The conical shape of a shuttlecock allows it to flip on impact. As a light and extended particle, it flies with a pure drag trajectory. We first study the flip phenomenon and the dynamics of the flight and then discuss the implications on the game. Lastly, a possible classification of different shots is proposed.

Double-slit diffraction is a corner stone of quantum mechanics. It illustrates key features of quantum mechanics: interference and the particle-wave duality of matter. In 1965, Richard Feynman presented a thought experiment to show these features. Here we demonstrate the full realization of his famous thought experiment. By placing a movable mask in front of a double-slit to control the transmission through the individual slits, probability distributions for single- and double-slit arrangements were observed. Also, by recording single electron detection events diffracting through a double-slit, a diffraction pattern was built up from individual events.

This tutorial introduces the theoretical and experimental basics of electromagnetically induced transparency (EIT) in thermal alkali vapors. We first give a brief phenomenological description of EIT in simple three-level systems of stationary atoms and derive analytical expressions for optical absorption and dispersion under EIT conditions. Then we focus on how the thermal motion of atoms affects various parameters of the EIT system. Specifically, we analyze the Doppler broadening of optical transitions, ballistic versus diffusive atomic motion in a limited-volume interaction region, and collisional depopulation and decoherence. Finally, we discuss the common trade-offs important for optimizing an EIT experiment and give a brief 'walk-through' of a typical EIT experimental setup. We conclude with a brief overview of current and potential EIT applications.

Hybrid quantum systems based on magnons in magnetic materials have made significant progress in the past decade. They are built based on the couplings of magnons with microwave photons, optical photons, vibration phonons, and superconducting qubits. In particular, the interactions among magnons, microwave cavity photons, and vibration phonons form the system of cavity magnomechanics (CMM), which lies in the interdisciplinary field of cavity QED, magnonics, quantum optics, and quantum information. Here, we review the experimental and theoretical progress of this emerging field. We first introduce the underlying theories of the magnomechanical coupling, and then some representative classical phenomena that have been experimentally observed, including magnomechanically induced transparency, magnomechanical dynamical backaction, magnon-phonon cross-Kerr nonlinearity, etc. We also discuss a number of theoretical proposals, which show the potential of the CMM system for preparing different kinds of quantum states of magnons, phonons, and photons, and hybrid systems combining magnomechanics and optomechanics and relevant quantum protocols based on them. Finally, we summarize this review and provide an outlook for the future research directions in this field.

Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as 'the quantum variational eigensolver' was developed (Peruzzo et al 2014 Nat. Commun. 5 4213) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.

In recent years, surface codes have become a leading method for quantum error correction in theoretical large-scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural two-dimensional nearest-neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect-based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance-3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.

Peace is not merely the absence of war and violence, rather 'positive peace' is the political, economic, and social systems that generate and sustain peaceful societies. Our international and multidisciplinary group is using physics inspired complex systems analysis methods to understand the factors and their interactions that together support and maintain peace. We developed causal loop diagrams and from them ordinary differential equation models of the system needed for sustainable peace. We then used that mathematical model to determine the attractors in the system, the dynamics of the approach to those attractors, and the factors and connections that play the most important role in determining the final state of the system. We used data science ('big data') methods to measure quantitative values of the peace factors from structured and unstructured (social media) data. We also developed a graphical user interface for the mathematical model so that social scientists or policy makers, can by themselves, explore the effects of changing the variables and parameters in these systems. These results demonstrate that complex systems analysis methods, previously developed and applied to physical and biological systems, can also be productively applied to analyze social systems such as those needed for sustainable peace.

