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A universal fault-tolerant quantum computer that can solve efficiently problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement towards realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e. qubits that are not error-corrected, and therefore perform imperfect operations in a limited coherence time. In the search for quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry and combinatorial optimization. The goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, we provide a thorough summary of NISQ computational paradigms and algorithms. We discuss the key structure of these algorithms, their limitations, and advantages. We additionally provide a comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices., Added new content, Modified certain parts and the paper structure

Bayesian optimization has emerged as a powerful strategy to accelerate scientific discovery by means of autonomous experimentation. However, expensive measurements are required to accurately estimate materials properties, and can quickly become a hindrance to exhaustive materials discovery campaigns. Here, we introduce Gemini: a data-driven model capable of using inexpensive measurements as proxies for expensive measurements by correcting systematic biases between property evaluation methods. We recommend using Gemini for regression tasks with sparse data and in an autonomous workflow setting where its predictions of expensive to evaluate objectives can be used to construct a more informative acquisition function, thus reducing the number of expensive evaluations an optimizer needs to achieve desired target values. In a regression setting, we showcase the ability of our method to make accurate predictions of DFT calculated bandgaps of hybrid organic-inorganic perovskite materials. We further demonstrate the benefits that Gemini provides to autonomous workflows by augmenting the Bayesian optimizer Phoenics to yeild a scalable optimization framework leveraging multiple sources of measurement. Finally, we simulate an autonomous materials discovery platform for optimizing the activity of electrocatalysts for the oxygen evolution reaction. Realizing autonomous workflows with Gemini, we show that the number of measurements of a composition space comprising expensive and rare metals needed to achieve a target overpotential is significantly reduced when measurements from a proxy composition system with less expensive metals are available., 12 pages, 5 figures, 2 tables

This paper focuses on Bayesian Optimization in combinatorial spaces. In many applications in the natural science. Broad applications include the study of molecules, proteins, DNA, device structures and quantum circuit designs, a on optimization over combinatorial categorical spaces is needed to find optimal or pareto-optimal solutions. However, only a limited amount of methods have been proposed to tackle this problem. Many of them depend on employing Gaussian Process for combinatorial Bayesian Optimizations. Gaussian Processes suffer from scalability issues for large data sizes as their scaling is cubic with respect to the number of data points. This is often impractical for optimizing large search spaces. Here, we introduce a variational Bayesian optimization method that combines variational optimization and continuous relaxations to the optimization of the acquisition function for Bayesian optimization. Critically, this method allows for gradient-based optimization and has the capability of optimizing problems with large data size and data dimensions. We have shown the performance of our method is comparable to state-of-the-art methods while maintaining its scalability advantages. We also applied our method in molecular optimization.

Superconducting circuits have emerged as a promising platform to build quantum processors. The challenge of designing a circuit is to compromise between realizing a set of performance metrics and reducing circuit complexity and noise sensitivity. At the same time, one needs to explore a large design space, and computational approaches often yield long simulation times. Here we automate the circuit design task using SCILLA, a software for automated discovery of superconducting circuits. SCILLA performs a parallelized, closed-loop optimization to design circuit diagrams that match pre-defined properties such as spectral features and noise sensitivities. We employ it to discover 4-local couplers for superconducting flux qubits and identify a circuit that outperforms an existing proposal with similar circuit structure in terms of coupling strength and noise resilience for experimentally accessible parameters. This work demonstrates how automated discovery can facilitate the design of complex circuit architectures for quantum information processing., 23 pages, 7 figures; shortened Sec. II Methodology; clarified Fig. 2; minor clarifying edits and typo corrections

Fast and inexpensive characterization of materials properties is a key element to discover novel functional materials. In this work, we suggest an approach employing three classes of Bayesian machine learning (ML) models to correlate electronic absorption spectra of nanoaggregates with the strength of intermolecular electronic couplings in organic conducting and semiconducting materials. As a specific model system, we consider PEDOT:PSS, a cornerstone material for organic electronic applications, and so analyze the couplings between charged dimers of closely packed PEDOT oligomers that are at the heart of the material's unrivaled conductivity. We demonstrate that ML algorithms can identify correlations between the coupling strengths and the electronic absorption spectra. We also show that ML models can be trained to be transferable across a broad range of spectral resolutions, and that the electronic couplings can be predicted from the simulated spectra with an 88 % accuracy when ML models are used as classifiers. Although the ML models employed in this study were trained on data generated by a multi-scale computational workflow, they were able to leverage leverage experimental data.

Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the capabilities of today's noisy intermediate-scale quantum (NISQ) devices. In this work, we revisit the problem of factoring, developing an alternative to Shor's algorithm, which employs established techniques to map the factoring problem to the ground state of an Ising Hamiltonian. The proposed variational quantum factoring (VQF) algorithm starts by simplifying equations over Boolean variables in a preprocessing step to reduce the number of qubits needed for the Hamiltonian. Then, it seeks an approximate ground state of the resulting Ising Hamiltonian by training variational circuits using the quantum approximate optimization algorithm (QAOA). We benchmark the VQF algorithm on various instances of factoring and present numerical results on its performance., 18 pages, 6 figures

Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning., 27 pages, 11 figures

In unsupervised data generation tasks, besides the generation of a sample based on previous observations, one would often like to give hints to the model in order to bias the generation towards desirable metrics. We propose a method that combines Generative Adversarial Networks (GANs) and reinforcement learning (RL) in order to accomplish exactly that. While RL biases the data generation process towards arbitrary metrics, the GAN component of the reward function ensures that the model still remembers information learned from data. We build upon previous results that incorporated GANs and RL in order to generate sequence data and test this model in several settings for the generation of molecules encoded as text sequences (SMILES) and in the context of music generation, showing for each case that we can effectively bias the generation process towards desired metrics., 10 pages, 7 figures

We present a study on the evolution of the Fenna-Matthews-Olson bacterial photosynthetic pigment-protein complex. This protein complex functions as an antenna. It transports absorbed photons - excitons - to a reaction center where photosynthetic reactions initiate. The efficiency of exciton transport is therefore fundamental for the photosynthetic bacterium's survival. We have reconstructed an ancestor of the complex to establish whether coherence in the exciton transport was selected for or optimized over time. We have also investigated on the role of optimizing free energy variation upon folding in evolution. We studied whether mutations which connect the ancestor to current day species were stabilizing or destabilizing from a thermodynamic view point. From this study, we established that most of these mutations were thermodynamically neutral. Furthermore, we did not see a large change in exciton transport efficiency or coherence and thus our results predict that exciton coherence was not specifically selected for.

Photosynthetic organisms rely on a series of self-assembled nanostructures with tuned electronic energy levels in order to transport energy from where it is collected by photon absorption, to reaction centers where the energy is used to drive chemical reactions. In the photosynthetic bacteria Chlorobaculum tepidum (Cba. tepidum), a member of the green sulphur bacteria (GSB) family, light is absorbed by large antenna complexes called chlorosomes. The exciton generated is transferred to a protein baseplate attached to the chlorosome, before traveling through the Fenna-Matthews-Olson (FMO) complex to the reaction center. The energy levels of these systems are generally defined by their chemical structure. Here we show that by placing bacteria within a photonic microcavity, we can access the strong exciton-photon coupling regime between a confined cavity mode and exciton states of the chlorosome, whereby a coherent exchange of energy between the bacteria and cavity mode results in the formation of polariton states. The polaritons have an energy distinct from that of the exciton and photon, and can be tuned in situ via the microcavity length. This results in real-time, non-invasive control over the relative energy levels within the bacteria. This demonstrates the ability to strongly influence living biological systems with photonic structures such as microcavities. We believe that by creating polariton states, that are in this case a superposition of a photon and excitons within a living bacteria, we can modify energy transfer pathways and therefore study the importance of energy level alignment on the efficiency of photosynthetic systems.

Chemical space is so large that brute force searches for new interesting molecules are infeasible. High-throughput virtual screening via computer cluster simulations can speed up the discovery process by collecting very large amounts of data in parallel, e.g., up to hundreds or thousands of parallel measurements. Bayesian optimization (BO) can produce additional acceleration by sequentially identifying the most useful simulations or experiments to be performed next. However, current BO methods cannot scale to the large numbers of parallel measurements and the massive libraries of molecules currently used in high-throughput screening. Here, we propose a scalable solution based on a parallel and distributed implementation of Thompson sampling (PDTS). We show that, in small scale problems, PDTS performs similarly as parallel expected improvement (EI), a batch version of the most widely used BO heuristic. Additionally, in settings where parallel EI does not scale, PDTS outperforms other scalable baselines such as a greedy search, $��$-greedy approaches and a random search method. These results show that PDTS is a successful solution for large-scale parallel BO., Accepted for publication in the proceedings of the 2017 ICML conference

