[Paper Review] Evolutionary Design in Biological Quantum Computing

Gábor Vattay, Stuart Kauffman|arXiv (Cornell University)|Nov 19, 2013

Spectroscopy and Quantum Chemical Studies10 references3 citations

TL;DR

This paper proposes a novel quantum computational model inspired by the Fenna-Matthews-Olson (FMO) light-harvesting complex, demonstrating that evolutionary optimization harnesses quantum dissipation and controlled decoherence to outperform both pure quantum and classical stochastic algorithms. The FMO complex achieves ultrafast exciton transport via environment-assisted quantum transport (ENAQT), with optimal phase breaking at 300 cm⁻¹ enabling a 7 ps transport time to the reaction center.

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.

Motivation & Objective

• To investigate whether biological quantum systems like the FMO complex exploit quantum effects for computational advantage at room temperature.
• To determine the role of quantum dissipation and decoherence in enhancing transport efficiency beyond pure quantum or classical models.
• To explore whether evolutionary optimization in biological systems leads to a computational mechanism superior to known quantum algorithms.
• To develop a new computational paradigm based on decoherent quantum evolution that leverages environmental interactions for speed and miniaturization.

Proposed method

• Modeling exciton transport in the FMO complex using the Lindblad master equation to describe open quantum systems with phase-breaking and dissipative coupling to the environment.
• Applying the Redfield equation in energy representation to derive the superoperator for non-Markovian dynamics, incorporating temperature-dependent bath correlations.
• Using the generalized Caldeira-Leggett approximation to simplify the Redfield equations into a form suitable for numerical solution, retaining second-order terms in inverse temperature β.
• Simulating transport dynamics in the Harper model with tunable localization parameter λ, using a golden mean quasiperiodic potential to model the FMO Hamiltonian.
• Calculating transport time and efficiency via numerical inversion of the superoperator, with fixed trapping rate (κ = 1 ps⁻¹) and exciton decay rate (Γ = 1 ns⁻¹).
• Comparing transport performance across different Hamiltonian structures, including extended vs. localized wavefunctions, to assess the impact of system design on efficiency.

Experimental results

Research questions

• RQ1 Can quantum dissipation in biological systems like the FMO complex be harnessed as a computational resource rather than a source of error?
• RQ2 Does the FMO complex operate at an evolutionary optimum where phase breaking and environmental coupling maximize transport speed and efficiency?
• RQ3 How does the performance of the FMO complex compare to idealized quantum algorithms like Grover’s search or classical random walks?
• RQ4 Is there a fundamental difference between the mechanism of quantum search in the FMO complex and known quantum algorithms, particularly in the role of decoherence?
• RQ5 Can the principles of environment-assisted quantum transport (ENAQT) be generalized into a new class of quantum computing architectures?

Key findings

• The FMO complex achieves a transport time of approximately 7 ps to the reaction center at a phase-breaking rate of 300 cm⁻¹, consistent with experimental observations.
• Quantum dissipation and controlled decoherence are not detrimental but essential: they prevent Anderson localization and Zeno trapping, enabling faster and more robust transport.
• At optimal phase breaking (γφ = 300 cm⁻¹), the system relaxes rapidly to a uniform probability distribution (ϱₙₙ = 1/N), maximizing the chance of trapping at the reaction center.
• The FMO complex outperforms both pure quantum and classical stochastic algorithms due to the synergistic interplay of quantum coherence and environmental coupling.
• The Harper model shows that the critical point (λ = 1) of the localization-delocalization transition yields the shortest transport time and highest efficiency in a 30-site chain at room temperature.
• The proposed decoherent quantum evolution model is robust, scalable, and potentially realizable on diverse material platforms, enabling miniaturization below the atomic scale.