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One-class classification is a fundamental problem in pattern recognition with a wide range of applications. This work presents a semi-supervised quantum machine learning algorithm for such a problem, which we call a variational quantum one-class classifier (VQOCC). The algorithm is suitable for noisy intermediate-scale quantum computing because the VQOCC trains a fully-parameterized quantum autoencoder with a normal dataset and does not require decoding. The performance of the VQOCC is compared with that of the one-class support vector machine (OC-SVM), the kernel principal component analysis (PCA), and the deep convolutional autoencoder (DCAE) using handwritten digit and Fashion-MNIST datasets. The numerical experiment examined various structures of VQOCC by varying data encoding, the number of parameterized quantum circuit layers, and the size of the latent feature space. The benchmark shows that the classification performance of VQOCC is comparable to that of OC-SVM and PCA, although the number of model parameters grows only logarithmically with the data size. The quantum algorithm outperformed DCAE in most cases under similar training conditions. Therefore, our algorithm constitutes an extremely compact and effective machine learning model for one-class classification., 12 pages, 5 figures

We present a quantum algorithm for calculating the vibronic spectrum of a molecule, a useful but classically hard problem in chemistry. We show several advantages over previous quantum approaches: vibrational anharmonicity is naturally included; after measurement, some state information is preserved for further analysis; and there are potential error-related benefits. Considering four triatomic molecules, we numerically study truncation errors in the harmonic approximation. Further, in order to highlight the fact that our quantum algorithm's primary advantage over classical algorithms is in simulating anharmonic spectra, we consider the anharmonic vibronic spectrum of sulfur dioxide. In the future, our approach could aid in the design of materials with specific light-harvesting and energy transfer properties, and the general strategy is applicable to other spectral calculations in chemistry and condensed matter physics., Primary edits: Anharmonic simulation of sulfur dioxide; DOI added

In this work, we present a linear optical implementation for analog quantum simulation of molecular vibronic spectra, incorporating the non-Condon scattering operation with a quadratically small truncation error. Thus far, analog and digital quantum algorithms for achieving quantum speedup have been suggested only in the Condon regime, which refers to a transition dipole moment that is independent of nuclear coordinates. For analog quantum optical simulation beyond the Condon regime (i.e., non-Condon transitions) the resulting non-unitary scattering operations must be handled appropriately in a linear optical network. In this paper, we consider the first and second-order Herzberg-Teller expansions of the transition dipole moment operator for the non-Condon effect, for implementation on linear optical quantum hardware. We believe the method opens a new way to approximate arbitrary non-unitary operations in analog and digital quantum simulations. We report in-silico simulations of the vibronic spectra for naphthalene, phenanthrene, and benzene to support our findings., Comment: 16 pages, 5 figures

Quantum coherence is a useful resource that is consumed to accomplish several tasks that classical devices are hard to fulfill. Especially, it is considered to be the origin of quantum speedup for many computational algorithms. In this work, we interpret the computational time cost of boson sampling with partially distinguishable photons from the perspective of coherence resource theory. With incoherent operations that preserve the diagonal elements of quantum states up to permutation, which we name \emph{permuted genuinely incoherent operation} (pGIO), we present some evidence that the decrease of coherence corresponds to a computationally less complex system of partially distinguishable boson sampling. Our result shows that coherence is one of crucial resources for the computational time cost of boson sampling. We expect our work presents an insight to understand the quantum complexity of the linear optical network system., Comment: 11 pages, 2 figures

A fundamental question in linear optical quantum computing is to understand the origin of the quantum supremacy in the physical system. It is found that the multimode linear optical transition amplitudes are calculated through the permanents of transition operator matrices, which is a hard problem for classical simulations (boson sampling problem). We can understand this problem by considering a quantum measure that directly determines the runtime for computing the transition amplitudes. In this paper, we suggest a quantum measure named "Fock state concurrence sum" $C_S$, which is the summation over all the members of "the generalized Fock state concurrence" (a measure analogous to the generalized concurrences of entanglement and coherence). By introducing generalized algorithms for computing the transition amplitudes of the Fock state boson sampling with an arbitrary number of photons per mode, we show that the minimal classical runtime for all the known algorithms directly depends on $C_S$. Therefore, we can state that \emph{the Fock state concurrence sum $C_S$ behaves as a collective measure that controls the computational complexity of Fock state BS}. We expect that our observation on the role of the Fock state concurrence in the generalized algorithm for permanents would provide a unified viewpoint to interpret the quantum computing power of linear optics., 11 pages, 1 figure

Linear optical computing (LOC) with thermal light has recently gained attention because the problem is connected to the permanent of a Hermitian positive semidefinite matrix (HPSM), which is of importance in the computational complexity theory. Despite the several theoretical analyses on the computational structure of an HPSM in connection to LOC, the experimental demonstration and the computational complexity analysis via the linear optical system have not been performed yet. We present, herein, experimental LOC for estimating the permanent of an HPSM. From the linear optical experiments and theoretical analysis, we find that the LOC efficiency for a multiplicative error is dependent on the value of the permanent and that the lower bound of the computation time scales exponentially. Furthermore, our results are generalized and applied to LOC of permanents of unitary matrices, which can be implemented with a multi-port quantum interferometer involving single-photons at the input ports. We find that LOC with single-photons, for the permanent estimation, is on average less efficient than the most efficient classical algorithm known to date, even in ideal conditions.

