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The quantum computation of electronic energies can break the curse of dimensionality that plagues many-particle quantum mechanics. It is for this reason that a universal quantum computer has the potential to fundamentally change computational chemistry and materials science, areas in which strong electron correlations present severe hurdles for traditional electronic structure methods. Here we present a state-of-the-art analysis of accurate energy measurements on a quantum computer for computational catalysis, using improved quantum algorithms with more than an order of magnitude improvement over the best previous algorithms. As a prototypical example of local catalytic chemical reactivity we consider the case of a ruthenium catalyst that can bind, activate, and transform carbon dioxide to the high-value chemical methanol. We aim at accurate resource estimates for the quantum computing steps required for assessing the electronic energy of key intermediates and transition states of its catalytic cycle. In particular, we present quantum algorithms for double-factorized representations of the four-index integrals that can significantly reduce the computational cost over previous algorithms, and we discuss the challenges of increasing active space sizes to accurately deal with dynamical correlations. We address the requirements for future quantum hardware in order to make a universal quantum computer a successful and reliable tool for quantum computing enhanced computational materials science and chemistry, and identify open questions for further research.
Vera von Burg; Guang Hao Low; Thomas Häner; Damian S. Steiger; Markus Reiher; Martin Roetteler; Matthias Troyer. Quantum computing enhanced computational catalysis. Physical Review Research 2021, 3, 033055 .
AMA StyleVera von Burg, Guang Hao Low, Thomas Häner, Damian S. Steiger, Markus Reiher, Martin Roetteler, Matthias Troyer. Quantum computing enhanced computational catalysis. Physical Review Research. 2021; 3 (3):033055.
Chicago/Turabian StyleVera von Burg; Guang Hao Low; Thomas Häner; Damian S. Steiger; Markus Reiher; Martin Roetteler; Matthias Troyer. 2021. "Quantum computing enhanced computational catalysis." Physical Review Research 3, no. 3: 033055.
Underwater photogrammetry is increasingly being used by marine ecologists because of its ability to produce accurate, spatially detailed, non-destructive measurements of benthic communities, coupled with affordability and ease of use. However, independent quality control, rigorous imaging system set-up, optimal geometry design and a strict modeling of the imaging process are essential to achieving a high degree of measurable accuracy and resolution. If a proper photogrammetric approach that enables the formal description of the propagation of measurement error and modeling uncertainties is not undertaken, statements regarding the statistical significance of the results are limited. In this paper, we tackle these critical topics, based on the experience gained in the Moorea Island Digital Ecosystem Avatar (IDEA) project, where we have developed a rigorous underwater photogrammetric pipeline for coral reef monitoring and change detection. Here, we discuss the need for a permanent, underwater geodetic network, which serves to define a temporally stable reference datum and a check for the time series of photogrammetrically derived three-dimensional (3D) models of the reef structure. We present a methodology to evaluate the suitability of several underwater camera systems for photogrammetric and multi-temporal monitoring purposes and stress the importance of camera network geometry to minimize the deformations of photogrammetrically derived 3D reef models. Finally, we incorporate the measurement and modeling uncertainties of the full photogrammetric process into a simple and flexible framework for detecting statistically significant changes among a time series of models.
Erica Nocerino; Fabio Menna; Armin Gruen; Matthias Troyer; Alessandro Capra; Cristina Castagnetti; Paolo Rossi; Andrew Brooks; Russell Schmitt; Sally Holbrook. Coral Reef Monitoring by Scuba Divers Using Underwater Photogrammetry and Geodetic Surveying. Remote Sensing 2020, 12, 3036 .
AMA StyleErica Nocerino, Fabio Menna, Armin Gruen, Matthias Troyer, Alessandro Capra, Cristina Castagnetti, Paolo Rossi, Andrew Brooks, Russell Schmitt, Sally Holbrook. Coral Reef Monitoring by Scuba Divers Using Underwater Photogrammetry and Geodetic Surveying. Remote Sensing. 2020; 12 (18):3036.
Chicago/Turabian StyleErica Nocerino; Fabio Menna; Armin Gruen; Matthias Troyer; Alessandro Capra; Cristina Castagnetti; Paolo Rossi; Andrew Brooks; Russell Schmitt; Sally Holbrook. 2020. "Coral Reef Monitoring by Scuba Divers Using Underwater Photogrammetry and Geodetic Surveying." Remote Sensing 12, no. 18: 3036.
