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Markovian quantum simulation of Fenna-Matthew-Olson (FMO) complex using one-parameter semigroup of generators

M. Mahdian, Hojatollah Yeganeh

Published Jan 10, 2019• 1 citation
OpenAlex

Abstract

The application of the theory of open quantum systems in biological processes such as photosynthetic complexes, has recently received renewed attention. In this paper, a quantum algorithm is presented for simulation of arbitrary Markovian dynamics of the FMO complex exist in photosynthesis using a 'universal set ' of one-parameter semigroup of generators. We investigate the detailed constitution of each generator that obtain from spectral decomposition of the Gorini-Kossakowski-Sudarshan (GKS) matrix by using of linear combination and unitary conjugation. Also, we design a quantum circuit for implementing of these generators.

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The simulation dynamics of light-harvesting complexes as open quantum systems in the weak and strong coupling regimes has been recently attended. In this paper, we investigate digital approach to quantum dynamics simulation of photosynthetic Fenna-Matthew-Olson (FMO) complex in contact with a Markovian bath, i.e., memoryless, with the nuclear spin-based quantum simulator. For this purpose, we use recoupling and decoupling method on nuclear magnetic resonance(NMR) quantum computation and Solovay-Kitaev decomposition strategy for single-qubit channels. Finally we use near-term quantum computer that developed by Rigetti to implement circuits. The results shows an efficient quantum simulation of photosynthesis system.

•Jan 10, 2019•1 citation

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The application of the theory of open quantum systems in biological processes such as photosynthetic complexes, has recently received renewed attention. In this paper, a quantum algorithm is presented for simulation of arbitrary Markovian dynamics of the FMO complex exist in photosynthesis using a 'universal set ' of one-parameter semigroup of generators. We investigate the detailed constitution of each generator that obtain from spectral decomposition of the Gorini-Kossakowski-Sudarshan (GKS) matrix by using of linear combination and unitary conjugation. Also, we design a quantum circuit for implementing of these generators.
The simulation dynamics of light-harvesting complexes as open quantum systems in the weak and strong coupling regimes has been recently attended. In this paper, we investigate digital approach to quantum dynamics simulation of photosynthetic Fenna-Matthew-Olson (FMO) complex in contact with a Markovian bath, i.e., memoryless, with the nuclear spin-based quantum simulator. For this purpose, we use recoupling and decoupling method on nuclear magnetic resonance(NMR) quantum computation and Solovay-Kitaev decomposition strategy for single-qubit channels. Finally we use near-term quantum computer that developed by Rigetti to implement circuits. The results shows an efficient quantum simulation of photosynthesis system.
Recently, the dynamics simulation of light-harvesting complexes as an open quantum system, in the weak and strong coupling regimes, has received much attention. In this paper, we investigate a digital quantum simulation approach of the Fenna–Matthews–Olson (FMO) photosynthetic pigment-protein complex surrounded with a Markovian bath, i.e. memoryless, based on a nuclear magnetic resonance (NMR) quantum computer. For this purpose, we apply the decoupling (recoupling) method, which is turn off (on) the couplings, and also Solovay–Kitaev techniques to decompose Hamiltonian and Lindbladians into efficient elementary gates on an NMR simulator. Finally, we design the quantum circuits for the unitary and nonunitary part due to the system-environment interactions of the open system dynamics.
Open quantum system approaches are widely used in the description of physical, chemical and biological systems. A famous example is electronic excitation transfer in the initial stage of photosynthesis, where harvested energy is transferred with remarkably high efficiency to a reaction center. This transport is affected by the motion of a structured vibrational environment, which makes simulations on a classical computer very demanding. Here we propose an analog quantum simulator of complex open system dynamics with a precisely engineered quantum environment. Our setup is based on superconducting circuits, a well established technology. As an example, we demonstrate that it is feasible to simulate exciton transport in the Fenna–Matthews–Olson photosynthetic complex. Our approach allows for a controllable single-molecule simulation and the investigation of energy transfer pathways as well as non-Markovian noise-correlation effects.
Using quantum algorithms to simulate complex physical processes and correlations in quantum matter has been a major direction of quantum computing research, towards the promise of a quantum advantage over classical approaches. In this work we develop a generalized quantum algorithm to simulate any dynamical process represented by either the operator sum representation or the Lindblad master equation. We then demonstrate the quantum algorithm by simulating the dynamics of the Fenna-Matthews-Olson (FMO) complex on the IBM QASM quantum simulator. This work represents a first demonstration of a quantum algorithm for open quantum dynamics with a moderately sophisticated dynamical process involving a realistic biological structure. We discuss the complexity of the quantum algorithm relative to the classical method for the same purpose, presenting a decisive query complexity advantage of the quantum approach based on the unique property of quantum measurement.
Abstract Quantum effects in photosynthetic energy transport in nature, especially for the typical Fenna-Matthews-Olson (FMO) complexes, are extensively studied in quantum biology. Such energy transport processes can be investigated as open quantum systems that blend the quantum coherence and environmental noise, and have been experimentally simulated on a few quantum devices. However, the existing experiments always lack a solid quantum simulation for the FMO energy transport due to their constraints to map a variety of issues in actual FMO complexes that have rich biological meanings. Here we successfully map the full coupling profile of the seven-site FMO structure by comprehensive characterisation and precise control of the evanescent coupling of the three-dimensional waveguide array. By applying a stochastic dynamical modulation on each waveguide, we introduce the base site energy and the dephasing term in coloured noise to faithfully simulate the power spectral density of the FMO complexes. We show our photonic model well interprets the phenomena including reorganisation energy, vibrational assistance, exciton transfer and energy localisation. We further experimentally demonstrate the existence of an optimal transport efficiency at certain dephasing strength, providing a window to closely investigate environment-assisted quantum transport.
The theory of open quantum systems has many applications ranging from simulating quantum dynamics in condensed phases to better understanding quantum-enabled technologies. At the center of theoretical chemistry are the developments of methodologies and computational tools for simulating charge and excitation energy transfer in solutions, biomolecules, and molecular aggregates. As a variety of these processes display non-Markovian behavior, classical computer simulation can be challenging due to exponential scaling with existing methods. With quantum computers holding the promise of efficient quantum simulations, in this paper, we present a new quantum algorithm based on Kraus operators that capture the exact non-Markovian effect at a finite temperature. The implementation of the Kraus operators on the quantum machine uses a combination of singular value decomposition (SVD) and optimal Walsh operators that result in shallow circuits. We demonstrate the feasibility of the algorithm by simulating the spin-boson dynamics and the exciton transfer in the Fenna-Matthews-Olson (FMO) complex. The NISQ results show very good agreement with the exact ones.