhanced modeling performance and stability.

Findings

Quantum model shows better log-likelihood than classical

Faster convergence in quantum-based optimization

Maintains biological interpretability with improved statistical fit

Abstract

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.