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Electromagnetically induced transparency and Autler-Townes splitting are two distinct yet related effects. These phenomena are relevant to quantum technologies, including quantum memory, quantum switching, and quantum transduction. Here, the similarities and differences between these phenomena along historical and conceptual lines are discussed and their realizations on various physical platforms including atomic gases, superconducting circuits, and optomechanics are elaborated. In particular, the author clarifies two approaches to assessing which phenomenon is observed based on a black-box approach of modeling the output, given a particular input vs analyzing the underpinning physics. Furthermore, the author highlights the ability to effect a continuous transition between the two seemingly disparate phenomena., 4 pp

We study maximal coin-position entanglement generation via a discrete-time quantum walk, in which the coin operation is randomly selected from one of two coin operators set at each step. We solve maximal entanglement generation as an optimization problem with quantum process fidelity as the cost function. Then we determine the maximal entanglement that can be rigorously generated for any step beyond the second regardless of initial condition with appropriate coin sequences. The simplest coin sequence comprising Hadamard and identity operations is equivalent to the generalized elephant quantum walk, which exhibits an increasingly faster spreading in terms of probability distribution. Experimentally, we demonstrate a ten-step quantum walk driven by such coin sequences with linear optics, and thereby show the desired high-dimensional bipartite entanglement as well as the transport behavior of faster spreading., 13 pages, 6 figures. Comments are welcome

Topological edge states arise in non-Hermitian parity-time ($\mathcal {PT}$)-symmetric systems, and manifest themselves as bright or dark edge states, depending on the imaginary components of their eigenenergies. As the spatial probabilities of dark edge states are suppressed during the non-unitary dynamics, it is a challenge to observe them experimentally. Here we report the experimental detection of dark edge states in photonic quantum walks with spontaneously broken $\mathcal {PT}$ symmetry, thus providing a complete description of the topological phenomena therein. We experimentally confirm that the global Berry phase in $\mathcal {PT}$-symmetric quantum-walk dynamics unambiguously defines topological invariants of the system in both the $\mathcal {PT}$-symmetry-unbroken and broken regimes. Our results establish a unified framework for characterizing topology in $\mathcal {PT}$-symmetric quantum-walk dynamics, and provide a useful method to observe topological phenomena in $\mathcal {PT}$-symmetric non-Hermitian systems in general.

I provide a perspective on the development of quantum computing for data science, including a dive into state-of-the-art for both hardware and algorithms and the potential for quantum machine learning, Comment: 20th International Workshop on Advanced Computing and Analysis Techniques in Physics Research 29/11/2021 - 03/12/2021 (current as of December 2021)

Constructing all extreme instances of the set of completely positive trace-preserving (CPTP) maps, i.e., quantum channels, is a challenging valuable open problem in quantum information theory. Here we introduce a systematic approach that enables us to construct exactly those extreme channels that are covariant with respect to a finite discrete group or a compact connected Lie group. Innovative labeling of quantum channels by group representations enables us to identify the subset of group-covariant channels whose elements are group-covariant generalized-extreme channels. Furthermore, we exploit essentials of group representation theory to introduce equivalence classes for the labels and also partition the set of group-covariant channels. As a result we show that it is enough to construct one representative of each partition. We construct Kraus operators for group-covariant generalized-extreme channels by solving systems of linear and quadratic equations for all candidates satisfying the necessary condition for being group-covariant generalized-extreme channels. Deciding whether these constructed instances are extreme or quasi-extreme is accomplished by solving system of linear equations. We formalize the problem of constructing and classifying group-covariant generalized extreme channels, thereby yielding an algorithmic approach to solving, which we express as pseudocode. To illustrate the application and value of our method, we solve for explicit examples of group-covariant extreme channels. With unbounded computational resources to execute our algorithm, our method always delivers a description of an extreme channel for any finite-dimensional Hilbert-space and furthermore guarantees a description of a group-covariant extreme channel for any dimension and for any finite-discrete or compact connected Lie group if such an extreme channel exists.