The manuscript "A Comparison of Quantum and Traditional Fourier Transform Computations" discusses a very important and often overlooked aspect of quantum computing, namely a fair and detailed comparison of a quantum algorithm, its classical simulation, and its classical counterpart taking into account the complexity of I/O. Such an article is valuable and worth publishing. The current manuscript, however, still contains some inaccuracies that should be fixed and I will make suggestion on how the presentation can be improved.Let me first summarize the main result in my own words: a quantum Fourier transform (QFT) can calculate the Fourier transform of a vector with time complexity \(O\left(\log^2N\right)\), compared to the complexity \(O\left(N\log N\right)\) of a classical FFT. However, if one needs to read out the full vector instead, the complexity becomes \(O\left(N \text{ polylog}(N) \right)\) again, without an advantage over the classical algorithm. It is actually worse than the author discusses, if one also takes into account the complexity of loading the initial state. Loading an initial classical data vector has complexity \(O\left(N\right)\), and this has to be repeated at every repetition, giving a complexity of \(O\left(N^2\ \text{polylog}\ N\right)\), worse than classical. As the author correctly mentions, the QFT is thus a useful algorithm if the input data is prepared algorithmically, and limited sampling of the result vector is sufficient, as is the case for Shor's algorithm.This is a valuable observation that deserves a paper in CiSE, since these important considerations are not all known to people outside the quantum computing community, and are sometimes ignored even by quantum computing specialists. I thus want to encourage the author to improve the presentation to make it more accessible to a broader audience and fix a couple of technical flaws.Before discussing presentation issues, I want to address one technical flaw and a few points where more clarity is needed: This statement towards the end is too simplistic and needs to be clarified: "... if we want to measure each coefficient, we must redo our operations for each coefficient (since our wave function will collapse for every measurement)." The manuscript does not explain how to read out a specific coefficient. If one samples the wave function, one measures the result and gets a certain value \((s_1, \cdots,\ s_N)\) with a probability depending on the wave function. More complex amplitude-estimation algorithms are needed to read out specific coefficients, which then takes time \(O(N/\epsilon)\). This needs to be better explained. This also raises another issue of normalization and precision. The quantum wave function has to be normalized to have an \(L_2\) norm of \(1\). We thus need to measure to a precision of epsilon divided by the \(L_2\) norm of the classical data, and if that increases with \(N\) the scaling is even worse. For example, if all entries are of order unity, the \(L_2\) norm is \(\sqrt{N}\). The one technical flaw in the paper is in preparing the input state to the QFT, and the complexity of the classical simulation of the quantum algorithm. There, the numbers are wrong. The classical complexity can easily be estimated by realizing that any sparse quantum gate (such as a 1-qubit or 1-qubit gate) can be simulated in time \(O(N)=O(2^n)\), where \(N=2^n\). Thus, the overhead is just \(O(N)\), not \(O(N^2)\), and the simulation complexity is just \(O(N)\) times the complexity of the quantum algorithm. This will be more apparent if, as I propose below, the author shows the quantum algorithm also through a sequence of quantum gates. However, note that in the simulation we then have the full vector, and thus do not incur the overhead of quantum state tomography. We need to simulate the algorithm only once and not \(O(N/\epsilon)\) times. This means the simulation remains at \(O(N\ \log^2{N})\) even if we read out all entries, which is not bad compared to the classical \(O(N\ \log{N})\) of the FFT. The reason why the author seems to end with a different complexity is that his Matlab simulation does not simulate the quantum algorithm but the computation of the effect of the QFT applied to just one basis state. That is a suboptimal implementation. I thus propose to replace the Matlab code by a discussion of how a quantum gate (Hadamard or controlled phase rotation) can be implemented, and that will then nicely give the scaling discussed above.As mentioned in my summary at the beginning, the value of the paper can be increased if the author could also discuss the complexity of quantum state preparation from classical input data, e.g., following Shende-Bullock-Markov \citep{markov2006}, which has a complexity of \(O\left(N\ \log\ \frac{1}{\epsilon}\right)\). That means, that if the data is read from a classical vector (and not computed as, e.g., in Shor's algorithm), then the complexity of state preparation of \(O\left(N\ \log\ \frac{1}{\epsilon}\right)\) completely dominates the QFT itself, and if one furthermore wants to read out the full vector instead of sampling it, the complexity becomes \(O\left(N^2\log^2\left(\frac{1}{\epsilon}\right)\right)\).In the conclusion the author writes that "QEC research is still in very early development and it is currently difficult to determine how the required resources for these corrections could scale with qubit usage." That is incorrect, as the overhead is pretty well known by now for certain QEC codes, such as the surface code. The asymptotic scaling of the overhead has long been known, and also detailed resource costs have been worked out for various algorithms. I suggest to focus the QEC section on the need for fault tolerance, and the large overhead associated with it. This is definitely not something that can be done on NISQ devices at an interesting scale. I would also use another reference for QEC than the Gil Kalai paper.Now, to suggestions for improved...
