Person: Aspuru-Guzik, Alan
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Aspuru-Guzik
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Aspuru-Guzik, Alan
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Publication A Quantum-Quantum Metropolis Algorithm(National Academy of Sciences, 2012) Yung, Man-Hong; Aspuru-Guzik, AlanThe classical Metropolis sampling method is a cornerstone of many statistical modeling applications that range from physics, chemistry, and biology to economics. This method is particularly suitable for sampling the thermal distributions of classical systems. The challenge of extending this method to the simulation of arbitrary quantum systems is that, in general, eigenstates of quantum Hamiltonians cannot be obtained efficiently with a classical computer. However, this challenge can be overcome by quantum computers. Here, we present a quantum algorithm which fully generalizes the classical Metropolis algorithm to the quantum domain. The meaning of quantum generalization is twofold: The proposed algorithm is not only applicable to both classical and quantum systems, but also offers a quantum speedup relative to the classical counterpart. Furthermore, unlike the classical method of quantum Monte Carlo, this quantum algorithm does not suffer from the negative-sign problem associated with fermionic systems. Applications of this algorithm include the study of low-temperature properties of quantum systems, such as the Hubbard model, and preparing the thermal states of sizable molecules to simulate, for example, chemical reactions at an arbitrary temperature.Publication Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance(Nature Publishing Group, 2011) Li, Zhaokai; Yung, Man-Hong; Chen, Hongwei; Lu, Dawei; Whitfield, James D.; Peng, Xinhua; Aspuru-Guzik, Alan; Du, JiangfengQuantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the \(10^{−5}\) decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wave functions than classical computersPublication Characterization and Quantification of the Role of Coherence in Ultrafast Quantum Biological Experiments Using Quantum Master Equations, Atomistic Simulations, and Quantum Process Tomography(Elsevier, 2011) Rebentrost, Frank Patrick; Shim, Sangwoo; Yuen-Zhou, Joel; Aspuru-Guzik, AlanLong-lived electronic coherences in various photosynthetic complexes at cryogenic and room temperature have generated vigorous efforts both in theory and experiment to understand their origins and explore their potential role to biological function. The ultrafast signals resulting from the experiments that show evidence for these coherences result from many contributions to the molecular polarization. Quantum process tomography (QPT) is a technique whose goal is that of obtaining the time-evolution of all the density matrix elements based on a designed set of experiments with different preparation and measurements. The QPT procedure was conceived in the context of quantum information processing to characterize and understand general quantum evolution of controllable quantum systems, for example while carrying out quantum computational tasks. We introduce our QPT method for ultrafast experiments, and as an illustrative example, apply it to a simulation of a two-chromophore subsystem of the Fenna-Matthews-Olson photosynthetic complex, which was recently shown to have long-lived quantum coherences. Our Fenna-Matthews-Olson model is constructed using an atomistic approach to extract relevant parameters for the simulation of photosynthetic complexes that consists of a quantum mechanics/molecular mechanics approach combined with molecular dynamics and the use of state-of-the-art quantum master equations. We provide a set of methods that allow for quantifying the role of quantum coherence, dephasing, relaxation and other elementary processes in energy transfer efficiency in photosynthetic complexes, based on the information obtained from the atomistic simulations, or, using QPT, directly from the experiment. The ultimate goal of the combination of this diverse set of methodologies is to provide a reliable way of quantifying the role of long-lived quantum coherences and obtain atomistic insight of their causes.Publication Conformation of Self-Assembled Porphyrin Dimers in Liposome Vesicles by Phase-Modulation 2D Fluorescence Spectroscopy(National Academy of Sciences, 2011) Lott, Geoffrey A.; Perdomo-Ortiz, Alejandro; Utterback, James K.; Widom, Julia R.; Aspuru-Guzik, Alan; Marcus, Andrew H.By applying a phase-modulation fluorescence approach to 2D electronic spectroscopy, we studied the conformation-dependent exciton coupling of a porphyrin dimer embedded in a phospholipid bilayer membrane. Our measurements specify the relative angle and separation between interacting electronic transition dipole moments and thus provide a detailed characterization of dimer conformation. Phase-modulation 2D fluorescence spectroscopy (PM-2D FS) produces 2D spectra with distinct optical features, similar to those obtained using 2D photon-echo spectroscopy. Specifically, we studied magnesium meso tetraphenylporphyrin dimers, which form in the amphiphilic regions of 1,2-distearoyl-sn-glycero-3-phosphocholine liposomes. Comparison between experimental and simulated spectra show that although a wide range of dimer conformations can be inferred by either the linear absorption spectrum or the 2D spectrum alone, consideration of both types of spectra constrain the possible structures to a “T-shaped” geometry. These experiments establish the PM-2D FS method as an effective approach to elucidate chromophore dimer conformation.Publication Electronic Transition Moments of 6-methyl Isoxanthopterin—A Fluorescent Analogue of the Nucleic Acid Base Guanine(Oxford University Press, 2012) Widom, Julia; Rappoport, Dmitrij; Perdomo-Ortiz, Alejandro; Thomsen, Hanna; Johnson, Neil P.; von Hippel, Peter H.; Aspuru-Guzik, Alan; Marcus, Andrew H.Fluorescent nucleic acid base analogues are important spectroscopic tools for understanding local structure and dynamics of DNA and RNA. We studied the orientations and magnitudes of the electric dipole transition moments (EDTMs) of 6-methyl isoxanthopterin (6-MI), a fluorescent analogue of guanine