Recent work has shown that a fully many-body treatment of noncovalent interactions, such as that given by the method of many-body dispersion (MBD), is vital to accurately modeling the structure and energetics of many molecular systems with density functional theory (DFT). To avoid double counting the correlation contributions of DFT and the MBD correction, a single-parameter range-separation scheme is typically employed. Coupling the MBD correction to a given exchange-correlation functional therefore requires calibrating the range-separation parameter. We perform this calibration for 24 popular DFT functionals by optimizing against the S66x8 benchmark set. Additionally, we report a linear equation that predicts near optimal range-separation parameters, dependent only on the class of the exchange functional and the value of the gradient enhancement factor. When a calibrated MBD correction is employed, most of the exchange-correlation functionals considered are capable of achieving agreement with CCSD(T)/CBS interaction energies in the S66x8 set to better than 1~kcal/mol mean absolute error., 24 pages, 3 figures

We present qHiPSTER, the Quantum High Performance Software Testing Environment. qHiPSTER is a distributed high-performance implementation of a quantum simulator on a classical computer, that can simulate general single-qubit gates and two-qubit controlled gates. We perform a number of single- and multi-node optimizations, including vectorization, multi-threading, cache blocking, as well as overlapping computation with communication. Using the TACC Stampede supercomputer, we simulate quantum circuits ("quantum software") of up to 40 qubits. We carry out a detailed performance analysis to show that our simulator achieves both high performance and high hardware efficiency, limited only by the sustainable memory and network bandwidth of the machine., 9 pages, 10 figures, 3 tables

We analyze standard theoretical models of solar energy conversion developed to study solar cells and photosynthetic systems. We show that the assumption that the energy transfer to the reaction center/electric circuit is through a decay rate or "sink", is in contradiction with the second law of thermodynamics. We put forward a thermodynamically consistent alternative by explicitly considering parts of the reaction center/electric circuit and by employing a Hamiltonian transfer. The predicted energy transfer by the new scheme differs from the one found using a decay rate, casting doubts on the validity of the conclusions obtained by models which include the latter.

We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision, an exponential improvement over all prior methods. The two algorithms developed in this work rely on a second quantized encoding of the wavefunction in which the state of an $N$ spin-orbital system is encoded in ${\cal O}(N)$ qubits. Our first algorithm requires at most $\widetilde{\cal O}(N^8 t)$ gates. Our second algorithm involves on-the-fly computation of molecular integrals, in a way that is exponentially more precise than classical sampling methods, by using the truncated Taylor series simulation technique. Our second algorithm has the lowest gate count of any approach to second quantized quantum chemistry simulation in the literature, scaling as $\widetilde{\cal O}(N^{5} t)$. The approaches presented here are readily applicable to a wide class of fermionic models, many of which are defined by simplified versions of the chemistry Hamiltonian., 13 pages, 1 figure. Part I of a two-paper series. For Part II see arXiv:1506.01029

The investigation of energy transfer properties in photosynthetic multi-protein networks gives insight into their underlying design principles.Here, we discuss excitonic energy transfer mechanisms of the photosystem II (PS-II) C$_2$S$_2$M$_2$ supercomplex, which is the largest isolated functional unit of the photosynthetic apparatus of higher plants.Despite the lack of a decisive energy gradient in C$_2$S$_2$M$_2$, we show that the energy transfer is directed by relaxation to low energy states. C$_2$S$_2$M$_2$ is not organized to form pathways with strict energetic downhill transfer, which has direct consequences on the transfer efficiency, transfer pathways and transfer limiting steps. The exciton dynamics is sensitive to small structural changes, which, for instance, are induced by the reorganization of vibrational coordinates. In order to incorporate the reorganization process in our numerical simulations, we go beyond rate equations and use the hierarchically coupled equation of motion approach (HEOM). While transfer from the peripherical antenna to the proteins in proximity to the reaction center occurs on a faster time scale, the final step of the energy transfer to the RC core is rather slow, and thus the limiting step in the transfer chain. Our findings suggest that the structure of the PS-II supercomplex guarantees photoprotection rather than optimized efficiency., 23 pages, 6 figures

Quantum heat machines (QHMs) models generally assume a weak coupling to the baths. This supposition is grounded in the separability principle between systems and allows the derivation of the evolution equation for this case. In the weak coupling regime, the machine's output is limited by the coupling strength, restricting their application. Seeking to overcome this limitation, we here analyze QHMs in the virtually unexplored strong coupling regime, where separability, as well as other standard thermodynamic assumptions, may no longer hold. We show that strongly coupled QHMs may be as efficient as their weakly coupled counterparts. In addition, we find a novel turnover behavior where their output saturates and disappears in the limit of ultra-strong coupling.