Matthias Troyer. Review: "A Comparison of Quantum and Traditional Fourier Transform Computations". 2020, 1 .
AMA StyleMatthias Troyer. Review: "A Comparison of Quantum and Traditional Fourier Transform Computations". . 2020; ():1.
Chicago/Turabian StyleMatthias Troyer. 2020. "Review: "A Comparison of Quantum and Traditional Fourier Transform Computations"." , no. : 1.
In this paper, we discuss the extension of the recently introduced subsystem embedding subalgebra coupled cluster (SES-CC) formalism to unitary CC formalisms. In analogy to the standard single-reference SES-CC formalism, its unitary CC extension allows one to include the dynamical (outside the active space) correlation effects in an SES induced complete active space (CAS) effective Hamiltonian. In contrast to the standard single-reference SES-CC theory, the unitary CC approach results in a Hermitian form of the effective Hamiltonian. Additionally, for the double unitary CC (DUCC) formalism, the corresponding CAS eigenvalue problem provides a rigorous separation of external cluster amplitudes that describe dynamical correlation effects—used to define the effective Hamiltonian—from those corresponding to the internal (inside the active space) excitations that define the components of eigenvectors associated with the energy of the entire system. The proposed formalism can be viewed as an efficient way of downfolding many-electron Hamiltonian to the low-energy model represented by a particular choice of CAS. In principle, this technique can be extended to any type of CAS representing an arbitrary energy window of a quantum system. The Hermitian character of low-dimensional effective Hamiltonians makes them an ideal target for several types of full configuration interaction type eigensolvers. As an example, we also discuss the algebraic form of the perturbative expansions of the effective DUCC Hamiltonians corresponding to composite unitary CC theories and discuss possible algorithms for hybrid classical and quantum computing. Given growing interest in quantum computing, we provide energies for H2 and Be systems obtained with the quantum phase estimator algorithm available in the Quantum Development Kit for the approximate DUCC Hamiltonians.
Nicholas P. Bauman; Eric J. Bylaska; Sriram Krishnamoorthy; Guang Hao Low; Nathan Wiebe; Christopher E. Granade; Martin Roetteler; Matthias Troyer; Karol Kowalski. Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms. The Journal of Chemical Physics 2019, 151, 014107 .
AMA StyleNicholas P. Bauman, Eric J. Bylaska, Sriram Krishnamoorthy, Guang Hao Low, Nathan Wiebe, Christopher E. Granade, Martin Roetteler, Matthias Troyer, Karol Kowalski. Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms. The Journal of Chemical Physics. 2019; 151 (1):014107.
Chicago/Turabian StyleNicholas P. Bauman; Eric J. Bylaska; Sriram Krishnamoorthy; Guang Hao Low; Nathan Wiebe; Christopher E. Granade; Martin Roetteler; Matthias Troyer; Karol Kowalski. 2019. "Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms." The Journal of Chemical Physics 151, no. 1: 014107.
Wannier tight-binding models are effective models constructed from first-principles calculations. As such, they bridge a gap between the accuracy of first-principles calculations and the computational simplicity of effective models. In this work, we extend the existing methodology of creating Wannier tight-binding models from first-principles calculations by introducing the symmetrization post-processing step, which enables the production of Wannier-like models that respect the symmetries of the considered crystal. Furthermore, we implement automatic workflows, which allow for producing a large number of tight-binding models for large classes of chemically and structurally similar compounds or materials subject to external influence such as strain. As a particular illustration, these workflows are applied to strained III-V semiconductor materials. These results can be used for further study of topological phase transitions in III-V quantum wells.
Dominik Gresch; Quansheng Wu; Georg W. Winkler; Rico Häuselmann; Matthias Troyer; Alexey A. Soluyanov. Automated construction of symmetrized Wannier-like tight-binding models from ab initio calculations. Physical Review Materials 2018, 2, 103805 .
AMA StyleDominik Gresch, Quansheng Wu, Georg W. Winkler, Rico Häuselmann, Matthias Troyer, Alexey A. Soluyanov. Automated construction of symmetrized Wannier-like tight-binding models from ab initio calculations. Physical Review Materials. 2018; 2 (10):103805.
Chicago/Turabian StyleDominik Gresch; Quansheng Wu; Georg W. Winkler; Rico Häuselmann; Matthias Troyer; Alexey A. Soluyanov. 2018. "Automated construction of symmetrized Wannier-like tight-binding models from ab initio calculations." Physical Review Materials 2, no. 10: 103805.
A programmable array of superconducting quantum bits can simulate phase transitions in quantum systems, a step towards the study of exotic physics that is difficult or inefficient to model using ordinary computers. Programmable quantum simulation based on superconducting qubits.
