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arXiv:1311.4688

Evolutionary Design in Biological Quantum Computing

Gábor Vattay, Stuart Alan Kauffman

Published Nov 19, 2013• 3 citations
arXivHTMLPDF

Abstract

The unique capability of quantum mechanics to evolve alternative possibilities in parallel is appealing and over the years a number of quantum algorithms have been developed offering great computational benefits. Systems coupled to the environment lose quantum coherence quickly and realization of schemes based on unitarity might be impossible. Recent discovery of room temperature quantum coherence in light harvesting complexes opens up new possibilities to borrow concepts from biology to use quantum effects for computational purposes. While it has been conjectured that light harvesting complexes such as the Fenna-Matthews-Olson (FMO) complex in the green sulfur bacteria performs an efficient quantum search similar to the quantum Grover's algorithm the analogy has yet to be established. In this work we show that quantum dissipation plays an essential role in the quantum search performed in the FMO complex and it is fundamentally different from known algorithms. In the FMO complex not just the optimal level of phase breaking is present to avoid both quantum localization and Zeno trapping but it can harness quantum dissipation as well to speed the process even further up. With detailed quantum calculations taking into account both phase breaking and quantum dissipation we show that the design of the FMO complex has been evolutionarily optimized and works faster than pure quantum or classical-stochastic algorithms. Inspired by the findings we introduce a new computational concept based on decoherent quantum evolution. While it is inspired by light harvesting systems, the new computational devices can also be realized on different material basis opening new magnitude scales for miniaturization and speed.

DOI
10.48550/arxiv.1311.4688

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The unique capability of quantum mechanics to evolve alternative possibilities in parallel is appealing and over the years a number of quantum algorithms have been developed offering great computational benefits. Systems coupled to the environment lose quantum coherence quickly and realization of schemes based on unitarity might be impossible. Recent discovery of room temperature quantum coherence in light harvesting complexes opens up new possibilities to borrow concepts from biology to use quantum effects for computational purposes. While it has been conjectured that light harvesting complexes such as the Fenna-Matthews-Olson (FMO) complex in the green sulfur bacteria performs an efficient quantum search similar to the quantum Grover's algorithm the analogy has yet to be established. In this work we show that quantum dissipation plays an essential role in the quantum search performed in the FMO complex and it is fundamentally different from known algorithms. In the FMO complex not just the optimal level of phase breaking is present to avoid both quantum localization and Zeno trapping but it can harness quantum dissipation as well to speed the process even further up. With detailed quantum calculations taking into account both phase breaking and quantum dissipation we show that the design of the FMO complex has been evolutionarily optimized and works faster than pure quantum or classical-stochastic algorithms. Inspired by the findings we introduce a new computational concept based on decoherent quantum evolution. While it is inspired by light harvesting systems, the new computational devices can also be realized on different material basis opening new magnitude scales for miniaturization and speed.
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Applications of the concepts of quantum information theory are usually related to the powerful and counter-intuitive quantum mechanical effects of superposition, interference and entanglement. In this thesis, I examine the role of coherence and entanglement in complex chemical systems. The research has focused mainly on two related projects: The first project is developing a theoretical model to explain the recent ultrafast experiments on excitonic migration in photosynthetic complexes that show long-lived coherence of the order of hundreds of femtoseconds and the second project developing the Grover algorithm for global optimization of complex systems. The first part can be divided into two sections. The first section is investigating the theoretical frame about the transfer of electronic excitation energy through the Fenna-Matthews-Olson (FMO) pigment-protein complex. The new developed modified scaled hierarchical equation of motion (HEOM) approach is employed for simulating the open quantum system. The second section is investigating the evolution of entanglement in the FMO complex based on the simulation result via scaled HEOM approach. We examine the role of multipartite entanglement in the FMO complex by direct computation of the convex roof optimization for a number of different measures, including pairwise, triplet, quadruple and quintuple sites entanglement. Our results support the hypothesis that multipartite entanglement is maximum primary along the two distinct electronic energy transfer pathways. The second part of this thesis can be separated into two sections. The first section demonstrated that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The second section is implementing the basic quantum logical gates upon arrays of trapped ultracold polar molecules as qubits for the quantum computer. Utilized herein is the Multi-Target Optimal Control Theory (MTOCT) as a means of manipulating the initial-to-target transition probability via external laser field. The detailed calculation is applied for the SrO molecule, an ideal candidate in proposed quantum computers using arrays of trapped ultra-cold polar molecules.
We study the evolution of quantum entanglement during exciton energy transfer (EET) in a network model of the Fenna-Matthews-Olson (FMO) complex, a biological pigment-protein complex involved in the early steps of photosynthesis in sulfur bacteria. The influence of Markovian as well as spatially and temporally correlated (non-Markovian) noise on the generation of entanglement across distinct chromophores (site entanglement) and different excitonic eigenstates (mode entanglement) is studied for different injection mechanisms, including thermal and coherent laser excitation. Additionally, we study the entangling power of the FMO complex under natural operating conditions. While quantum information processing tends to favor maximal entanglement, near unit EET is achieved as the result of an intricate interplay between coherent and noisy processes where the initial part of the evolution displays intermediate values of both forms of entanglement.
Abstract Biological systems are currently analysed from deeper approaches considering not only their chemical features but also their quantum ones. Such elusive features sometimes account for specific phenomena related to their evolution and survival. Green sulphur bacteria are very simple microorganisms performing a highly photosynthetic process to survive. The Fenna-Mathew-Olson (FMO) complex is a macro-molecule responsible for such efficiency exhibiting interesting quantum features. Post-experimental biology together with Physics able the possibility to research and analyse them. In the current work, a synthetic roadmap for the FMO simulation is presented with comprehensive literature. The density matrix evolution is obtained to then discuss other derived features such as coherence, entanglement, state transference, and energy transmission efficiency.