Recently, we have theoretically proposed and experimentally demonstrated an exact and efficient quantum simulation of photosynthetic light harvesting in nuclear magnetic resonance (NMR), cf. B. X. Wang, textit{et al.} npj Quantum Inf.~textbf{4}, 52 (
2018). In this paper, we apply this approach to simulate the open quantum dynamics in various photosynthetic systems with different Hamiltonians. By numerical simulations, we show that for Drude-Lorentz spectral density the dimerized geometries with strong couplings within the donor and acceptor clusters respectively exhibit significantly-improved efficiency. Based on the optimal geometry, we also demonstrate that the overall energy transfer can be further optimized when the energy gap between the donor and acceptor clusters matches the peak of the spectral density. Moreover, by exploring the quantum dynamics for different types of spectral densities, e.g. Ohmic, sub-Ohmic, and super-Ohmic spectral densities, we show that our approach can be generalized to effectively simulate open quantum dynamics for various Hamiltonians and spectral densities. Because $log_{2}N$ qubits are required for quantum simulation of an $N$-dimensional quantum system, this quantum simulation approach can greatly reduce the computational complexity compared with popular numerically-exact methods.
There is a remarkable characteristic of photosynthesis in nature, that is, the energy transfer efficiency is close to 100%. Recently, due to the rapid progress made in the experimental techniques, quantum coherent effects have been experimentally dem
onstrated. Traditionally, the incoherent theories are capable of calculating the energy transfer efficiency, e.g., (generalized) Forster theory and modified Redfield theory. However, in order to describe the quantum coherent effects in photosynthesis, the coherent theories have been developed, such as hierarchical equation of motion, quantum path integral, coherent modified Redfield theory, small-polaron quantum master equation, and general Bloch-Redfield theory in addition to the Redfield theory. Here, we summarize the main points of the above approaches, which might be beneficial to the quantum simulation of quantum dynamics of exciton energy transfer in natural photosynthesis, and shed light on the design of artificial light-harvesting devices.
We propose a scheme to simulate the exciton energy transfer (EET) of photosynthetic complexes in a quantum superconducting circuit system. Our system is composed of two pairs of superconducting charge qubits coupled to two separated high-Q supercondu
cting transmission line resonators (TLRs) connected by a capacitance. When the frequencies of the qubits are largely detuned with those of the TLRs, we simulate the process of the EET from the first qubit to the fourth qubit. By tuning the couplings between the qubits and the TLRs, and the coupling between the two TLRs, we can modify the effective coupling strengths between the qubits and thus demonstrate the geometric effects on the EET. It is shown that a moderate clustered geometry supports optimal EET by using exciton delocalization and energy matching condition. And the population loss during the EET has been trapped in the two TLRs.