Matthias Troyer. Topological phenomena explored in a programmable quantum simulation. Nature 2018, 560, 438 -439.
AMA StyleMatthias Troyer. Topological phenomena explored in a programmable quantum simulation. Nature. 2018; 560 (7719):438-439.
Chicago/Turabian StyleMatthias Troyer. 2018. "Topological phenomena explored in a programmable quantum simulation." Nature 560, no. 7719: 438-439.
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework into the particle-hole picture, which offers a better starting point for the expansion of the system wave function. The state of the molecular system at study is parametrized so as to constrain the sampling of the corresponding wave function within the sector of the molecular Fock space that contains the desired solution. To this end, we explore different mapping schemes to encode the molecular ground state wave function in a quantum register. Taking advantage of known post-Hartree-Fock quantum chemistry approaches and heuristic Hilbert space search quantum algorithms, we propose a new family of quantum circuits based on exchange-type gates that enable accurate calculations while keeping the gate count (i.e., the circuit depth) low. The particle-hole implementation of the unitary coupled-cluster (UCC) method within the variational quantum eigensolver approach gives rise to an efficient quantum algorithm, named q-UCC, with important advantages compared to the straightforward translation of the classical coupled-cluster counterpart. In particular, we show how a single Trotter step in the expansion of the system wave function can accurately and efficiently reproduce the ground-state energy of simple molecular systems.
Panagiotis Kl. Barkoutsos; Jerome F. Gonthier; Igor Sokolov; Nikolaj Moll; Gian Salis; Andreas Fuhrer; Marc Ganzhorn; Daniel J. Egger; Matthias Troyer; Antonio Mezzacapo; Stefan Filipp; Ivano Tavernelli. Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions. Physical Review A 2018, 98, 022322 .
AMA StylePanagiotis Kl. Barkoutsos, Jerome F. Gonthier, Igor Sokolov, Nikolaj Moll, Gian Salis, Andreas Fuhrer, Marc Ganzhorn, Daniel J. Egger, Matthias Troyer, Antonio Mezzacapo, Stefan Filipp, Ivano Tavernelli. Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions. Physical Review A. 2018; 98 (2):022322.
Chicago/Turabian StylePanagiotis Kl. Barkoutsos; Jerome F. Gonthier; Igor Sokolov; Nikolaj Moll; Gian Salis; Andreas Fuhrer; Marc Ganzhorn; Daniel J. Egger; Matthias Troyer; Antonio Mezzacapo; Stefan Filipp; Ivano Tavernelli. 2018. "Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions." Physical Review A 98, no. 2: 022322.
Antoine Collin; Camille Ramambason; Yves Pastol; Elisa Casella; Alessio Rovere; Lauric Thiault; Benoît Espiau; Gilles Siu; Franck Lerouvreur; Nao Nakamura; James L. Hench; Russell J. Schmitt; Sally J. Holbrook; Matthias Troyer; Neil Davies. Very high resolution mapping of coral reef state using airborne bathymetric LiDAR surface-intensity and drone imagery. International Journal of Remote Sensing 2018, 39, 5676 -5688.
AMA StyleAntoine Collin, Camille Ramambason, Yves Pastol, Elisa Casella, Alessio Rovere, Lauric Thiault, Benoît Espiau, Gilles Siu, Franck Lerouvreur, Nao Nakamura, James L. Hench, Russell J. Schmitt, Sally J. Holbrook, Matthias Troyer, Neil Davies. Very high resolution mapping of coral reef state using airborne bathymetric LiDAR surface-intensity and drone imagery. International Journal of Remote Sensing. 2018; 39 (17):5676-5688.
Chicago/Turabian StyleAntoine Collin; Camille Ramambason; Yves Pastol; Elisa Casella; Alessio Rovere; Lauric Thiault; Benoît Espiau; Gilles Siu; Franck Lerouvreur; Nao Nakamura; James L. Hench; Russell J. Schmitt; Sally J. Holbrook; Matthias Troyer; Neil Davies. 2018. "Very high resolution mapping of coral reef state using airborne bathymetric LiDAR surface-intensity and drone imagery." International Journal of Remote Sensing 39, no. 17: 5676-5688.
We present two techniques that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations. The first technique realizes that to prepare the ground state of some Hamiltonian, it is not necessary to implement the time-evolution operator: any unitary operator which is a function of the Hamiltonian will do. We propose one such unitary operator which can be implemented exactly, circumventing any Taylor or Trotter approximation errors. The second technique is tailored to lattice models, and is targeted at reducing the use of generic single-qubit rotations, which are very expensive to produce by standard fault tolerant techniques. In particular, the number of generic single-qubit rotations used by our method scales with the number of parameters in the Hamiltonian, which contrasts with a growth proportional to the lattice size required by other techniques.