that has been particularly useful in biological studies. Using a combination of absorption spectroscopy, linear dichroism (LD) and quantum chemical calculations, we identified six electronic transitions that occur within the 25 000–50 000 \(cm^{−1}\) spectral range. Our results indicate that the two experimentally observed lowest-energy transitions, which occur at 29 687 \(cm^{−1}\) (337 nm) and 34 596 \(cm^{−1}\) (289 nm), are each polarized within the plane of the 6-MI base. A third in-plane polarized transition is experimentally observed at 47 547 \(cm^{−1}\) (210 nm). The theoretically predicted orientation of the lowest-energy transition moment agrees well with experiment. Based on these results, we constructed an exciton model to describe the absorption spectra of a 6-MI dinucleotide–substituted double-stranded DNA construct. This model is in good agreement with the experimental data. The orientations and intensities of the low-energy electronic transitions of 6-MI reported here should be useful for studying local conformations of DNA and RNA in biologically important complexes.Publication Positivity in the Presence of Initial System-Environment Correlation(American Physical Society, 2012) Modi, Kavan; Rodríguez-Rosario, César A.; Aspuru-Guzik, AlanThe constraints imposed by the initial system-environment correlation can lead to nonpositive dynamical maps. We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map. Any initial system-environment correlations make the assignment map nonpositive, while the positivity of the dynamical map depends on the interplay between the assignment map and the system-environment coupling. We show how this interplay can reveal or hide the nonpositivity of the assignment map. We discuss the role of this interplay in Markovian models.Publication MultiDK: A Multiple Descriptor Multiple Kernel Approach for Molecular Discovery and Its Application to Organic Flow Battery Electrolytes(American Chemical Society (ACS), 2017-04-10) Sung-jin Kim, Adrián; Aspuru-Guzik, AlanWe propose a multiple descriptor multiple kernel (MultiDK) method for efficientmolecular discovery using machine learning. We show that the MultiDK method im-proves both the speed and the accuracy of molecular property prediction. We applythe method to the discovery of electrolyte molecules for aqueous redox flow batteries.Usingmultiple-type - as opposed to single-type - descriptors, more relevant featuresfor machine learning can be obtained. Following the principle of the ’wisdom of thecrowds’, the combination of multiple-type descriptors significantly boosts predictionperformance. Moreover, MultiDK can exploit irregularities between molecular struc-ture and property relations better than the linear regression method by employingmultiple kernels - more than one kernel functions for a set of the input descriptors.The multiple kernels consist of the Tanimoto similarity function and a linear kernelfor a set of binary descriptors and a set of non-binary descriptors, respectively. UsingMultiDK, we achieve average performance ofr2= 0.92 with a set of molecules for solubility prediction. We also extend MultiDK to predict pH-dependent solubility andapply it to solubility estimation of quinone molecules with ionizable functional groupsas strong candidates of flow battery electrolytes.Publication Equivalence between spin Hamiltonians and boson sampling(American Physical Society (APS), 2017-03-24) Peropadre, Borja; Aspuru-Guzik, Alan; García-Ripoll, Juan JoséAaronson and Arkhipov showed that predicting or reproducing the measurement statistics of a general linear optics circuit with a single Fock-state input is a classically hard problem. Here we show that this problem, known as boson sampling, is as hard as simulating the short time evolution of a large but simple spin model with long-range X Y interactions. The conditions for this equivalence are the same for efficient boson sampling, namely, having a small number of photons (excitations) as compared to the number of modes (spins). This mapping allows efficient implementations of boson sampling in small quantum computers and simulators and sheds light on the complexity of time evolution with critical spin models.Publication Quantum autoencoders for efficient compression of quantum data(IOP Publishing, 2017-08-18) Romero, Jonathan; Olson, Jonathan P; Aspuru-Guzik, AlanClassical autoencoders are neural networks that can learn efficient low dimensional representations of data in higher dimensional space. The task of an autoencoder is, given an input x, is to map x to a lower dimensional point y such that x can likely be recovered from y. The structure of the underlying autoencoder network can be chosen to represent the data on a smaller dimension, effectively compressing the input. Inspired by this idea, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a particular dataset of quantum states, where a classical compression algorithm cannot be employed. The parameters of the quantum autoencoder are trained using classical optimization algorithms. We show an example of a simple programmable circuit that can be trained as an efficient autoencoder. We apply our model in the context of quantum simulation to compress ground states of the Hubbard model and molecular Hamiltonians.Publication Bounding the costs of quantum simulation of many-body physics in real space(IOP Publishing, 2017-06-29) Kivlichan, Ian D; Wiebe, Nathan; Babbush, Ryan; Aspuru-Guzik, AlanWe present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system and using a high-order finite difference approximation to the kinetic energy operator. We find that our algorithm can simulateηinteracting particles using a number of calculations of the pairwise interactions that scales, for a fixed spatial grid spacing,as ̃O(η2), versus the ̃O(η5) time required by previous methods (assuming the number of orbitals is proportional toη), and scales super-polynomially better with the error tolerance than algorithms based on the Lie-Trotter-Suzuki product formula. Finally, we analyze discretization errors that arise from the spatial grid and show that under some circumstances these errors can remove the exponential speedups typically afforded by quantum simulation.