Simulation of quantum systems promises to deliver physical and chemical predictions for the frontiers of technology. Unfortunately, the exact representation of these systems is plagued by the exponential growth of dimension with the number of particles, or colloquially, the curse of dimensionality. The success of approximation methods has hinged on the relative simplicity of physical systems with respect to the exponentially complex worst case. Exploiting this relative simplicity has required detailed knowledge of the physical system under study. In this work, we introduce a general and efficient black box method for many-body quantum systems that utilizes technology from compressed sensing to find the most compact wavefunction possible without detailed knowledge of the system. It is a Multicomponent Adaptive Greedy Iterative Compression (MAGIC) scheme. No knowledge is assumed in the structure of the problem other than correct particle statistics. This method can be applied to many quantum systems such as spins, qubits, oscillators, or electronic systems. As an application, we use this technique to compute ground state electronic wavefunctions of hydrogen fluoride and recover 98% of the basis set correlation energy or equivalently 99.996% of the total energy with $50$ configurations out of a possible $10^7$. Building from this compactness, we introduce the idea of nuclear union configuration interaction for improving the description of reaction coordinates and use it to study the dissociation of hydrogen fluoride and the helium dimer.

In quantum information theory, there is an explicit mapping between general unitary dynamics and Hermitian ground state eigenvalue problems known as the Feynman-Kitaev Clock. A prominent family of methods for the study of quantum ground states are quantum Monte Carlo methods, and recently the full configuration interaction quantum Monte Carlo (FCIQMC) method has demonstrated great promise for practical systems. We combine the Feynman-Kitaev Clock with FCIQMC to formulate a new technique for the study of quantum dynamics problems. Numerical examples using quantum circuits are provided as well as a technique to further mitigate the sign problem through time-dependent basis rotations. Moreover, this method allows one to combine the parallelism of Monte Carlo techniques with the locality of time to yield an effective parallel-in-time simulation technique.

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm can efficiently find the eigenvalue of a given eigenvector but requires fully coherent evolution. We present an alternative approach that greatly reduces the requirements for coherent evolution and we combine this method with a new approach to state preparation based on ans\"atze and classical optimization. We have implemented the algorithm by combining a small-scale photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry: calculating the ground state molecular energy for He-H+, to within chemical accuracy. The proposed approach, by drastically reducing the coherence time requirements, enhances the potential of the quantum resources available today and in the near future.

We discuss the application of graphical processing units (GPUs) to accelerate real-space density functional theory (DFT) calculations. To make our implementation efficient, we have developed a scheme to expose the data parallelism available in the DFT approach; this is applied to the different procedures required for a real-space DFT calculation. We present results for current-generation GPUs from AMD and Nvidia, which show that our scheme, implemented in the free code Octopus, can reach a sustained performance of up to 90 GFlops for a single GPU, representing a significant speed-up when compared to the CPU version of the code. Moreover, for some systems our implementation can outperform a GPU Gaussian basis set code, showing that the real-space approach is a competitive alternative for DFT simulations on GPUs., 16 pages, 19 figures

Optimization problems associated with the interaction of linked particles are at the heart of polymer science, protein folding and other important problems in the physical sciences. In this review we explain how to recast these problems as constraint satisfaction problems such as linear programming, maximum satisfiability, and pseudo-boolean optimization. By encoding problems this way, one can leverage substantial insight and powerful solvers from the computer science community which studies constraint programming for diverse applications such as logistics, scheduling, artificial intelligence, and circuit design. We demonstrate how to constrain and embed lattice heteropolymer problems using several strategies. Each strikes a unique balance between number of constraints, complexity of constraints, and number of variables. Finally, we show how to reduce the locality of couplings in these energy functions so they can be realized as Hamiltonians on existing quantum annealing machines. We intend that this review be used as a case study for encoding related combinatorial optimization problems in a form suitable for adiabatic quantum optimization., 44 pages, 21 figures

In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems, thermal-state preparation, simulation of time dynamics, adiabatic quantum simulation, and density functional theory., 44 pages, 5 figures; comments or suggestions for improvement are welcome