We suggest a formalism to illustrate the entanglement of identical particles in the first quantization language (1QL). Our 1QL formalism enables one to exploit all the well-established quantum information tools to understand the indistinguishable ones, including the reduced density matrix and familiar entanglement measures. The rigorous quantitative relation between the amount of entanglement and the spatial coherence of particles is possible in this formalism. Our entanglement detection process is a generalization of the entanglement extraction protocol for identical particles with mode splitting proposed by Killoran et al. (2014)., 11 pages, 5 figures, Revtex 4.1; (v2) minor corrections, some references added; (v3) minor corrections and clarifications; (v4) Accepted version (PRA)

Particle identity and entanglement are two fundamental quantum properties that work as major resources for various quantum information tasks. However, it is still a challenging problem to understand the correlation of the two properties in the same system. While recent theoretical studies have shown that the spatial overlap between identical particles is necessary for nontrivial entanglement, the exact role of particle indistinguishability in the entanglement of identical particles has never been analyzed quantitatively before. Here, we theoretically and experimentally investigate the behavior of entanglement between two bosons as spatial overlap and indistinguishability simultaneously vary. The theoretical computation of entanglement for generic two bosons with pseudospins is verified experimentally in a photonic system. Our results show that the amount of entanglement is a monotonically increasing function of both quantities. We expect that our work provides an insight into deciphering the role of the entanglement in quantum networks that consist of identical particles., Comment: Comments are welcome

In this paper, we present numerical schemes for evaluating the matrix elements of Gaussian/non-Gaussian operators in the Fock state basis, which are identified as multivariate Hermite polynomials (MHPs). Using the integral transformation operator to perform the multimode Bogoliubov transformation, Husimi's Q-functions of Gaussian/non-Gaussian operators are easily derived as the generating functions of MHPs., 9 pages

This work shows that the majorization of photon distributions is related to the runtime of classically simulating multimode passive linear optics, which explains one aspect of the boson sampling hardness. A Shur-concave quantity which we name the \emph{Boltzmann entropy of elementary quantum complexity} ($S_B^q$) is introduced to present some quantitative analysis of the relation between the majorization and the classical runtime for simulating linear optics. We compare $S_B^q$ with two quantities that are important criteria for understanding the computational cost of the photon scattering process, $\mathcal{T}$ (the runtime for the classical simulation of linear optics) and $\mathcal{E}$ (the additive error bound for an approximated amplitude estimator). First, for all the known algorithms for computing the permanents of matrices with repeated rows and columns, the runtime $\mathcal{T}$ becomes shorter as the input and output distribution vectors are more majorized. Second, the error bound $\mathcal{E}$ decreases as the majorization difference of input and output states increases. We expect that our current results would help in understanding the feature of linear optical networks from the perspective of quantum computation., Comment: 12 pages, 4 figures; (v3) Accepted version (Journal of Physics A)

Chlorosomes are the largest and most efficient natural light-harvesting antenna systems. They contain thousands of pigment molecules - bacteriochlorophylls (BChls)- that are organized into supramolecular aggregates and form a very efficient network for excitonic energy migration. Here, we present a theoretical study of excitation energy transfer (EET) in the chlorosome based on experimental evidence of the molecular assembly. Our model for the exciton dynamics throughout the antenna combines a stochastic time propagation of the excitonic wave function with molecular dynamics simulations of supramolecular structure, and electronic structure calculations of the excited states. The simulation results reveal a detailed picture of the EET in the chlorosome. Coherent energy transfer is significant only for the first 50 fs after the initial excitation, and the wavelike motion of the exciton is completely damped at 100 fs. Characteristic time constants of incoherent energy transfer, subsequently, vary from 1 ps to several tens of ps. We assign the time scales of the EET to specific physical processes by comparing our results with the data obtained from time-resolved spectroscopy experiments.

