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Comment on “Orientation dependence of the optical spectra in graphene at high frequencies”




Zhang et al. [Phys. Rev. B 77, 241402(R) (2008)] reported a theoretical study of the optical spectra of monolayer graphene employing the Kubo formula within a tight-binding model. Their calculations predicted that at high frequencies the optical conductivity of graphene becomes strongly anisotropic. In particular, at frequencies comparable to the energy separation of the upper and lower bands at the


point, the optical conductivity is strongly suppressed if the field polarization is along the zigzag direction whereas it is significantly high for the armchair one. We find that, unfortunately, this result is just a consequence of the incorrect determination of the current operator in


space. Here, we present a standard scheme to obtain this operator correctly. As a result, we show that the optical conductivity of monolayer graphene is indeed isotropic, which is consistent with the results of other (both theoretical and experimental) studies in the literature.

  • Received 31 May 2016


©2016 American Physical Society

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  1. Physical Systems
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Condensed Matter & Materials Physics



Probing nonclassicality with matrices of phase-space distributions




Martin Bohmann1,2, Elizabeth Agudelo1, and Jan Sperling3

1Institute for Quantum Optics and Quantum Information – IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
2QSTAR, INO-CNR, and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
3Integrated Quantum Optics Group, Applied Physics, Paderborn University, 33098 Paderborn, Germany

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We devise a method to certify nonclassical features via correlations of phase-space distributions by unifying the notions of quasiprobabilities and matrices of correlation functions. Our approach complements and extends recent results that were based on Chebyshev’s integral inequality [65]. The method developed here correlates arbitrary phase-space functions at arbitrary points in phase space, including multimode scenarios and higher-order correlations. Furthermore, our approach provides necessary and sufficient nonclassicality criteria, applies to phase-space functions beyond $s$-parametrized ones, and is accessible in experiments. To demonstrate the power of our technique, the quantum characteristics of discrete- and continuous-variable, single- and multimode, as well as pure and mixed states are certified only employing second-order correlations and Husimi functions, which always resemble a classical probability distribution. Moreover, nonlinear generalizations of our approach are studied. Therefore, a versatile and broadly applicable framework is devised to uncover quantum properties in terms of matrices of phase-space distributions.

The intuitively accessible representation of quantum effects via quasiprobabilities, defying the nonnegativity requirement of classical probabilities, is a common technique to identify quantum features. However, the complexity of the reconstruction of such distributions increases with their sensitivity to uncover nonclassical signatures. Conversely, approaches based on correlation functions are experimentally available but less intuitive.

The method devised in our paper overcomes such disadvantageous features by unifying both aforementioned techniques. That is, quasiprobabilities can be correlated to unveil nonclassical properties even if the individual distributions are not sensitive enough to identify quantum properties. For example, it is shown that this necessary and sufficient approach applies to discrete- and continuous-variable, single- and multimode, pure and mixed states of light using phase-space distributions that can never become negative.

Thereby, we demonstrate the usefulness of our novel method to certify quantum characteristics in a practical manner that formthe basis for current and future quantum technologies.

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► References

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Cited by

[1] Jiyong Park, Jaehak Lee, and Hyunchul Nha, “Verifying nonclassicality beyond negativity in phase space”, arXiv:2005.05739.

[2] Nicola Biagi, Martin Bohmann, Elizabeth Agudelo, Marco Bellini, and Alessandro Zavatta, “Experimental certification of nonclassicality via phase-space inequalities”, arXiv:2010.00259.

The above citations are from SAO/NASA ADS (last updated successfully 2020-10-16 02:17:01). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2020-10-16 02:16:59).


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A quantum extension of SVM-perf for training nonlinear SVMs in almost linear time




Jonathan Allcock and Chang-Yu Hsieh

Tencent Quantum Laboratory

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We propose a quantum algorithm for training nonlinear support vector machines (SVM) for feature space learning where classical input data is encoded in the amplitudes of quantum states. Based on the classical SVM-perf algorithm of Joachims [1], our algorithm has a running time which scales linearly in the number of training examples $m$ (up to polylogarithmic factors) and applies to the standard soft-margin $ell_1$-SVM model. In contrast, while classical SVM-perf has demonstrated impressive performance on both linear and nonlinear SVMs, its efficiency is guaranteed only in certain cases: it achieves linear $m$ scaling only for linear SVMs, where classification is performed in the original input data space, or for the special cases of low-rank or shift-invariant kernels. Similarly, previously proposed quantum algorithms either have super-linear scaling in $m$, or else apply to different SVM models such as the hard-margin or least squares $ell_2$-SVM which lack certain desirable properties of the soft-margin $ell_1$-SVM model. We classically simulate our algorithm and give evidence that it can perform well in practice, and not only for asymptotically large data sets.

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Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design




Xiu-Zhe Luo1,2,3,4, Jin-Guo Liu1, Pan Zhang2, and Lei Wang1,5

1Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
3Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada
4Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
5Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

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We introduce $texttt{Yao}$, an extensible, efficient open-source framework for quantum algorithm design. $texttt{Yao}$ features generic and differentiable programming of quantum circuits. It achieves state-of-the-art performance in simulating small to intermediate-sized quantum circuits that are relevant to near-term applications. We introduce the design principles and critical techniques behind $texttt{Yao}$. These include the quantum block intermediate representation of quantum circuits, a builtin automatic differentiation engine optimized for reversible computing, and batched quantum registers with GPU acceleration. The extensibility and efficiency of $texttt{Yao}$ help boost innovation in quantum algorithm design.

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[5] Tong Liu, Jin-Guo Liu, and Heng Fan, “Probabilistic Nonunitary Gate in Imaginary Time Evolution”, arXiv:2006.09726.

[6] Jin-Guo Liu, Lei Wang, and Pan Zhang, “Tropical Tensor Network for Ground States of Spin Glasses”, arXiv:2008.06888.

[7] Jin-Guo Liu and Taine Zhao, “Differentiate Everything with a Reversible Domain-Specific Language”, arXiv:2003.04617.

[8] Carsten Bauer, “Fast and stable determinant quantum Monte Carlo”, arXiv:2003.05286.

[9] Chen Zhao and Xiao-Shan Gao, “QDNN: DNN with Quantum Neural Network Layers”, arXiv:1912.12660.

[10] The Quingo Development Team, “Quingo: A Programming Framework for Heterogeneous Quantum-Classical Computing with NISQ Features”, arXiv:2009.01686.

[11] Andrea Mari, Thomas R. Bromley, and Nathan Killoran, “Estimating the gradient and higher-order derivatives on quantum hardware”, arXiv:2008.06517.

[12] Stavros Efthymiou, Sergi Ramos-Calderer, Carlos Bravo-Prieto, Adrián Pérez-Salinas, Diego García-Martín, Artur Garcia-Saez, José Ignacio Latorre, and Stefano Carrazza, “Qibo: a framework for quantum simulation with hardware acceleration”, arXiv:2009.01845.

[13] Vincent Paul Su, “Variational Preparation of the Sachdev-Ye-Kitaev Thermofield Double”, arXiv:2009.04488.

The above citations are from SAO/NASA ADS (last updated successfully 2020-10-16 04:52:30). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2020-10-16 04:52:29).


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