Feedback-Based Quantum Control for Safe and Synergistic Drug Combination Design

TL;DR

This work tackles the challenge of selecting safe and effective multi-drug regimens under complex drug–drug interactions by formulating MSS and SCO as Ising Hamiltonians and solving them with the feedback-based quantum control algorithm FALQON and its imaginary-time extension ITE-FALQON. By encoding clinical DDI data into $\mathcal{H}_{\mathrm{MSS}}$ and $\mathcal{H}_{\mathrm{SCO}}$, the authors demonstrate rapid convergence and high-quality solutions on small drug networks, including a six-drug testbed and a COVID-19 drug-panel case study. Key contributions include (i) a MSS formulation that maximizes safe drug subsets, (ii) a SCO formulation that balances synergy, harm, and subset size, and (iii) empirical evidence that FALQON and ITE-FALQON converge efficiently on near-term quantum hardware. The results indicate potential for quantum-assisted decision support in rational multi-drug therapy design, leveraging sparse, modular real-world DDI graphs to scale to larger libraries with suitable preprocessing.

Abstract

Drug-drug interactions (DDIs) strongly affect the safety and efficacy of combination therapies. Despite the availability of large DDI databases, selecting optimal multi-drug combinations that balance safety, therapeutic benefit, and regimen size remains a challenging combinatorial optimization problem. Here, we present a quantum-control-based framework for DDI-aware drug combination optimization, in which known harmful and synergistic interactions are encoded into Ising Hamiltonians as penalties and rewards, respectively. The optimization is performed using the feedback-based quantum algorithm FALQON, a gradient-free variational approach. We study two clinically motivated tasks: the Maximum Safe Subset problem and the Synergy-Constrained Optimization problem. Numerical simulations using interaction data from Drugs.com and SYNERGxDB demonstrate efficient convergence and high-quality solutions for clinically relevant drug sets, including COVID-19 case studies.

Figures (7)

• Figure 1: Interaction graph of the six-drug network. Nodes represent individual drugs, while edges indicate pairwise interactions. Red edges denote harmful interactions and green edges denote synergistic interactions. Numbers on the edges indicate the corresponding interaction weights.
• Figure 2: Energy evolution obtained using FALQON and ITE-FALQON for different penalty coefficients $\alpha$. While FALQON reliably identifies the correct optimal bitstring, its final energy remains slightly above the exact ground-state energy due to the purely unitary nature of the dynamics, which does not explicitly suppress excited-state components. In contrast, ITE-FALQON rapidly reaches the ground-state energy by effectively filtering out higher-energy contributions through imaginary-time evolution. This comparison highlights the complementary roles of feedback-based control and non-unitary energy filtering in accelerating convergence.
• Figure 3: Final probability distributions and dominant MSS solutions. (a) FALQON concentrates probability on two harm-free bitstrings, $111000$ and $110100$, while suppressing unsafe configurations. (b) ITE-FALQON further sharpens this distribution, projecting almost entirely onto the same two degenerate MSS solutions. The shaded graphs depict the corresponding drug subsets.
• Figure 4: SCO results obtained using ITE-FALQON. (a) Energy convergence for target cardinalities $K=3$ and $K=4$. (b, c) Final measurement probability distributions and corresponding interaction graphs for $K=3$ and $K=4$, respectively. In both cases, the dynamics concentrate almost entirely on a single dominant bitstring, indicating a unique optimal drug combination. The inset graphs visualize the selected subsets and their internal interactions, illustrating the balance between synergistic benefit and interaction risk as the cardinality constraint is increased.
• Figure 5: Interaction graph of the 9-drug network.