David Poulin; Alexei Kitaev; Damian S. Steiger; Matthew B. Hastings; Matthias Troyer. Quantum Algorithm for Spectral Measurement with a Lower Gate Count. Physical Review Letters 2018, 121, 010501 .
AMA StyleDavid Poulin, Alexei Kitaev, Damian S. Steiger, Matthew B. Hastings, Matthias Troyer. Quantum Algorithm for Spectral Measurement with a Lower Gate Count. Physical Review Letters. 2018; 121 (1):010501.
Chicago/Turabian StyleDavid Poulin; Alexei Kitaev; Damian S. Steiger; Matthew B. Hastings; Matthias Troyer. 2018. "Quantum Algorithm for Spectral Measurement with a Lower Gate Count." Physical Review Letters 121, no. 1: 010501.
We benchmark the ground state energies and the density profiles of atomic repulsive Fermi gases in optical lattices (OLs) computed via density functional theory (DFT) against the results of diffusion Monte Carlo (DMC) simulations. The main focus is on a half-filled one-dimensional OLs, for which the DMC simulations performed within the fixed-node approach provide unbiased results. This allows us to demonstrate that the local spin-density approximation (LSDA) to the exchange-correlation functional of DFT is very accurate in the weak and intermediate interactions regime, and also to underline its limitations close to the strongly-interacting Tonks–Girardeau limit and in very deep OLs. We also consider a three-dimensional OL at quarter filling, showing also in this case the high accuracy of the LSDA in the moderate interaction regime. The one-dimensional data provided in this study may represent a useful benchmark to further develop DFT methods beyond the LSDA and they will hopefully motivate experimental studies to accurately measure the equation of state of Fermi gases in higher-dimensional geometries.
Sebastiano Pilati; Ilia Zintchenko; Matthias Troyer; Francesco Ancilotto. Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena. The European Physical Journal B 2018, 91, 70 .
AMA StyleSebastiano Pilati, Ilia Zintchenko, Matthias Troyer, Francesco Ancilotto. Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena. The European Physical Journal B. 2018; 91 (4):70.
Chicago/Turabian StyleSebastiano Pilati; Ilia Zintchenko; Matthias Troyer; Francesco Ancilotto. 2018. "Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena." The European Physical Journal B 91, no. 4: 70.
Worldwide the coastal land-sea interface is increasingly subject to natural and anthropogenic hazards. Monitoring this crucial interface may be addressed with satellite imagery as a cost-efficient mapping solution. Topography and bathymetry, defining the structural complexity of the coast, are commonly studied separately given specific thematic and methodological contexts, yet many science questions and societal challenges require an integrated approach (e.g., coastal inundation). In such cases, triplet multispectral imagery represents an affordable solution based on a single satellite product. Here we examine how Pleiades-1 triplet imagery may be used to retrieve a seamless and accurate topobathymetry digital surface model (DSM, from −20 to 1207 m) over an entire, socio-ecologically complex island: Moorea, French Polynesia. Creation of the topography DSMs was based on stereo and tri-stereo photogrammetry, and the bathymetry DSMs relied on quasi-nadiral multispectral data subject to light/water interaction modelling. Results were compared with over 3.9 million airborne LiDAR topobathymetry measurements to quantify how the spatio-spectral mode, the third imagery, and the level of radiometric correction act on two- and three-dimensional accuracy. Horizontal accuracy of the tri-stereo panchromatic dataset (ERMSE = 4.22 and NRMSE = 7.59 m) was better than the multispectral (ERMSE = 5.06 and NRMSE = 7.51 m) dataset. Topography point cloud density increased by a factor of three in the tri-stereo panchromatic (9.11 points/m2) or multispectral (0.23 points/m2) datasets. Topography vertical accuracy enhanced with tri-stereo + level-1 radiometric correction (RMSE = 7.40 m) for panchromatic and with stereo + level-1/-2 radiometric correction (RMSE = 7.77/7.77 m) as well as tri-stereo without radiometric correction (RMSE = 7.85 m) for multispectral datasets. Bathymetry vertical accuracy improved with level-2 (atmospheric) correction (RMSE = 0.83 m). Topobathymetry DSM derived from this optimized method has a wide spectrum of applications along coastal margins.
Antoine Collin; James L. Hench; Yves Pastol; Serge Planes; Lauric Thiault; Russell J. Schmitt; Sally J. Holbrook; Neil Davies; Matthias Troyer. High resolution topobathymetry using a Pleiades-1 triplet: Moorea Island in 3D. Remote Sensing of Environment 2018, 208, 109 -119.