Topological insulators host topology-linked boundary states, whose spin and charge degrees of freedom could be exploited to design topological devices with enhanced functionality. We experimentally observe that dissipationless chiral edge states in a spin-orbit coupled anomalous Floquet topological phase exhibit topological spin texture on boundaries, realized via a two-dimensional quantum walk. Our experiment shows that, for a walker traveling around a closed loop along the boundary in real space, its spin evolves and winds through a great circle on the Bloch sphere, which implies that edge-spin texture has nontrivial winding. This winding is linked to the bulk Dirac Hamiltonian around the energy-gap opening point. Our experiment confirms that two-dimensional anomalous Floquet topological systems exhibit topological spin texture on the boundary, which could inspire novel topology-based spintronic phenomena and devices., Comment: 6 pages, 4 figures

We propose an atomic grating based on an electromagnetically induced transparency phenomenon that switches between zeroth-order diffraction to a distinct higher-order diffraction pattern by driving a planar gaseous medium of a four-level tripod ( ⋔ ) atoms with three laser beams: modulation of standing wave control beam propagating nearly perpendicular to the planar medium, while vortex and weak plane probe beams directed perpendicular to the medium. We numerically investigate the behavior of the amplitude, phase modulations, and probe field diffraction intensities of different orders by the variation of the field detunings and orbital angular momentum number of the composite vortex light beam. Specifically, in the off-resonant case, the interplay between a square lattice of the control and an additional spatial variation of the vortex beam allows the emergence of higher diffraction orders and variable gain due to double transparency windows in this complex optical system. We believe that our proposed scheme might be useful in optical memory devices via the storage of information to diffraction orders of the atomic grating.

Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph states to be in TQO-1, which is a class of quantum error correction code states whose code distance scales macroscopically with the number of physical qubits. Using these criteria, we consider a number of specific graph families, including the star and complete graphs, and the line graphs of complete and completely bipartite graphs, and discuss which are topologically ordered and how to construct the codewords. The formalism is then employed to construct several codes with macroscopic distance, including a three-dimensional topological code generated by local stabilizers that also has a macroscopic number of encoded logical qubits. The results indicate that graph states provide a fruitful approach to the construction and characterization of topological stabilizer quantum error correction codes., 21 pages, 7 figures

Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate-time and gate error-rate. We describe two-qubit gates with addressed Raman beams within a linear trapped-ion chain by a quantum master equation (QME). The QME incorporates the single-ion two-photon effective Rabi frequency, Autler-Townes and vibrational Bloch-Siegert energy shifts, off-resonant transitions, Raman and Rayleigh scattering, laser-power fluctuations, motional heating, cross-Kerr phonon coupling, laser spillover, asymmetric addressing beams and an imperfect initial motional ground state, with no fitting parameters. Whereas state-of-the-art methods are oblivious to these effects in the gate design procedure. We employ global optimization to design pulse sequences for achieving a robust rapid two-qubit gate for seven trapped $^{171}$Yb$^{+}$ ions by optimizing over numerically integrated QME solutions. Here, robust means resilient against slow drift of motional frequencies, and rapid means gate execution where the effective Rabi frequency is comparable to the detuning of the laser from the ion's bare electronic transition. Our robust quantum control delivers rapid high-quality two-qubit gates in long ion chains, enabling scalable quantum computing with trapped ions., Comment: Seven pages, two figures

A neutral-atom system serves as a promising platform for realizing gate-based quantum computing because of its capability to trap and control several atomic qubits in different geometries and the ability to perform strong, long-range interactions between qubits; however, the two-qubit entangling gate fidelity lags behind competing platforms such as superconducting systems and trapped ions. The aim of our work is to design a fast, robust, high-fidelity controlled-Z (CZ) gate, based on the Rydberg-blockade mechanism, for neutral atoms. We propose a gate procedure that relies on simultaneous and transitionless quantum driving of a pair of atoms using broadband lasers. By simulating a system of two interacting Caesium atoms, including spontaneous emission from excited levels and parameter fluctuations, we yield a Rydberg-blockade CZ gate with fidelity 0.9985 over an operation time of $0.12~\mu$s. Our gate procedure delivers CZ gates that are superior than the state-of-the-art experimental CZ gate and the simulated CZ gates based on adiabatic driving of atoms. Our results show that our gate procedure carries significant potential for achieving scalable quantum computing using neutral atoms., Comment: 22 pages

We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be stated as follows: if we evolve the dynamical system for $n$ time steps and then we disturb it, it is the same as first disturbing the system with the same influence and then letting the system evolve for $n$ time steps. Applying the powerful machinery of resource theories, we develop a theory of covariant influences both when there is a purely deterministic evolution and when randomness is involved. Subsequently, we provide necessary and sufficient conditions for the transition between states under deterministic covariant influences and necessary conditions in the presence of stochastic covariant influences, predicting which transitions between states are forbidden. Our approach, for the first time, employs the framework of resource theories, borrowed from quantum information theory, to the study of finite discrete dynamical systems. The laws we articulate unify the behavior of different types of finite discrete dynamical systems, and their mathematical flavor makes them rigorous and checkable., 23 + 3 pages, 4 figures

