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Underlying physical principles for the high efficiency of excitation energy transfer in light-harvesting complexes are not fully understood. Notably, the degree of robustness of these systems for transporting energy is not known considering their realistic interactions with vibrational and radiative environments within the surrounding solvent and scaffold proteins. In this work, we employ an efficient technique to estimate energy transfer efficiency of such complex excitonic systems. We observe that the dynamics of the Fenna-Matthews-Olson (FMO) complex leads to optimal and robust energy transport due to a convergence of energy scales among all important internal and external parameters. In particular, we show that the FMO energy transfer efficiency is optimum and stable with respect to important parameters of environmental interactions including reorganization energy λ, bath frequency cutoff γ , temperature T, and bath spatial correlations. We identify the ratio of k B λT /¯γ g as a single key parameter governing quantum transport efficiency, where g is the average excitonic energy gap. © 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.

Abstract. 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.

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. Machine learning algorithms can be categorized along a spectrum of supervised and unsupervised learning [1][2][3][4]. In strictly unsupervised learning, the task is to find structure such as clusters in unlabeled data. Supervised learning involves a training set of already classified data, from which inferences are made to classify new data. In both cases, recent "big data" applications exhibit a growing number of features and input data. A Support Vector Machine (SVM) is a supervised machine learning algorithm that classifies vectors in a feature space into one of two sets, given training data from the sets [5]. It operates by constructing the optimal hyperplane dividing the two sets, either in the original feature space or in a higherdimensional kernel space. The SVM can be formulated as a quadratic programming problem [6], which can be solved in time proportional to O( logðϵ −1 ÞpolyðN; MÞ), with N the dimension of the feature space, M the number of training vectors, and ϵ the accuracy. In a quantum setting, binary classification was discussed in terms of Grover's search in [7] and using the adiabatic algorithm in [8][9][10][11]. Quantum learning was also discussed in [12,13].In this Letter, we show that a quantum support vector machine can be implemented with Oðlog NMÞ run time in both training and classification stages. The performance in N arises due to a fast quantum evaluation of inner products, discussed in a general machine learning context by us in [14]. For the performance in M, we reexpress the SVM as an approximate least-squares problem [15] that allows for a quantum solution with the matrix inversion algorithm [16,17]. We employ a technique for the exponentiation of nonsparse matrices recently developed in [18]. This allows us to reveal efficiently in quantum form the largest eigenvalues and corresponding eigenvectors of the training data overlap (kernel) and covariance matrices. We thus efficiently perform a low-rank approximation of these matrices [Principal Component Analysis (PCA)]. PCA is a common task arising here and in other machine learning algorithms [19][20][21]. The error dependence in the training stage is O(polyðϵ −1 K ; ϵ −1 Þ), where ϵ K is the smallest eigenvalue considered and ϵ is the accuracy. In cases when a low-rank approximation is appropriate, our quantum SVM operates on the full training set in logarithmic run time.Support vector machine.-The task for the S...

The usual way to reveal properties of an unknown quantum state, given many copies of a system in that state, is to perform measurements of different observables and to analyze the measurement results statistically. Here we show that the unknown quantum state can play an active role in its own analysis. In particular, given multiple copies of a quantum system with density matrix \rho, then it is possible to perform the unitary transformation e^{-i\rho t}. As a result, one can create quantum coherence among different copies of the system to perform quantum principal component analysis, revealing the eigenvectors corresponding to the large eigenvalues of the unknown state in time exponentially faster than any existing algorithm.Comment: 9 pages, Plain Te

