  The LH-II of purple bacteria Rhodospirillum (Rs.) molischianum and
Rhodopseudomonas (Rps.) acidophila adopts a highly symmetrical ring shape, with
a radius of about 7 nm. In the case of Rps. acidophila the ring has a ninefold
symmetry axis, and in LH-II from Rs. molischianum the ring has an eightfold
symmetry axis. These rings are found to exibit two bands of excitons. A
simplified mathematical description of the exciton states is given in Hu, X. &
Schulten, K. (1997) Physics Today 50, 28-34. Using this description, we will
show, by suitable labeling of the lowest energy (Qy) excited states of
individual BChls, that the resulting exciton states are the quantum Fourier
transform of the BChls excited states. For Rs. molischianum ring exciton states
will be modeled as the four qubit quantum Fourier transform and the explicit
circuit will be derived. Exciton states for Rps. acidophila ring cannot be
modeled with an integer number of qubits. Both quantum Fourier transforms are
instances of the hidden subgroup problem and this opens up a possibility that
both purple bacteria implement an efficient quantum circuit for light
harvesting.