Coherent-state superpositions are of great importance for many quantum subjects, ranging from foundational to technological, e.g., from tests of collapse models to quantum metrology. Here we explore various aspects of these states, related to the connection between sub-Planck structures present in their Wigner function and their sensitivity to displacements (ultimately determining their metrological potential). We review this for the usual Heisenberg-Weyl algebra associated to a harmonic oscillator, and extend it to find analogous results for the $\mathfrak{su}(2)$ algebra, typically associated with angular momentum. In particular, in the Heisenberg-Weyl case, we identify phase-space structures with support smaller than the Planck action in both Schr\"{o}dinger-cat-state mixtures and superpositions, the latter known as compass states. However, as compared to coherent states, compass states are shown to have $\sqrt{N}$-enhanced sensitivity against displacements in all phase-space directions ($N$ is the average number of quanta), whereas cat states and cat mixtures show such enhanced sensitivity only for displacements in specific directions. We then show that these same properties apply for analogous SU(2) states provided (i) coherent states are restricted to the equator of the sphere that plays the role of phase space for this group, (ii) we associate the role of the Planck action to the size of SU(2) coherent states in such a sphere, and (iii) we associate the role of $N$ with the total angular momentum.

International audience; A cyclic atomic level scheme interacting with an optical and a microwave field is proposed for the generation and group-delay control of few-photon optical pulses. Our analysis exploits a hybrid second order-nonlinearity under conditions of electromagnetically induced transparency to generate an optical pulse. The generated pulse can be delayed or advanced through microwave intensity control of the absolute phase of the second-order-nonlinearity. Importantly, this handle on group delay of the generated pulse is number density-independent. Our scheme is thus ideally suited for the generation and control of few-photon optical pulses using ultra-dilute atomic samples. Our results will enable microscopic atomic interface systems that serve as controllable delay channels for both classical and quantum signal processing.

We seek to design experimentally feasible broadband, temporally multiplexed optical quantum memory with near-term applications to telecom bands. Specifically, we devise dispersion compensation (DC) for an impedance-matched narrow-band quantum memory by exploiting Raman processes over two three-level atomic subensembles, one for memory and the other for DC. DC provides impedance matching over more than a full cavity linewidth. Combined with 1 s spin-coherence lifetime the memory could be capable of power efficiency exceeding 90% leading to 106 modes for temporal multiplexing. Our design could lead to significant multiplexing enhancement for quantum repeaters to be used for telecom quantum networks.

We aim to create deterministic collisions between orbiting bodies by applying a time-dependent external force to one or both bodies, whether the bodies are mutually repulsive, as in the two- or multielectron atomic case, or mutually attractive, as in the planetary-orbit case. Specifically, we have devised a mathematical framework for causing deterministic collisions by launching an inner orbiting body to a higher energy such that this inner body is guaranteed to collide with the outer body. Our method first expresses the problem mathematically as coupled nonlinear differential equations with a time-dependent driving force and solves to find a feasible solution for the force function. Although our calculation is based strictly on classical physics, our approach is suitable for the case of helium with two highly excited electrons and is also valid for creating collisions in the gravitational case, such as for our solar system.

Continuous-variable codes are an expedient solution for quantum information processing and quantum communication involving optical networks. Here we characterize the squeezed comb, a finite superposition of equidistant squeezed coherent states on a line, and its properties as a continuous-variable encoding choice for a logical qubit. The squeezed comb is a realistic approximation to the ideal code proposed by Gottesman, Kitaev, and Preskill [Phys. Rev. A 64, 012310 (2001)], which is fully protected against errors caused by the paradigmatic types of quantum noise in continuous-variable systems: damping and diffusion. This is no longer the case for the code space of finite squeezed combs, and noise robustness depends crucially on the encoding parameters. We analyze finite squeezed comb states in phase space, highlighting their complicated interference features and characterizing their dynamics when exposed to amplitude damping and Gaussian diffusion noise processes. We find that squeezed comb state are more suitable and less error-prone when exposed to damping, which speaks against standard error correction strategies that employ linear amplification to convert damping into easier-to-describe isotropic diffusion noise., 10 pages, 10 figures

