Abstract
It has been suggested that excitation transport in photosynthetic light-harvesting complexes features speedups analogous to those found in quantum algorithms. Here we compare the dynamics in these light-harvesting systems to the dynamics of quantum walks, in order to elucidate the limits of such quantum speedups. For the Fenna–Matthews–Olson complex of green sulfur bacteria, we show that while there is indeed speedup at short times, this is short lived (70 fs) despite longer-lived (ps) quantum coherence. Remarkably, this timescale is independent of the details of the decoherence model. More generally, we show that the distinguishing features of light-harvesting complexes not only limit the extent of quantum speedup but also reduce the rates of diffusive transport. These results suggest that quantum coherent effects in biological systems are optimized for efficiency or robustness rather than the more elusive goal of quantum speedup.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. In the first stage of photosynthesis, energy from photons is transferred through light-harvesting complexes containing chains of chlorophyll molecules. Recently, the discovery of long-lived quantum coherences in several such light-harvesting complexes has generated a great deal of interest and surprise, since biomolecular environments have generally been considered to be unfavorable for supporting fragile quantum coherences. In order to explain the presence of coherence in these highly optimized systems for efficient energy transfer, it has been suggested that photosynthesis may be exploiting features of quantum search algorithms.
Main results. We focus our investigations on the Fenna–Matthews–Olson (FMO) complex of green sulfur bacteria, a prototypical light-harvesting structure in which experiments have identified quantum coherence. Using analogies with quantum walks and their relation to quantum algorithms, we analyze the extent of dynamical speedup enabled by quantum coherence in FMO. We find that a quantum speedup is extremely short-lived (~70 fs) in this system, despite long-lived quantum coherence extending to several picoseconds. We generalize the model for FMO to investigate the interplay between energetic disorder and environmental fluctuations in generic light harvesting complexes, and use this to characterize the optimal conditions for energy transport in these systems.
Wider implications. Our results suggest that the distinguishing features of light-harvesting complexes such as FMO do not allow them to perform quantum algorithms. Any quantum advantage bestowed by the coherence must appear in other characteristics of energy transfer.
Figure. A monomer of the FMO complex contains seven chlorophyll molecules (green) embedded in a protein cage (white).