Noise-assisted transport in quantum systems occurs when quantum time-evolution and decoherence conspire to produce a transport efficiency that is higher than what would be seen in either the purely quantum or purely classical cases. In disordered systems, it has been understood as the suppression of coherent quantum localisation through noise, which brings detuned quantum levels into resonance and thus facilitates transport. We report several new mechanisms of environment-assisted transport in ordered systems, in which there is no localisation to overcome and where one would naively expect that coherent transport is the fastest possible. Although we are particularly motivated by the need to understand excitonic energy transfer in photosynthetic light-harvesting complexes, our model is general---transport in a tight-binding system with dephasing, a source, and a trap---and can be expected to have wider application.

The reduced density matrix of excitons coupled to a phonon bath at a finite temperature is studied using the path integral Monte Carlo method. Appropriate choices of estimators and importance sampling schemes are crucial to the performance of the Monte Carlo simulation. We show that by choosing the population-normalized estimator for the reduced density matrix, an efficient and physically-meaningful sampling function can be obtained. In addition, the nonadiabatic phonon probability density is obtained as a byproduct during the sampling procedure. For importance sampling, we adopted the Metropolis-adjusted Langevin algorithm. The analytic expression for the gradient of the target probability density function associated with the population-normalized estimator cannot be obtained in closed form without a matrix power series. An approximated gradient that can be efficiently calculated is explored to achieve better computational scaling and efficiency. Application to a simple one-dimensional model system from the previous literature confirms the correctness of the method developed in this manuscript. The displaced harmonic model system within the single exciton manifold shows the numerically exact temperature dependence of the coherence and population of the excitonic system. The sampling scheme can be applied to an arbitrary anharmonic environment, such as multichromophoric systems embedded in the protein complex. The result of this study is expected to stimulate further development of real time propagation methods that satisfy the detailed balance condition for exciton populations., 16 pages, 5 figures

Intermediate band photovoltaics hold the promise of being highly efficient and cost effective photovoltaic cells. Intermediate states in the band gap, however, are known to facilitate nonradiative recombination. Much effort has been dedicated to producing metallic intermediate bands in hopes of producing lifetime recovery -- an increase in carrier lifetime as doping levels increase. We show that lifetime recovery induced by the insulator-to-metal transition will not occur, because the metallic extended states will be localised by phonons during the recombination process. Only trivial forms of lifetime recovery, e.g., from an overall shift in intermediate levels, are possible. Future work in intermediate band photovoltaics must focus on optimizing subgap optical absorption and minimizing recombination, but not via lifetime recovery., 8 pages

We propose a new approach to approximate the exchange and correlation (XC) functional in density functional theory. The XC potential is considered as an electrostatic potential, generated by a fictitious XC density, which is in turn a functional of the electronic density. We apply the approach to develop a correction scheme that fixes the asymptotic behavior of any approximated XC potential for finite systems. Additionally, the correction procedure gives the value of the derivative discontinuity; therefore it can directly predict the fundamental gap as a ground-state property., 5 pages, 4 figures

Is it possible to infer the time evolving quantum state of a multichromophoric system from a sequence of two-dimensional electronic spectra (2D-ES) as a function of waiting time? Here we provide a positive answer for a tractable model system: a coupled dimer. After exhaustively enumerating the Liouville pathways associated to each peak in the 2D-ES, we argue that by judiciously combining the information from a series of experiments varying the polarization and frequency components of the pulses, detailed information at the amplitude level about the input and output quantum states at the waiting time can be obtained. This possibility yields a quantum process tomography (QPT) of the single-exciton manifold, which completely characterizes the open quantum system dynamics through the reconstruction of the process matrix. This is the first of a series of two articles. In this manuscript, we specialize our results to the case of a homodimer, where we prove that signals stemming from coherence to population transfer and viceversa vanish upon isotropic averaging, and therefore, only a partial QPT is possible in this case. However, this fact simplifies the spectra, and it follows that only two polarization controlled experiments (and no pulse-shaping requirements) suffice to yield the elements of the process matrix which survive under isotropic averaging. The angle between the two site transition dipole moments is self-consistently obtained from the 2D-ES. Model calculations are presented, as well as an error analysis in terms of the angle between the dipoles and peak overlap. In the second article accompanying this study, we numerically exemplify the theory for heterodimers and carry out a detailed error analysis for such case. This investigation provides an important benchmark for more complex proposals of quantum process tomography (QPT) via multidimensional spectroscopic experiments.