15 pags., 4 figs., 3 apps., In this work, we propose a flexible architecture of microwave resonators with tunable couplings to perform quantum simulations of problems from the field of molecular chemistry. The architecture builds on the experience of the D-Wave design, working with nearly harmonic circuits instead of qubits. This architecture, or modifications of it, can be used to emulate molecular processes such as vibronic transitions. Furthermore, we discuss several aspects of these emulations, such as dynamical ranges of the physical parameters, quenching times necessary for diabaticity, and, finally, the possibility of implementing anharmonic corrections to the force fields by exploiting certain nonlinear features of superconducting devices., This work has been supported by MINECO/FEDER Project No. FIS2015-70856-P and CAM PRICYT Research Network QUITEMAD+ S2013/ICE-2801. D. G. O. acknowledges support from MINECO through FPI Grant No. BES-2013-066486. B. P. acknowledges the Air Force of Scientific Research for support under Grant No. FA9550-12-1-0046. J. H. acknowledges support from the Basic Science Research Program through the National Research Foundation of Korea (Grant No. NRF- 2015R1A6A3A04059773) and the Mueunjae Institute for Chemistry (MIC) postdoctoral fellowship.

8 pags., 2 figs., -- Open Access funded by Creative Commons Atribution Licence 4.0, We show that the Dynamical Casimir Effect (DCE), realized on two multimode coplanar waveg-uide resonators, implements a gaussian boson sampler (GBS). The appropriate choice of the mirror acceleration that couples both resonators translates into the desired initial gaussian state and many-boson interference in a boson sampling network. In particular, we show that the proposed quantum simulator naturally performs a classically hard task, known as scattershot boson sampling. Our result unveils an unprecedented computational power of DCE, and paves the way for using DCE as a resource for quantum simulation., B.P. acknowledges the Air Force of Scientific Research for support under award: FA9550-12-1-0046. C.S. acknowledges financial support from Fundación General CSIC (Programa ComFuturo). J. H. acknowledges supports by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2015R1A6A3A04059773.

Molecular vibroic spectroscopy, where the transitions involve non-trivial Bosonic correlation due to the Duschinsky Rotation, is strongly believed to be in a similar complexity class as Boson Sampling. At finite temperature, the problem is represented as a Boson Sampling experiment with correlated Gaussian input states. This molecular problem with temperature effect is intimately related to the various versions of Boson Sampling sharing the similar computational complexity. Here we provide a full description to this relation in the context of Gaussian Boson Sampling. We find a hierarchical structure, which illustrates the relationship among various Boson Sampling schemes. Specifically, we show that every instance of Gaussian Boson Sampling with an initial correlation can be simulated by an instance of Gaussian Boson Sampling without initial correlation, with only a polynomial overhead. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling associated with a product of vacuum modes. We refer such a generalized Gaussian Boson Sampling motivated by the molecular sampling problem as Vibronic Boson Sampling.

Boson sampling (BS) is a multimode linear optical problem that is expected to be intractable on classical computers. It was recently suggested that molecular vibronic spectroscopy (MVS) is computationally as complex as BS. In this review, we discuss the correspondence relation between BS and MVS and briefly introduce the experimental demonstrations of the molecular spectroscopic process using quantum devices. The similarity of the two theories results in another BS setup, which is called "vibronic BS". The hierarchical structure of vibronic BS, which includes the original BS and other Gaussian BS, is also explained.

Quantum computers are expected to be more efficient in performing certain computations than any classical machine. Unfortunately, the technological challenges associated with building a full-scale quantum computer have not yet allowed the experimental verification of such an expectation. Recently, boson sampling has emerged as a problem that is suspected to be intractable on any classical computer, but efficiently implementable with a linear quantum optical setup. Therefore, boson sampling may offer an experimentally realizable challenge to the Extended Church-Turing thesis and this remarkable possibility motivated much of the interest around boson sampling, at least in relation to complexity-theoretic questions. In this work, we show that the successful development of a boson sampling apparatus would not only answer such inquiries, but also yield a practical tool for difficult molecular computations. Specifically, we show that a boson sampling device with a modified input state can be used to generate molecular vibronic spectra, including complicated effects such as Duschinsky rotations., 10 pages, 6 figures

Environmentally induced fluctuations of the optical gap play a crucial role in electronic energy transfer dynamics. One of the simplest approaches to incorporate such fluctuations in energy transfer dynamics is the well known Haken-Strobl-Reineker (HSR) model, in which the energy-gap fluctuation is approximated as white noise. Recently, several groups have employed molecular dynamics simulations and excited-state calculations in conjunction to account for excitation energies' thermal fluctuations. On the other hand, since the original work of HSR, many groups have employed stochastic models to simulate the same transfer dynamics. Here, we discuss a rigorous connection between the stochastic and the atomistic bath models. If the phonon bath is treated classically, time evolution of the exciton-phonon system can be described by Ehrenfest dynamics. To establish the relationship between the stochastic and atomistic bath models, we employ a projection operator technique to derive the generalized Langevin equations for the energy-gap fluctuations. The stochastic bath model can be obtained as an approximation of the atomistic Ehrenfest equations via the generalized Langevin approach. Based on this connection, we propose a novel scheme to take account of reorganization effects within the framework of stochastic models. The proposed scheme provides a better description of the population dynamics especially in the regime of strong exciton-phonon coupling. Finally, we discuss the effect of the bath reorganization in the absorption and fluorescence spectra of ideal J-aggregates in terms of the Stokes shifts. We find a simple expression that relates the reorganization contribution to the Stokes shifts - the reorganization shift - to the ideal or non-ideal exciton delocalization in a J-aggregate. The reorganization shift can be described by three parameters: the monomer reorganization energy, the relaxation time of the optical gap, and the exciton delocalization length. This simple relationship allows one to understand the physical origin of the Stokes shifts in molecular aggregates.

