The Efficiency Problem
Photosynthesis converts sunlight into chemical energy with remarkable efficiency. In green sulfur bacteria, the excitation from absorbed photons travels from the chlorosome antenna to the reaction centre — a distance of several nanometres — and does so with near-perfect transfer efficiency even in warm, noisy, biological environments.
This is puzzling. At the nanometre scale, quantum coherence should be destroyed almost instantly by thermal fluctuations. Classical models of energy transfer — treating the excitation as a random walk between chromophores — predict much lower efficiency and cannot match the observed timescales.
In 2007, Fleming and colleagues measured quantum beating signals in the FMO (Fenna-Matthews-Olson) complex of green sulfur bacteria lasting hundreds of femtoseconds at 77K — far longer than expected. The subsequent decade of debate produced a clear conclusion: quantum coherence is not incidental to photosynthesis, it is part of the mechanism.
The FMO Complex
The FMO complex is a trimer of identical subunits, each containing 7 bacteriochlorophyll-a (BChl-a) chromophores embedded in a protein scaffold. Its function is to channel excitation energy from the chlorosome antenna (BChl-1) to the reaction centre (BChl-3).
In QRL, the full 7-chromophore Hamiltonian uses published parameters from Adolphs & Renger (2006):
fmo = fmo_complex(temperature_k=300)
eff = fmo.energy_transfer_efficiency("BChl-1", "BChl-3") # 0.274
coh = fmo.coherence_lifetime("BChl-1", "BChl-2") # 0.133 psThe site energies span a 420 cm⁻¹ range (12,210–12,630 cm⁻¹), and the inter-chromophore couplings range from −70.7 cm⁻¹ (BChl-4/BChl-5, strongly coupled) to −0.9 cm⁻¹ (BChl-4/BChl-6, weakly coupled). The coupling pattern creates a directed energy funnel.
The chromophore entanglement — the von Neumann entropy of the reduced density matrix — reveals the quantum structure:
fmo.chromophore_entanglement("BChl-1", "BChl-2") # 1.000 ebit
fmo.chromophore_entanglement("BChl-3", "BChl-4") # 1.000 ebit
fmo.chromophore_entanglement("BChl-1", "BChl-3") # 0.535 ebitBChl-1/BChl-2 and BChl-3/BChl-4 are maximally entangled pairs — they share a full ebit of quantum correlation. This is not a metaphor. The two-chromophore system is in a superposition of excitation states, not a mixture. The excitation does not live on one chromophore at a time.
Environment-Assisted Quantum Transport
The classical expectation is that thermal noise destroys quantum coherence and reduces efficiency. The opposite happens in the FMO complex. This is ENAQT — Environment-Assisted Quantum Transport.
The Lindblad master equation governs the dynamics:
\[\dot{\rho} = -\frac{i}{\hbar}[H, \rho] + \sum_k \left(L_k \rho L_k^\dagger - \frac{1}{2}\{L_k^\dagger L_k, \rho\}\right)\]
where the Lindblad operators \(L_k\) encode phonon-induced dephasing, fluorescence, and the irreversible trap at BChl-3 (the reaction centre sink).
The QRL computation runs this evolution for 5 ps and measures the population accumulated in the trap:
| Temperature | Transfer efficiency η |
|---|---|
| 77 K | 0.135 |
| 150 K | 0.201 |
| 200 K | 0.232 |
| 250 K | 0.255 |
| 300 K | 0.274 |
| 350 K | 0.289 |
Efficiency increases monotonically with temperature. Phonon fluctuations from the protein scaffold are not noise to be tolerated — they are a functional part of the transport mechanism. The fluctuations break destructive interference pathways and help the excitation find the energetically downhill route to BChl-3.
This is the QRL perspective: the quantum network between chromophores, coupled to a phonon bath, computes the optimal transport path. The entanglement is the resource; the bath is the catalyst.
The Radical Pair: A Quantum Compass
Quantum biology is not limited to photosynthesis. European robins (Erithacus rubecula) and other migratory birds navigate using the Earth’s magnetic field with extraordinary precision. The mechanism is the radical pair — a quantum spin system in the cryptochrome protein of the bird’s eye.
When cryptochrome absorbs a photon, it produces a pair of radicals: two electrons in a spin-correlated singlet state
\[|\psi_0\rangle = \frac{1}{\sqrt{2}}\left(|\uparrow\downarrow\rangle - |\downarrow\uparrow\rangle\right)\]
This is a Bell state. The singlet state evolves under the competition between:
- Zeeman interaction: the Earth’s magnetic field (\(B \approx 50\) μT) shifts the spin precession frequency
- Hyperfine coupling: the electron spin couples to nuclear spins (\(^1\)H, \(^{14}\)N), mixing singlet and triplet states at a rate that depends on the field orientation
The singlet yield — the probability of the radical pair returning to the singlet state — depends on the inclination angle \(\theta\) of the magnetic field relative to the cryptochrome axis:
pair = RadicalPair("cryptochrome")
pair.set_hyperfine(14.0) # ¹⁴N hyperfine coupling, MHz
pair.set_field(B_uT=50, theta_deg=0)
pair.singlet_triplet_yield() # 0.867
pair.set_field(B_uT=50, theta_deg=90)
pair.singlet_triplet_yield() # 1.000The variation is 0.867 to 1.000 across inclination angles — a 15% modulation of the singlet yield purely from the orientation of a 50 μT field. The bird’s nervous system detects this modulation as a compass signal.
This is a quantum effect in the precise sense: the directional sensitivity comes from spin-state superposition and hyperfine mixing. A classical random walk of spins produces no directional signal.
Hore & Mouritsen (2016) showed that disrupting cryptochrome function with radio-frequency fields at the Larmor frequency — which disrupts the coherent spin evolution — eliminates the birds’ ability to navigate. The compass fails when you destroy the quantum coherence.
Asking Bell
Bell can compute both of these from first principles:
“Does quantum coherence in the FMO photosynthetic complex contribute to energy transfer efficiency?”
“How does the entanglement between BChl-1 and BChl-2 in the FMO complex vary with temperature?”
“What is the singlet yield in the cryptochrome radical pair at 45° field inclination? How does it change with angle?”
“Why does adding noise improve quantum transport in the FMO complex?”
The underlying computation uses the Lindblad master equation with published FMO parameters (Adolphs & Renger 2006) for photosynthesis, and the Schulten/Ritz radical pair Hamiltonian for the avian compass (Ritz et al. 2000). No empirical fits — the numbers come from integrating the equations.
The reason quantum biology matters for quantum computing is that biology solved the decoherence problem first. A photosynthetic complex maintains functional quantum coherence at 300K and 100% humidity, coupled to a protein scaffold that would horrify any quantum hardware engineer. Understanding how it does this — and computing it quantitatively — is not a side project. It is the blueprint.