Patrick Rebentrost

Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer

Energy transfer within photosynthetic systems can display quantum effects such as delocalized excitonic transport. Recently, direct evidence of long-lived coherence has been experimentally demonstrated for the dynamics of the Fenna-Matthews-Olson (FMO) protein complex [Engel et al., Nature (London) 446, 782 (2007)]. However, the relevance of quantum dynamical processes to the exciton transfer efficiency is to a large extent unknown. Here, we develop a theoretical framework for studying the role of quantum interference effects in energy transfer dynamics of molecular arrays interacting with a thermal bath within the Lindblad formalism. To this end, we generalize continuous-time quantum walks to nonunitary and temperature-dependent dynamics in Liouville space derived from a microscopic Hamiltonian. Different physical effects of coherence and decoherence processes are explored via a universal measure for the energy transfer efficiency and its susceptibility. In particular, we demonstrate that for the FMO complex, an effective interplay between the free Hamiltonian evolution and the thermal fluctuations in the environment leads to a substantial increase in energy transfer efficiency from about 70% to 99%.

Environment-Assisted Quantum Transport

Transport phenomena at the nanoscale are of interest due to the presence of both quantum and classical behavior. In this work, we demonstrate that quantum transport efficiency can be enhanced by a dynamical interplay of the system Hamiltonian with pure dephasing induced by a fluctuating environment. This is in contrast to fully coherent hopping that leads to localization in disordered systems, and to highly incoherent transfer that is eventually suppressed by the quantum Zeno effect. We study these phenomena in the Fenna–Matthews–Olson protein complex as a prototype for larger photosynthetic energy transfer systems. We also show that the disordered binary tree structures exhibit enhanced transport in the presence of dephasing.

Role of quantum coherence and environmental fluctuations in chromophoric energy transport.

The role of quantum coherence in the dynamics of photosynthetic energy transfer in chromophoric complexes is not fully understood. In this work, we quantify the biological importance of fundamental physical processes, such as the excitonic Hamiltonian evolution and phonon-induced decoherence, by their contribution to the efficiency of the primary photosynthetic event. We study the effect of spatial correlations in the phonon bath and slow protein scaffold movements on the efficiency and the contributing processes. To this end, we develop two theoretical approaches based on a Greens function method and energy transfer susceptibilities. We investigate the Fenna-Matthews-Olson protein complex, in which we find a contribution of coherent dynamics of about 10% in the presence of uncorrelated phonons and about 30% in the presence of realistically correlated ones.The role of quantum coherence and the environment in the dynamics of excitation energy transfer is not fully understood. In this work, we introduce the concept of dynamical contributions of various physical processes to the energy transfer efficiency. We develop two complementary approaches, based on a Greens function method and energy transfer susceptibilities, and quantify the importance of the Hamiltonian evolution, phonon-induced decoherence, and spatial relaxation pathways. We investigate the Fenna-Matthews-Olson protein complex, where we find a contribution of coherent dynamics of about 10% and of relaxation of 80%.

Atomistic Study of the Long-Lived Quantum Coherences in the Fenna-Matthews-Olson Complex

A remarkable amount of theoretical research has been carried out to elucidate the physical origins of the recently observed long-lived quantum coherence in the electronic energy transfer process in biological photosynthetic systems. Although successful in many respects, several widely used descriptions only include an effective treatment of the protein-chromophore interactions. In this work, by combining an all-atom molecular dynamics simulation, time-dependent density functional theory, and open quantum system approaches, we successfully simulate the dynamics of the electronic energy transfer of the Fenna-Matthews-Olson pigment-protein complex. The resulting characteristic beating of populations and quantum coherences is in good agreement with the experimental results and the hierarchy equation of motion approach. The experimental absorption, linear, and circular dichroism spectra and dephasing rates are recovered at two different temperatures. In addition, we provide an extension of our method to include zero-point fluctuations of the vibrational environment. This work thus presents, to our knowledge, one of the first steps to explain the role of excitonic quantum coherence in photosynthetic light-harvesting complexes based on their atomistic and molecular description.

Quantum Support Vector Machine for Big Data Classification

Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.

Quantum principal component analysis

Characterizing an unknown quantum state typically relies on analysing the outcome of a large set of measurements. Certain quantum-processing tasks are now shown to be realizable using only approximate knowledge of the state, which can be gathered with exponentially fewer resources.

Modified-scaled hierarchical equation of motion approach for the study of quantum coherence in photosynthetic complexes

We present a detailed theoretical study of the transfer of electronic excitation energy through the Fenna-Matthews-Olson (FMO) pigment-protein complex, using the newly developed modified scaled hierarchical approach (Shi, Q.; et al. J. Chem. Phys. 2009, 130, 084105). We show that this approach is computationally more efficient than the original hierarchical approach. The modified approach reduces the truncation levels of the auxiliary density operators and the correlation function. We provide a systematic study of how the number of auxiliary density operators and the higher-order correlation functions affect the exciton dynamics. The time scales of the coherent beating are consistent with experimental observations. Furthermore, our theoretical results exhibit population beating at physiological temperature. Additionally, the method does not require a low-temperature correction to obtain the correct thermal equilibrium at long times.

Quantum Machine Learning

Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Quantum systems produce atypical patterns that classical systems are thought not to produce efficiently, so it is reasonable to postulate that quantum computers may outperform classical computers on machine learning tasks. The field of quantum machine learning explores how to devise and implement quantum software that could enable machine learning that is faster than that of classical computers. Recent work has produced quantum algorithms that could act as the building blocks of machine learning programs, but the hardware and software challenges are still considerable.

Simple pulses for elimination of leakage in weakly nonlinear qubits.

In realizations of quantum computing, a two-level system (qubit) is often singled out from the many levels of an anharmonic oscillator. In these cases, simple qubit control fails on short time scales because of coupling to leakage levels. We provide an easy to implement analytic formula that inhibits this leakage from any single-control analog or pixelated pulse. It is based on adding a second control that is proportional to the time derivative of the first. For realistic parameters of superconducting qubits, this strategy reduces the error by an order of magnitude relative to the state of the art, all based on smooth and feasible pulse shapes. These results show that even weak anharmonicity is sufficient and in general not a limiting factor for implementing quantum gates.

Non-Markovian Quantum Jumps in Excitonic Energy Transfer

We utilize the novel non-Markovian quantum jump (NMQJ) approach to stochastically simulate exciton dynamics derived from a time-convolutionless master equation. For relevant parameters and time scales, the time-dependent, oscillatory decoherence rates can have negative regions, a signature of non-Markovian behavior and of the revival of coherences. This can lead to non-Markovian population beatings for a dimer system at room temperature. We show that strong exciton-phonon coupling to low frequency modes can considerably modify transport properties. We observe increased exciton transport, which can be seen as an extension of recent environment-assisted quantum transport concepts to the non-Markovian regime. Within the NMQJ method, the Fenna-Matthew-Olson protein is investigated as a prototype for larger photosynthetic complexes.