The fundamental problem faced in quantum chemistry is the calculation of molecular properties, which are of practical importance in fields ranging from materials science to biochemistry. Within chemical precision, the total energy of a molecule as well as most other properties, can be calculated by solving the Schrödinger equation. However, the computational resources required to obtain exact solutions on a conventional computer generally increase exponentially with the number of atoms involved 1,2 . This renders such calculations intractable for all but the smallest of systems. Recently, an efficient algorithm has been proposed enabling a quantum computer to overcome this problem by achieving only a polynomial resource scaling with system size 2,3,4 . Such a tool would therefore provide an extremely powerful tool for new science and technology. Here we present a photonic implementation for the smallest problem: obtaining the energies of H 2 , the hydrogen molecule in a minimal basis. We perform a key algorithmic step-the iterative phase estimation algorithm 5,6,7,8 -in full, achieving a high level of precision and robustness to error. We implement other algorithmic steps with assistance from a classical computer and explain how this non-scalable approach could be avoided. Finally, we provide new theoretical results which lay the foundations for the next generation of simulation experiments using quantum computers. We have made early experimental progress towards the long-term goal of exploiting quantum information to speed up quantum chemistry calculations.Experimentalists are just beginning to command the level of control over quantum systems required to explore their information processing capabilities. An important long-term application is to simulate and calculate properties of other many-body quantum systems. Pioneering experiments were first performed using nuclear-magnetic-resonance-based systems to simulate quantum oscillators 9 , leading up to recent simulations of a pairing Hamiltonian 7,10 . Very recently the phase transitions of a two-spin quantum magnet were simulated 11 using an ion-trap system. Here we simulate a quantum chemical system and calculate its energy spectrum, using a photonic system. Molecular energies are represented as the eigenvalues of an associated time-independent HamiltonianĤ and can be efficiently obtained to fixed accuracy, using a quantum algorithm with three distinct steps 6 : encoding a molecular wavefunction into qubits; simulating its time evolution using quantum logic gates; and extracting the approximate energy using the phase estimation algorithm 3,12 . The latter is a general-purpose quantum algorithm for evaluating the eigenvalues of arbitrary Hermitian or unitary operators. The algorithm estimates the phase, φ, accumulated by a molecular eigenstate, |Ψ , under the action of the time-evolution operator,Û =e −iĤt/ , i.e.,where E is the energy eigenvalue of |Ψ . Therefore, estimating the phase for each eigenstate amounts to estimating the eigenvalues of the Hamiltonia...

The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can be applied only to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and interelectronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the Born-Oppenheimer approximation but faster and more efficient as well, for all reactions with more than about four atoms. This is the case even though the entire electronic wave function is propagated on a grid with appropriately short time steps. Although the preparation and measurement of arbitrary states on a quantum computer is inefficient, here we demonstrate how to prepare states of chemical interest efficiently. We also show how to efficiently obtain chemically relevant observables, such as stateto-state transition probabilities and thermal reaction rates. Quantum computers using these techniques could outperform current classical computers with 100 qubits.electronic structure ͉ quantum computation ͉ quantum simulation A ccurate simulations of quantum-mechanical processes have greatly expanded our understanding of the fundamentals of chemical reaction dynamics. In particular, recent years have seen tremendous progress in methods development, which has enabled simulations of increasingly complex quantum systems. Although it is, strictly speaking, true that exact quantum simulation requires resources that scale exponentially with system size, several techniques are available that can treat realistic chemical problems, at a given accuracy, with only a polynomial cost. Certain fully quantum methods-such as multiconfigurational time-dependent Hartree (MCTDH) (1), matching pursuit/split-operator Fourier transform (MP/SOFT) (2), or full multiple spawning (FMS) (3)-solve the nuclear Schrödinger equation, including nonadiabatic effects, given analytic expressions for the potential energy surfaces and the couplings between them. These techniques have permitted the simulation of large systems; as examples we can give MCTDH simulations of a pentaatomic chemical reaction (4) and of a spin-boson model with 80 degrees of freedom (5) or an MP/SOFT simulation of photoisomerization in rhodopsin with 25 degrees of freedom (6). Ab initio molecular-dynamics techniques such as ab initio multiple spawning (AIMS) (7) avoid analytic expressions for potential energy surfaces and instead solve electronic Schrödinger equations at every time step. This allows one to gain insight into dynamical problems such as isomerizations through conical intersections (8).However, there are also chemical processes that are best treated by completely avoiding the Born-Oppenheimer approximation. As examples, we can cite strong-field electronic dynamics in atoms and multielectron ionization (9, 10) or atomic and molecular fragmentation cau...

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 Green's 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%.