Adaptive low-rank variational quantum algorithm for simulating dissipative dynamics in photosynthetic complexes

Simulating open quantum system dynamics via exact density-matrix propagation faces exponential complexity, scaling as [Formula: see text] and becoming intractable beyond approximately 15 chromophores on classical hardware-despite specialised approaches such as the Hierarchy Of Pure States (HOPS), Meso-HOPS, and multi-Davydov variational methods having extended tractability for specific regimes. We develop an adaptive low-rank variational quantum algorithm (LR-VQA) achieving polynomial scaling [Formula: see text] through singular value decomposition-based tensor compression and dissipation-engineered cost functions, providing a quantum-hardware-compatible framework complementary to existing classical techniques. Benchmarking on Fenna-Matthews-Olson (FMO) complexes spanning 5-12 chromophores yields mean fidelities 0.87-0.95 across 50 independent trials with 95 % confidence intervals below 0.001, validated by one-way analysis of variance (ANOVA) ([Formula: see text]). Noisy intermediate-scale quantum (NISQ) device viability is demonstrated through realistic simulations using IBM Heron noise specifications, achieving fidelity [Formula: see text] for the 7-site complex. Comparative scaling analysis reveals a computational crossover at [Formula: see text] chromophores, beyond which LR-VQA provides the sole quantum-hardware-compatible tractable simulation pathway while exact density-matrix methods become computationally prohibitive. Agreement with experimental energy transfer timescales within 3 % validates physical accuracy. A complete open-source implementation achieves sub-90-second runtimes. This framework opens a pathway toward quantum advantage in quantum biology with natural extensions to non-Markovian dynamics and experimental photosynthetic antenna systems containing 50-300 chromophores.