Within the last two decades, quantum technologies (QT) have made tremendous progress, moving from Nobel Prize award-winning experiments on quantum physics (1997: Chu, Cohen-Tanoudji, Phillips; 2001: Cornell, Ketterle, Wieman; 2005: Hall, Hänsch-, Glauber; 2012: Haroche, Wineland) into a cross-disciplinary field of applied research. Technologies are being developed now that explicitly address individual quantum states and make use of the 'strange' quantum properties, such as superposition and entanglement. The field comprises four domains: quantum communication, where individual or entangled photons are used to transmit data in a provably secure way; quantum simulation, where well-controlled quantum systems are used to reproduce the behaviour of other, less accessible quantum systems; quantum computation, which employs quantum effects to dramatically speed up certain calculations, such as number factoring; and quantum sensing and metrology, where the high sensitivity of coherent quantum systems to external perturbations is exploited to enhance the performance of measurements of physical quantities. In Europe, the QT community has profited from several EC funded coordination projects, which, among other things, have coordinated the creation of a 150-page QT Roadmap (http://qurope.eu/h2020/qtflagship/roadmap2016). This article presents an updated summary of this roadmap.

It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on the case, by a or a topological invariant. This is an exhaustive classification. Here we construct representatives of topological insulators and superconductors for all five classes and in arbitrary spatial dimension d, in terms of Dirac Hamiltonians. Using these representatives we demonstrate how topological insulators (superconductors) in different dimensions and different classes can be related via 'dimensional reduction' by compactifying one or more spatial dimensions (in 'Kaluza–Klein'-like fashion). For -topological insulators (superconductors) this proceeds by descending by one dimension at a time into a different class. The -topological insulators (superconductors), on the other hand, are shown to be lower-dimensional descendants of parent -topological insulators in the same class, from which they inherit their topological properties. The eightfold periodicity in dimension d that exists for topological insulators (superconductors) with Hamiltonians satisfying at least one reality condition (arising from time-reversal or charge-conjugation/particle–hole symmetries) is a reflection of the eightfold periodicity of the spinor representations of the orthogonal groups SO(N) (a form of Bott periodicity). Furthermore, we derive for general spatial dimensions a relation between the topological invariant that characterizes topological insulators and superconductors with chiral symmetry (i.e., the winding number) and the Chern–Simons invariant. For lower-dimensional cases, this formula relates the winding number to the electric polarization (d=1 spatial dimensions) or to the magnetoelectric polarizability (d=3 spatial dimensions). Finally, we also discuss topological field theories describing the spacetime theory of linear responses in topological insulators (superconductors) and study how the presence of inversion symmetry modifies the classification of topological insulators (superconductors).

Computing excited-state properties of molecules and solids is considered one of the most important near-term applications of quantum computers. While many of the current excited-state quantum algorithms differ in circuit architecture, specific exploitation of quantum advantage, or result quality, one common feature is their rooting in the Schrödinger equation. However, through contracting (or projecting) the eigenvalue equation, more efficient strategies can be designed for near-term quantum devices. Here we demonstrate that when combined with the Rayleigh–Ritz variational principle for mixed quantum states, the ground-state contracted quantum eigensolver (CQE) can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two excited-state (anti-Hermitian) CQEs that perform the excited-state calculation while inheriting many of the remarkable features of the original ground-state version of the algorithm, such as its scalability. To showcase our approach, we study several model and chemical Hamiltonians and investigate the performance of different implementations.

Eigensolvers have a wide range of applications in machine learning. Quantum eigensolvers have been developed for achieving quantum speedup. Here, we propose a parallel quantum eigensolver (PQE) for solving a set of machine learning problems, which is based on quantum multi-resonant transitions that simultaneously trigger multiple energy transitions in the systems on demand. PQE has a polylogarithmic cost in problem size under certain circumstances and is hardware efficient, such that it is implementable in near-term quantum computers. As a verification, we utilize it to construct a collaborative filtering quantum recommendation system and implement an experiment of the movie recommendation tasks on a nuclear spin quantum processor. As a result, our recommendation system accurately suggests movies to the user that he/she might be interested in. We further demonstrate the applications of PQE in classification and image completion. In the future, our work will shed light on more applications in quantum machine learning.