The dissipative dynamics of many-electron systems interacting with a thermal environment has remained a long-standing challenge within time-dependent density functional theory (TDDFT). Recently, the formal foundations of open quantum systems time-dependent density functional theory (OQS-TDDFT) within the master equation approach were established. It was proven that the exact time-dependent density of a many-electron open quantum system evolving under a master equation can be reproduced with a closed (unitarily evolving) and non-interacting Kohn-Sham system. This potentially offers a great advantage over previous approaches to OQS-TDDFT, since with suitable functionals one could obtain the dissipative open-systems dynamics by simply propagating a set of Kohn-Sham orbitals as in usual TDDFT. However, the properties and exact conditions of such open-systems functionals are largely unknown. In the present article, we examine a simple and exactly-solvable model open quantum system: one electron in a harmonic well evolving under the Lindblad master equation. We examine two different representitive limits of the Lindblad equation (relaxation and pure dephasing) and are able to deduce a number of properties of the exact OQS-TDDFT functional. Challenges associated with developing approximate functionals for many-electron open quantum systems are also discussed., 12 pages, 9 figures

We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical evidence that this model displays the same universal behavior as the standard Anderson model. We use finite-size-scaling to find the localization length as a function of energy and density, including localized states away from the delocalization transition. Results at many energies all fit onto the same universal scaling curve., 5+ pages

Non-Markovian and non-equilibrium phonon effects are believed to be key ingredients in the energy transfer in photosynthetic complexes, especially in complexes which exhibit a regime of intermediate exciton-phonon coupling. In this work, we utilize a recently-developed measure for non-Markovianity to elucidate the exciton-phonon dynamics in terms of the information flow between electronic and vibrational degrees of freedom. We study the measure in the hierarchical equation of motion approach which captures strong system-bath coupling effects and non-equilibrium molecular reorganization. We propose an additional trace-distance measure for the information flow that could be extended to other master equations. We find that for a model dimer system and the Fenna-Matthews-Olson complex that non-Markovianity is significant under physiological conditions., 4 pages, 2 figures

Recently, the idea of classical Metropolis sampling through Markov chains has been generalized for quantum Hamiltonians. However, the underlying Markov chain of this algorithm is still classical in nature. Due to Szegedy's method, the Markov chains of classical Hamiltonians can achieve a quadratic quantum speedup in the eigenvalue gap of the corresponding transition matrix. A natural question to ask is whether Szegedy's quantum speedup is merely a consequence of employing classical Hamiltonians, where the eigenstates simply coincide with the computational basis, making cloning of the classical information possible. We solve this problem by introducing a quantum version of the method of Markov-chain quantization combined with the quantum simulated annealing (QSA) procedure, and describe explicitly a novel quantum Metropolis algorithm, which exhibits a quadratic quantum speedup in the eigenvalue gap of the corresponding Metropolis Markov chain for any quantum Hamiltonian. This result provides a complete generalization of the classical Metropolis method to the quantum domain., 7 pages

It is known that quantum computers, if available, would allow an exponential decrease in the computational cost of quantum simulations. We extend this result to show that the computation of molecular properties (energy derivatives) could also be sped up using quantum computers. We provide a quantum algorithm for the numerical evaluation of molecular properties, whose time cost is a constant multiple of the time needed to compute the molecular energy, regardless of the size of the system. Molecular properties computed with the proposed approach could also be used for the optimization of molecular geometries or other properties. For that purpose, we discuss the benefits of quantum techniques for Newton's method and Householder methods. Finally, global minima for the proposed optimizations can be found using the quantum basin hopper algorithm, which offers an additional quadratic reduction in cost over classical multi-start techniques., 6 pages

We extend the Runge-Gross theorem for a very general class of Markovian and non-Markovian open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) Time-Dependent Density Functional Theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential, thus placing the interactions between the particles of the system and the coupling to the environment on the same footing. A Markovian bath functional inspired by the theory of nonlinear Schrodinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented., 5 pages

This is a book chapter soon to appear (2002) in the "Handbook for Numerical Analysis" volume dedicated to "Computational Chemistry" edited by Claude Le Bris. The series editors are P.G. Ciarlet and J. L. Lions. [North Holland/Elservier]. This review deals with some of the methods known under the umbrella term quantum Monte Carlo (QMC), specifically those that have been most commonly used for electronic structure., 54 pages Recently corrected a sign typo