Quantum information processing is likely to have a far-reaching impact in the field of artificial intelligence. Noisy, intermediate-scale quantum devices provide a platform for exploring the possibility of attaining a quantum advantage through hybrid quantum-classical machine-learning algorithms. One example of such a hybrid algorithm is ``quantum kitchen sinks,'' which builds upon a classical algorithm known as ``random kitchen sinks'' to leverage a gate model quantum computer for machine-learning applications. We propose an alternative algorithm called ``analog-quantum kitchen sinks'' (AQKSs), which employs an analog-quantum computer for mapping data features into new features in a nonlinear manner. The new features can then be used by a classical algorithm to perform machine-learning tasks. We show the effectiveness of our algorithm for performing binary classification on both a synthetic dataset and a real-world dataset by simulating the operations of a quantum annealer. We demonstrate that the AQKS algorithm reduces the classification error of a linear classifier from $50\mathrm{%}$ to $0.6\mathrm{%}$ for the synthetic dataset and from $4.4\mathrm{%}$ to $1.6\mathrm{%}$ for the other dataset. Our proposed AQKS algorithm presents the possibility to use current quantum annealers for solving practical machine-learning problems.

Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement -- a highly non-classical correlation -- remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50\%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement., 6 pages with 5 figures

We analyze neutral atom Rydberg $C_Z$ gates based on adiabatic pulses applied symmetrically to both atoms. Analysis with smooth pulse shapes and Cs atom parameters predicts the gates can create Bell states with fidelity ${\mathcal F}>0.999$ using adiabatic rapid passage (ARP) pulses. With globally optimized adiabatic pulse shapes, in a two-photon excitation process, we generate Bell states with fidelity ${\mathcal F}=0.997$. The analysis fully accounts for spontaneous emission from intermediate and Rydberg states, including the Rydberg lifetime in a room temperature environment, but does not include errors arising from laser noise. The gate protocols do not require individual addressing and are shown to be robust against Doppler shifts due to atomic motion., 10 figures, added robustness analysis with respect to laser intensity and frequency

The uncertainty principle, first introduced by Heisenberg in inertial frames, clearly distinguishes quantum theories from classical mechanics. In non-inertial frames, its information-theoretic expressions, namely entropic uncertainty relations, have been extensively studied through delocalized quantum fields, and localization of the quantum fields were discussed as well. However, infeasibility of measurements applied on a delocalized quantum field due to the finite size of measurement apparatuses is left unexplained. Therefore, physical clarification of a quantum protocol revealing entropic uncertainty relations still needs investigation. Building on advances in quantum field theories and theoretical developments in entropic uncertainty relations, we demonstrate a relativistic protocol of an uncertainty game in the presence of localized fermionic quantum fields inside cavities. Moreover, a novel lower bound for entropic uncertainty relations with multiple quantum memories is given in terms of the Holevo quantity, which implies how acceleration affects uncertainty relations., 9 pages, 3 figures

A fully homomorphic encryption system hides data from unauthorized parties, while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more powerful server without revealing their inputs, a fully homomorphic cryptosystem can be used as a building block in the construction of a number of cryptographic functionalities. Designing such a scheme remained an open problem until 2009, decades after the idea was first conceived, and the past few years have seen the generalization of this functionality to the world of quantum machines. Quantum schemes prior to the one implemented here were able to replicate some features in particular use-cases often associated with homomorphic encryption but lacked other crucial properties, for example, relying on continual interaction to perform a computation or leaking information about the encrypted data. We present the first experimental realisation of a quantum fully homomorphic encryption scheme. We further present a toy two-party secure computation task enabled by our scheme. Finally, as part of our implementation, we also demonstrate a post-selective two-qubit linear optical controlled-phase gate with a much higher post-selection success probability (1/2) when compared to alternate implementations, e.g. with post-selective controlled-$Z$ or controlled-$X$ gates (1/9)., 11 pages, 16 figures, 2 tables

We devise a multiphoton interferometry scheme for sampling a quadratic function of a specific immanant for any submatrix of a unitary matrix and its row permutations. The full unitary matrix describes a passive, linear interferometer, and its submatrix is used when photons enter in and are detected at subsets of possible input and output channels. Immanants are mathematical constructs that interpolate between the permanent and determinant; contrary to determinants and permanents, which have meaningful physical applications, immanants are devoid of physical meaning classically but here are shown to be meaningful in a quantum setting. Our quadratic form of immanants is sampled by injecting vacuum and single photons into interferometer input ports such that the photon arrival times are entangled, in contrast to previous methods that control arrival times without entangling. Our method works for any number of photons, and we solve explicitly the quadratic form for the two-, three- and four-photon cases., Comment: 10 pages, 2 figures

The quanhim switch is a tool that allows coherently controlling the order in which two operations are applied. We report the first experimental demonstration of the exponential advantage in communication complexity enabled by this tool.