Transmission losses through optical fibers are one of the main obstacles preventing both long-distance quantum communications and continuous-variable quantum key distribution. Optical amplification provides a tool to obtain, at least partially, signal restoration. In this work, we address a key distribution protocol over a multi-span link employing either phase-insensitive (PIA) or phase-sensitive (PSA) amplifiers, considering Gaussian modulation of coherent states followed by homodyne detection at the receiver's side. We perform the security analysis under both unconditional and conditional security frameworks by assuming in the latter case only a single span of the whole communication link to be untrusted. We compare the resulting key generation rate (KGR) for both kinds of amplified links with the no-amplifier protocol, identifying the enhancement introduced by optical amplification. We prove an increase in the KGR for the PSA link in the unconditional scenario and for both PSA and PIA in the conditional security setting depending on position of the attack and the measured quadrature.

We demonstrate theoretically and experimentally an electromagnetic lensing concept using the magnetic vector potential—in a region free of classical electromagnetic fields—via the Aharonov–Bohm (AB) effect. This toroid-shaped lens with poloidal current flow allows for electromagnetic lensing which can be tuned to be convex or concave with a spherical aberration coefficient of opposite polarity to its focal length. This field-free lens combines the advantages of traditional electromagnetic and electrostatic field-based lenses and opens up additional possibilities for the optical design of charged-particle systems. More generally, these results demonstrate that the AB effect can shape charged particle wavefronts beyond simple step shifts if topologies beyond simple flux lines are considered and further supports the physical significance of the magnetic vector potential.

Van der Waals heterostructures with tunable band alignments are the promising candidates for the fabrication of high-performance multifunctional nano-optoelectronic devices. In this work, we investigate the band alignments and optical properties of two-dimensional MoSSe/C₃N₄ and C₃N₄/MoSSe heterostructures using first-principles methods. The two most stable MoSSe/C₃N₄ (C₃N₄-Se) and C₃N₄/MoSSe (C₃N₄-S) heterostructures (labeled as A2 and B2, respectively) out of the twelve possible heterostructures are selected for the corresponding properties research. It is found that the A2 exhibits type-I band alignment, making it suitable for light-emitting applications, while the B2 exhibits typical type-II band alignment, which is favorable for carrier separation. Moreover, the band alignment of the two heterostructures can be modulated by the external electric fields, that is, band alignment transition between type-I and type-II. In addition, the main absorption peaks of both heterostructures in their pristine state are located in the visible light region (approximately 2.9 eV), and the peak values of the absorption peaks can be enhanced (weaken) via applying positive (negative) external electric fields. Our findings demonstrate that the C₃N₄/C₃N₄ and C₃N₄/MoSSe heterostructures hold significant potential for applications in multifunctional electronic devices including light-emitting, carrier separation, optical modulators, etc.

Twisted two-dimensional materials have recently attracted tremendous interest owing to their unique structures and fantastic electronic properties. However, the effect of interlayer twisting on the phonon transport properties is less known, especially for the twist-angle-dependent lattice thermal conductivity ($\kappa_{\textrm{L}}$). Using the emerging Janus SnSSe bilayer as a prototypical example, we develop an accurate machine learning potential, which is adopted to efficiently predict the $\kappa_{\textrm{L}}$ at a series of twist angles via iterative solution of the Boltzmann transport equation. It is found that the $\kappa_{\textrm{L}}$ exhibits a distinct non-monotonous dependence on the twist angle, which can be traced back to the bonding heterogeneity between high-symmetry stacking regions inside the moiré unit cell. In contrast to the general belief, the optical phonons make a major contribution toward the $\kappa_{\textrm{L}}$ of the twisted structures. Moreover, we demonstrate that four-phonon scattering can significantly reduce the $\kappa_{\textrm{L}}$ of SnSSe bilayer at higher temperatures, which becomes more pronounced by interlayer twisting. Our work not only highlights the strong predictive power of machine learning potential, but also offers new insights into the design of thermal smart materials with tunable $\kappa_{\textrm{L}}$.

