Stochastic Approach to Pharmacokinetics vs Principles of Quantum Mechanics

Mohamed Hatifi, Ralph Willox, Thomas Durt

Walter Lehr

Mikio Namiki

Isshaan Singh, Nandan Patel

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.

Achile Solomon Egbunu, Peter Adetokunbo, Okedoye Akindele Michael

The optimization of multidrug cancer treatment schedules is a high-dimensional combinatorial optimization problem involving nonlinear tumor dynamics, pharmacokinetic interactions, and stringent toxicity constraints. When exploring large therapeutic search spaces, conventional optimization algorithms often exhibit limited scalability and become trapped in local optima. This simulation study proposes a hybrid quantum-classical optimization framework that employs QA to generate adaptive treatment schedules for precision oncology. The treatment scheduling problem is formulated as a quadratic unconstrained binary optimization (QUBO) model, which encodes drug combinations, dosing intervals, toxicity constraints, and synergistic interactions within an Ising Hamiltonian compatible with D-Wave quantum annealing hardware. Global combinatorial optimization is performed using a D-Wave Advantage quantum annealer, while sequential least squares programming refines continuous dosage parameters under pharmacokinetic and toxicity constraints. Tumor progression is represented using a modified Gompertz growth model coupled with first-order pharmacokinetic dynamics. The proposed framework was evaluated using synthetic Digital Twin datasets generated from clinically realistic pharmacokinetic and tumor growth parameters. Simulation results demonstrated a maximum tumor regression ratio of 0.98 ± 0.02, compared with 0.82 ± 0.05 for standard-of-care protocols, while maintaining a lower cumulative toxicity index (40 ± 5 versus 75 ± 8) and reducing optimization time to less than 2 s for 120-variable scheduling problems. The hybrid framework exhibited near-linear computational scalability and maintained robustness under stochastic dosage perturbations (TRR > 0.95 at σ = 0.25). However, predictive classification performance remained limited (AUC = 0.49), highlighting the need for validation using longitudinal clinical datasets and multimodal patient-specific data. These findings demonstrate the potential of hybrid quantum-classical optimization as a scalable computational framework for adaptive treatment scheduling and personalized precision oncology.