AMA StyleAntoine Collin, James L. Hench, Yves Pastol, Serge Planes, Lauric Thiault, Russell J. Schmitt, Sally J. Holbrook, Neil Davies, Matthias Troyer. High resolution topobathymetry using a Pleiades-1 triplet: Moorea Island in 3D. Remote Sensing of Environment. 2018; 208 ():109-119.
Chicago/Turabian StyleAntoine Collin; James L. Hench; Yves Pastol; Serge Planes; Lauric Thiault; Russell J. Schmitt; Sally J. Holbrook; Neil Davies; Matthias Troyer. 2018. "High resolution topobathymetry using a Pleiades-1 triplet: Moorea Island in 3D." Remote Sensing of Environment 208, no. : 109-119.
We present an open-source software package WannierTools, a tool for investigation of novel topological materials. This code works in the tight-binding framework, which can be generated by another software package Wannier90. It can help to classify the topological phase of given materials by calculating the Wilson loop and can get the surface state spectrum which is detected by angle-resolved photoemission (ARPES) and in scanning tunneling microscopy (STM) experiments. It also identifies positions of Weyl/Dirac points and nodal line structures, calculates the Berry phase around a closed momentum loop and Berry curvature in a part of the Brillouin zone.Comment: The supplementary files (WannierTools source and documentation) can be downloaded from https://github.com/quanshengwu/wannier_tool
Quansheng Wu; Shengnan Zhang; Hai-Feng Song; Matthias Troyer; Alexey Soluyanov. WannierTools: An open-source software package for novel topological materials. Computer Physics Communications 2018, 224, 405 -416.
AMA StyleQuansheng Wu, Shengnan Zhang, Hai-Feng Song, Matthias Troyer, Alexey Soluyanov. WannierTools: An open-source software package for novel topological materials. Computer Physics Communications. 2018; 224 ():405-416.
Chicago/Turabian StyleQuansheng Wu; Shengnan Zhang; Hai-Feng Song; Matthias Troyer; Alexey Soluyanov. 2018. "WannierTools: An open-source software package for novel topological materials." Computer Physics Communications 224, no. : 405-416.
The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods to validate and fully exploit quantum resources. Quantum state tomography (QST) aims to reconstruct the full quantum state from simple measurements, and therefore provides a key tool to obtain reliable analytics1,2,3. However, exact brute-force approaches to QST place a high demand on computational resources, making them unfeasible for anything except small systems4,5. Here we show how machine learning techniques can be used to perform QST of highly entangled states with more than a hundred qubits, to a high degree of accuracy. We demonstrate that machine learning allows one to reconstruct traditionally challenging many-body quantities—such as the entanglement entropy—from simple, experimentally accessible measurements. This approach can benefit existing and future generations of devices ranging from quantum computers to ultracold-atom quantum simulators6,7,8.
Giacomo Torlai; Guglielmo Mazzola; Juan Carrasquilla; Matthias Troyer; Roger Melko; Giuseppe Carleo. Neural-network quantum state tomography. Nature Physics 2018, 14, 447 -450.
AMA StyleGiacomo Torlai, Guglielmo Mazzola, Juan Carrasquilla, Matthias Troyer, Roger Melko, Giuseppe Carleo. Neural-network quantum state tomography. Nature Physics. 2018; 14 (5):447-450.
Chicago/Turabian StyleGiacomo Torlai; Guglielmo Mazzola; Juan Carrasquilla; Matthias Troyer; Roger Melko; Giuseppe Carleo. 2018. "Neural-network quantum state tomography." Nature Physics 14, no. 5: 447-450.
We introduce ProjectQ, an open source software effort for quantum computing. The first release features a compiler framework capable of targeting various types of hardware, a high-performance simulator with emulation capabilities, and compiler plug-ins for circuit drawing and resource estimation. We introduce our Python-embedded domain-specific language, present the features, and provide example implementations for quantum algorithms. The framework allows testing of quantum algorithms through simulation and enables running them on actual quantum hardware using a back-end connecting to the IBM Quantum Experience cloud service. Through extension mechanisms, users can provide back-ends to further quantum hardware, and scientists working on quantum compilation can provide plug-ins for additional compilation, optimization, gate synthesis, and layout strategies.
Damian S. Steiger; Thomas Häner; Matthias Troyer. ProjectQ: an open source software framework for quantum computing. Quantum 2018, 2, 49 .
AMA StyleDamian S. Steiger, Thomas Häner, Matthias Troyer. ProjectQ: an open source software framework for quantum computing. Quantum. 2018; 2 ():49.