The Hong-Ou-Mandel effect is considered a signature of the quantumness of light, as the dip in coincidence probability using semi-classical theories has an upper bound of 50%. Here we show, theoretically and experimentally, that, with proper phase control of the signals, classical pulses can mimic a Hong-Ou-Mandel-like dip. We demonstrate a dip of 99.635 +/- 0.002% with classical microwave fields. Quantumness manifests in wave-particle complementarity of the two-photon state. We construct quantum and classical interferometers for the complementarity test and show that while the two-photon state shows wave-particle complementarity, the classical pulses do not., Comment: Version to appear in Physical Review A

The well studied quantum optical Schr\"{o}dinger cat state is a superposition of two distinguishable states, with quantum coherence between these macroscopically distinguishable states being of foundational and, in the context of quantum-information processing, practical use. We refer to these quantum-optical cat states as quantum dichotomous states, reflecting that the state is a superposition of two options, and we introduce the term quantum multichotomous state to refer to a superposition of multiple macroscopically distinguishable options. For a single degree of freedom, such as position, we construct the quantum multichotomous states as a superposition of Gaussian states on the position line in phase space. Using this nomenclature, a quantum tetrachotomous state (QTS) is a coherent superposition of four macroscopically distinguishable states. We define, analyze and show how to create such states, and our focus on the QTS is due to their exhibition of much richer phenomena than for the quantum dichotomous states with lessons to going to general multichotomous states with the quantum comb state as a limiting case. Our characterization of the QTS involves the Wigner function, its marginal distributions, and the photon-number distribution, and we discuss the QTS's approximate realization in a multiple coupled-well system., Comment: 14+ pages, 12 figures

We propose a scheme to achieve nuclear-nuclear indirect interactions mediated by a mechanically driven nitrogen-vacancy (NV) center in diamond. Here we demonstrate two-qubit entangling gates and quantum-state transfer between two carbon nuclei. When dipole-dipole interaction strength is much larger than the driving field strength, the scheme is robust against decoherence caused by coupling between the NV center (nuclear spins) and the environment. Conveniently, precise control of dipole coupling is not required so this scheme is insensitive to fluctuating positions of the nuclear spins and the NV center. Our scheme provides a general blueprint for multi-nuclear-spin gates and for multi-party communication., 15 pages,7 figures

We develop a concept for a waveguide that exploits spatial control of nonlinear surface-polaritonic waves. Our scheme includes an optical cavity with four-level $\text{N}$-type atoms in a lossless dielectric placed above a negative-index metamaterial layer. We propose exciting a polaritonic Akhmediev breather at a certain position of the interface between the atomic medium and the metamaterial by modifying laser-field intensities and detunings. Furthermore, we propose generating position-dependent polaritonic frequency combs by engineering widths of the electromagnetically induced transparency window commensurate with the surface-polaritonic modulation instability. Therefore, this waveguide acts as a high-speed polaritonic modulator and position-dependent frequency-comb generator, which can be applied to compact photonic chips.

We aim to devise feasible, efficient verification schemes for bosonic channels. To this end, we construct an average-fidelity witness that yields a tight lower bound for average fidelity plus a general framework for verifying optimal quantum channels. For both multi-mode unitary Gaussian channels and single-mode amplification channels, we present experimentally feasible average-fidelity witnesses and reliable verification schemes, for which sample complexity scales polynomially with respect to all channel specification parameters. Our verification scheme provides an approach to benchmark the performance of bosonic channels on a set of Gaussian-distributed coherent states by employing only two-mode squeezed vacuum states and local homodyne detections. Our results demonstrate how to perform feasible tests of quantum components designed for continuous-variable quantum information processing., 23 pages, 2 figures

Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring resonator yields two counter-propagating modes with equal frequencies. We show that such a system enables implementation of many types of scattering peculiarities, which are either the second or fourth order. The spectral singularities separate parameter regions where the spectrum is either pure real or else comprises complex eigenvalues; hence, they represent the points of the phase transition. By modifying the gain-loss relation for the resonators such an optical scatterer can act as a laser, as a coherent perfect absorber, be unidirectionally reflectionless or transparent, and support bound states either growing or decaying in time. These characteristics are observed for a discrete series of the incident-radiation wavelengths., accepted for Optics Letters