Hybrid quantum systems based on magnons in magnetic materials have made significant progress in the past decade. They are built based on the couplings of magnons with microwave photons, optical photons, vibration phonons, and superconducting qubits. In particular, the interactions among magnons, microwave cavity photons, and vibration phonons form the system of cavity magnomechanics (CMM), which lies in the interdisciplinary field of cavity QED, magnonics, quantum optics, and quantum information. Here, we review the experimental and theoretical progress of this emerging field. We first introduce the underlying theories of the magnomechanical coupling, and then some representative classical phenomena that have been experimentally observed, including magnomechanically induced transparency, magnomechanical dynamical backaction, magnon-phonon cross-Kerr nonlinearity, etc. We also discuss a number of theoretical proposals, which show the potential of the CMM system for preparing different kinds of quantum states of magnons, phonons, and photons, and hybrid systems combining magnomechanics and optomechanics and relevant quantum protocols based on them. Finally, we summarize this review and provide an outlook for the future research directions in this field.

Recently, there has been considerable interest in the application of information geometry to quantum many body physics. This interest has been driven by three separate lines of research, which can all be understood as different facets of quantum information geometry. First, the study of topological phases of matter characterized by Chern number is rooted in the symplectic structure of the quantum state space, known in the physics literature as Berry curvature. Second, in the study of quantum phase transitions, the fidelity susceptibility has gained prominence as a universal probe of quantum criticality, even for systems that lack an obviously discernible order parameter. Finally, the study of quantum Fisher information in many body systems has seen a surge of interest due to its role as a witness of genuine multipartite entanglement and owing to its utility as a quantifier of quantum resources, in particular those useful in quantum sensing. Rather than a thorough review, our aim is to connect key results within a common conceptual framework that may serve as an introductory guide to the extensive breadth of applications, and deep mathematical roots, of quantum information geometry, with an intended audience of researchers in quantum many body and condensed matter physics.

Nonlinear optics has been a very dynamic field of research with spectacular phenomena discovered mainly after the invention of lasers. The combination of high intensity fields with resonant systems has further enhanced the nonlinearity with specific additional effects related to the resonances. In this paper we review a limited range of these effects which has been studied in the past decades using close-to-room-temperature atomic vapors as the nonlinear resonant medium. In particular we describe four-wave mixing and generation of nonclassical light in atomic vapors. One-and two-mode squeezing as well as photon correlations are discussed. Furthermore, we present some applications for optical and quantum memories based on hot atomic vapors. Finally, we present results on the recently developed field of quantum fluids of light using hot atomic vapors.

Realistic nuclear reaction cross-section models are an essential ingredient of reliable heavy-ion transport codes. Such codes are used for risk evaluation of manned space exploration missions as well as for ion-beam therapy dose calculations and treatment planning. Therefore, in this study, a collection of total nuclear reaction cross-section data has been generated within a GSI-ESA-NASA collaboration. The database includes the experimentally measured total nucleus–nucleus reaction cross-sections. The Tripathi, Kox, Shen, Kox–Shen, and Hybrid-Kurotama models are systematically compared with the collected data. Details about the implementation of the models are given. Literature gaps are pointed out and considerations are made about which models fit best the existing data for the most relevant systems to radiation protection in space and heavy-ion therapy.

The next core-collapse supernova in the Milky Way or its satellites will represent a once-in-a-generation opportunity to obtain detailed information about the explosion of a star and provide significant scientific insight for a variety of fields because of the extreme conditions found within. Supernovae in our galaxy are not only rare on a human timescale but also happen at unscheduled times, so it is crucial to be ready and use all available instruments to capture all possible information from the event. The first indication of a potential stellar explosion will be the arrival of a bright burst of neutrinos. Its observation by multiple detectors worldwide can provide an early warning for the subsequent electromagnetic fireworks, as well as signal to other detectors with significant backgrounds so they can store their recent data. The supernova early warning system (SNEWS) has been operating as a simple coincidence between neutrino experiments in automated mode since 2005. In the current era of multi-messenger astronomy there are new opportunities for SNEWS to optimize sensitivity to science from the next galactic supernova beyond the simple early alert. This document is the product of a workshop in June 2019 towards design of SNEWS 2.0, an upgraded SNEWS with enhanced capabilities exploiting the unique advantages of prompt neutrino detection to maximize the science gained from such a valuable event.