Chicago/Turabian StyleDamian S. Steiger; Thomas Häner; Matthias Troyer. 2018. "ProjectQ: an open source software framework for quantum computing." Quantum 2, no. : 49.
Multiferroism can originate from the breaking of inversion symmetry caused by magnetic-spiral order. The usual mechanism for stabilizing a magnetic spiral is competition between magnetic exchange interactions differing by their range and sign, such as nearest-neighbor and next-nearest-neighbor interactions. In insulating compounds, it is unusual for these interactions to be both comparable in magnitude and of a strength that can induce magnetic ordering at room temperature. Therefore, the onset temperatures for multiferroism through this mechanism are typically low. By considering a realistic model for multiferroic YBaCuFeO5, we propose an alternative mechanism for magnetic-spiral order, and hence for multiferroism, that occurs at much higher temperatures. We show, using Monte Carlo simulations and electronic structure calculations based on density functional theory, that the Heisenberg model on a geometrically nonfrustrated lattice with only nearest-neighbor interactions can have a spiral phase up to high temperature when frustrating bonds are introduced randomly along a single crystallographic direction as caused, e.g., by a particular type of chemical disorder. This long-range correlated pattern of frustration avoids ferroelectrically inactive spin-glass order. Finally, we provide an intuitive explanation for this mechanism and discuss its generalization to other materials.
Andrea Scaramucci; Hiroshi Shinaoka; Maxim V. Mostovoy; Markus Müller; Christopher Mudry; Matthias Troyer; Nicola Spaldin. Multiferroic Magnetic Spirals Induced by Random Magnetic Exchanges. Physical Review X 2018, 8, 011005 .
AMA StyleAndrea Scaramucci, Hiroshi Shinaoka, Maxim V. Mostovoy, Markus Müller, Christopher Mudry, Matthias Troyer, Nicola Spaldin. Multiferroic Magnetic Spirals Induced by Random Magnetic Exchanges. Physical Review X. 2018; 8 (1):011005.
Chicago/Turabian StyleAndrea Scaramucci; Hiroshi Shinaoka; Maxim V. Mostovoy; Markus Müller; Christopher Mudry; Matthias Troyer; Nicola Spaldin. 2018. "Multiferroic Magnetic Spirals Induced by Random Magnetic Exchanges." Physical Review X 8, no. 1: 011005.
Quantum computers promise to transform our notions of computation by offering a completely new paradigm. To achieve scalable quantum computation, optimizing compilers and a corresponding software design flow will be essential. We present a software architecture for compiling quantum programs from a high-level language program to hardware-specific instructions. We describe the necessary layers of abstraction and their differences and similarities to classical layers of a computer-aided design flow. For each layer of the stack, we discuss the underlying methods for compilation and optimization. Our software methodology facilitates more rapid innovation among quantum algorithm designers, quantum hardware engineers, and experimentalists. It enables scalable compilation of complex quantum algorithms and can be targeted to any specific quantum hardware implementation.
Thomas Haener; Damian S Steiger; Krysta Svore; Matthias Troyer. A software methodology for compiling quantum programs. Quantum Science and Technology 2018, 3, 020501 .
AMA StyleThomas Haener, Damian S Steiger, Krysta Svore, Matthias Troyer. A software methodology for compiling quantum programs. Quantum Science and Technology. 2018; 3 (2):020501.
Chicago/Turabian StyleThomas Haener; Damian S Steiger; Krysta Svore; Matthias Troyer. 2018. "A software methodology for compiling quantum programs." Quantum Science and Technology 3, no. 2: 020501.
We present a quantum algorithm to compute the entanglement spectrum of arbitrary quantum states. The interesting universal part of the entanglement spectrum is typically contained in the largest eigenvalues of the density matrix which can be obtained from the lower Renyi entropies through the Newton-Girard method. Obtaining the p largest eigenvalues (λ1>λ2⋯>λp) requires a parallel circuit depth of O[p(λ1/λp)p] and O[plog(N)] qubits where up to p copies of the quantum state defined on a Hilbert space of size N are needed as the input. We validate this procedure for the entanglement spectrum of the topologically ordered Laughlin wave function corresponding to the quantum Hall state at filling factor ν=1/3. Our scaling analysis exposes the tradeoffs between time and number of qubits for obtaining the entanglement spectrum in the thermodynamic limit using finite-size digital quantum computers. We also illustrate the utility of the second Renyi entropy in predicting a topological phase transition and in extracting the localization length in a many-body localized system.
Sonika Johri; Damian S. Steiger; Matthias Troyer. Entanglement spectroscopy on a quantum computer. Physical Review B 2017, 96, 195136 .
AMA StyleSonika Johri, Damian S. Steiger, Matthias Troyer. Entanglement spectroscopy on a quantum computer. Physical Review B. 2017; 96 (19):195136.