Living organisms have to adjust to their surrounding in order to survive in stressful conditions. We study this mechanism in one of most primitive creatures - photosynthetic green sulfur bacteria. These bacteria absorb photons very efficiently using the chlorosome antenna complexes and perform photosynthesis in extreme low-light environments. How the chlorosomes in green sulfur bacteria are acclimated to the stressful light conditions, for instance, if the spectrum of light is not optimal for absorption, is unknown. Studying Chlorobaculum tepidum cultures with far-red to near-infrared light-emitting diodes, we found that these bacteria react to changes in energy flow by regulating the amount of light-absorbing pigments and the size of the chlorosomes. Surprisingly, our results indicate that the bacteria can survive in near-infrared lights capturing low-frequency photons by the intermediate units of the light-harvesting complex. The latter strategy may be used by the species recently found near hydrothermal vents in the Pacific Ocean., Comment: 17 pages including SI

In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly-coupled multiple parallel chains. The transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics., Comment: 9 pages, 6 figures

Phototrophic organisms such as plants, photosynthetic bacteria and algae use microscopic complexes of pigment molecules to absorb sunlight. Within the light-harvesting complexes, which frequently have several functional and structural subunits, the energy is transferred in the form of molecular excitations with very high efficiency. Green sulfur bacteria are considered to be amongst the most efficient light-harvesting organisms. Despite multiple experimental and theoretical studies of these bacteria the physical origin of the efficient and robust energy transfer in their light-harvesting complexes is not well understood. To study excitation dynamics at the systems level we introduce an atomistic model that mimics a complete light-harvesting apparatus of green sulfur bacteria. The model contains approximately 4000 pigment molecules and comprises a double wall roll for the chlorosome, a baseplate and six Fenna-Matthews-Olson trimer complexes. We show that the fast relaxation within functional subunits combined with the transfer between collective excited states of pigments can result in robust energy funneling. Energy transfer is robust on the initial excitation conditions and temperature changes. Moreover, the same mechanism describes the coexistence of multiple timescales of excitation dynamics frequently observed in ultrafast optical experiments. While our findings support the hypothesis of supertransfer, the model reveals energy transport through multiple channels on different length scales., Comment: 15 pages, 14 figures

When existing, cumulants can provide valuable information about a given distribution and can in principle be used to either fully reconstruct or approximate the parent distribution function. A previously reported cumulant expansion approach for Franck-Condon profiles [Faraday Discuss., 150, 363 (2011)] is extended to describe also the profiles of vibronic transitions that are weakly allowed or forbidden in the Franck-Condon approximation (non-Condon profiles). In the harmonic approximation the cumulants of the vibronic spectral profile can be evaluated analytically and numerically with a coherent state-based generating function that accounts for the Duschinsky effect. As illustration, the one-photon $1 ^{1}\mathrm{A_{g}}\rightarrow1 ^{1}\mathrm{B_{2u}}$ UV absorption spectrum of benzene in the electric dipole and (linear) Herzberg-Teller approximation is presented herein for zero Kelvin and finite temperatures., Comment: 7 pages, 1 figure; complexity discussed, method section significantly extended, computational details added, technical details explained, additional references included

Green photosynthetic bacteria adjust the structure and functionality of the chlorosome - the light absorbing antenna complex - in response to environmental stress factors. The chlorosome is a natural self-assembled aggregate of bacteriochlorophyll (BChl) molecules. In this study we report the regulation of the biogenesis of the Chlorobaculum tepidum chlorosome by carbon assimilation in conjunction with temperature changes. Our studies indicate that the carbon source and thermal stress culture of Cba. tepidum grows slower and incorporates less BChl c in the chlorosome. Compared with the chlorosome from other cultural conditions we investigated, the chlorosome from the carbon source and thermal stress culture displays: (a) smaller cross-sectional radius and overall size; (b) simplified BChl c homologues with smaller side chains; (c) blue-shifted Qy absorption maxima and (d) a sigmoid-shaped circular dichroism (CD) spectra. Using a theoretical model we analyze how the observed spectral modifications can be associated with structural changes of BChl aggregates inside the chlorosome. Our report suggests a mechanism of metabolic regulation for chlorosome biogenesis., 32 pages, 14 figures