Chicago/Turabian StyleSonika Johri; Damian S. Steiger; Matthias Troyer. 2017. "Entanglement spectroscopy on a quantum computer." Physical Review B 96, no. 19: 195136.
Quantum tunneling is ubiquitous across different fields, from quantum chemical reactions and magnetic materials to quantum simulators and quantum computers. While simulating the real-time quantum dynamics of tunneling is infeasible for high-dimensional systems, quantum tunneling also shows up in quantum Monte Carlo (QMC) simulations, which aim to simulate quantum statistics with resources growing only polynomially with the system size. Here we extend the recent results obtained for quantum spin models [Phys. Rev. Lett. 117, 180402 (2016)], and we study continuous-variable models for proton transfer reactions. We demonstrate that QMC simulations efficiently recover the scaling of ground-state tunneling rates due to the existence of an instanton path, which always connects the reactant state with the product. We discuss the implications of our results in the context of quantum chemical reactions and quantum annealing, where quantum tunneling is expected to be a valuable resource for solving combinatorial optimization problems.
Guglielmo Mazzola; Vadim N. Smelyanskiy; Matthias Troyer. Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing. Physical Review B 2017, 96, 134305 .
AMA StyleGuglielmo Mazzola, Vadim N. Smelyanskiy, Matthias Troyer. Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing. Physical Review B. 2017; 96 (13):134305.
Chicago/Turabian StyleGuglielmo Mazzola; Vadim N. Smelyanskiy; Matthias Troyer. 2017. "Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing." Physical Review B 96, no. 13: 134305.
In spite of their intrinsic one-dimensional nature, matrix product states have been systematically used to obtain remarkably accurate results for two-dimensional systems. Motivated by basic entropic arguments favoring projected entangled-pair states as the method of choice, we assess the relative performance of infinite matrix product states and infinite projected entangled-pair states on cylindrical geometries. By considering the Heisenberg and half-filled Hubbard models on the square lattice as our benchmark cases, we evaluate their variational energies as a function of both bond dimension and cylinder width. In both examples, we find crossovers at moderate cylinder widths, i.e., for the largest bond dimensions considered, we find an improvement on the variational energies for the Heisenberg model by using projected entangled-pair states at a width of about eleven sites, whereas for the half-filled Hubbard model, this crossover occurs at about seven sites.
Juan Osorio Iregui; Matthias Troyer; Philippe Corboz. Infinite matrix product states versus infinite projected entangled-pair states on the cylinder: A comparative study. Physical Review B 2017, 96, 115113 .
AMA StyleJuan Osorio Iregui, Matthias Troyer, Philippe Corboz. Infinite matrix product states versus infinite projected entangled-pair states on the cylinder: A comparative study. Physical Review B. 2017; 96 (11):115113.
Chicago/Turabian StyleJuan Osorio Iregui; Matthias Troyer; Philippe Corboz. 2017. "Infinite matrix product states versus infinite projected entangled-pair states on the cylinder: A comparative study." Physical Review B 96, no. 11: 115113.
Recent experiments on Majorana fermions in semiconductor nanowires [S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, and C. M. Marcus, Nature (London) 531, 206 (2016)] revealed a surprisingly large electronic Landé g factor, several times larger than the bulk value—contrary to the expectation that confinement reduces the g factor. Here we assess the role of orbital contributions to the electron g factor in nanowires and quantum dots. We show that an L·S coupling in higher subbands leads to an enhancement of the g factor of an order of magnitude or more for small effective mass semiconductors. We validate our theoretical finding with simulations of InAs and InSb, showing that the effect persists even if cylindrical symmetry is broken. A huge anisotropy of the enhanced g factors under magnetic field rotation allows for a straightforward experimental test of this theory.
Georg W. Winkler; Dániel Varjas; Rafal Skolasinski; Alexey Soluyanov; Matthias Troyer; Michael Wimmer. Orbital Contributions to the Electron g Factor in Semiconductor Nanowires. Physical Review Letters 2017, 119, 037701 .
AMA StyleGeorg W. Winkler, Dániel Varjas, Rafal Skolasinski, Alexey Soluyanov, Matthias Troyer, Michael Wimmer. Orbital Contributions to the Electron g Factor in Semiconductor Nanowires. Physical Review Letters. 2017; 119 (3):037701.
Chicago/Turabian StyleGeorg W. Winkler; Dániel Varjas; Rafal Skolasinski; Alexey Soluyanov; Matthias Troyer; Michael Wimmer. 2017. "Orbital Contributions to the Electron g Factor in Semiconductor Nanowires." Physical Review Letters 119, no. 3: 037701.