Arbitrary Superposition Research Articles

Far field operator splitting and completion in inverse medium scattering

Abstract We study scattering of time-harmonic plane waves by compactly supported inhomogeneous objects in a homogeneous background medium. The far field operator associated to a fixed scatterer describes multi-static remote observations of scattered fields corresponding to arbitrary superpositions of plane wave incident fields at a single frequency. In this work we consider far field operators for systems of two well-separated scattering objects, and we discuss the nonlinear inverse problem to recover the far field operators associated to each of these two scatterers individually. This is closely related to the question whether the two components of the scatterer can be distinguished by means of inverse medium scattering in a stable way. We also study the restoration of missing or inaccurate components of an observed far field operator and comment on the benefits of far field operator splitting in this context. Both problems are ill-posed without further assumptions, but we give sufficient conditions on the diameter of the supports of the scatterers, the distance between them, and the size of the missing or corrupted data component to guarantee stable recovery whenever sufficient a priori information on the location of the unknown scatterers is available. We provide algorithms, error estimates, a stability analysis, and we demonstrate our theoretical predictions by numerical examples.

Quantum state engineering in a five-state chainwise system by generalized coincident pulse technique.

In this paper, an exact analytical solution is presented for achieving coherent population transfer and creating arbitrary coherent superposition states in a five-state chainwise system by a train of coincident pulses. We show that the solution of a five-state chainwise system can be reduced to an equivalent three-state Λ-type one with the simplest resonant coupling under the assumption of adiabatic elimination together with a requirement of the relation among the four coincident pulses. In this method, the four coincident pulses at each step all have the same time dependence, but with specific magnitudes. The results show that, by using a train of appropriately coincident pulses, this technique not only enables complete population transfer, but also creates any desired coherent superposition between the initial and final states, while the population in all intermediate states is effectively suppressed. Furthermore, this technique can also exhibit a one-way population transfer behavior. The results are of potential interest in applications where high-fidelity multi-state quantum control is essential, e.g., quantum information, atom optics, formation of ultracold molecules, cavity QED, nuclear coherent population transfer, and light transfer in waveguide arrays.

Frequency domain‐based analytical solutions for one‐dimensional soil water flow in layered soils

AbstractSolutions of the linearized Richardson–Richards Equation (RRE) for one‐dimensional soil water flow in layered soils with sinusoidal flux in the frequency domain are derived. We evaluate the accuracy of our analytical and other analytical solutions by comparing them with results from a standard numerical model. Our analytical solution agrees with the numerical solution under multi‐layered heterogeneous soil, while others disagree. We also demonstrate the capability of the proposed solution to simulate soil moisture dynamics under a realistic, multi‐frequency flux case. The procedure described in the paper is valid for any series of arbitrary periodic flux superpositions for layered heterogeneous . Moreover, our solution is efficient in the calculation compared with numerical solutions, especially when dealing with long‐time series soil moisture, which can provide a validation of numerical models.

SU(N) symmetry of coherent photons controlled by rotated waveplates

The coherent state from a laser source has spin and orbital degrees of freedom, which allow an arbitrary superposition state among orthogonal states with varying amplitudes and phases. Here, we theoretically show coherent photons with SU(N) symmetry are characterised by expectation values of angular momentum shown on a hypersphere in SO(N2−1) space. To demonstrate expected unitary transformations in experiments, we have constructed generators of transformations in the Lie group simply by combining widely available optical components such as waveplates and vortex lenses. We show a superposition state between twisted and Gaussian states is characterised by the dynamics of the topological charge upon the transformation in SU(3) states. We also realised photonic singlet and triplet states corresponding to SU(4) states, which were projected to SU(2)×SU(2) states upon passing through a rotated polariser.

Анализ компромисса между точностью и сложностью идентифицированных моделей динамических систем

One of the rapidly developing areas of the modern control theory is the identification of systems associated with the construction of mathematical models of systems in the form of a set of mathematical relationships that adequately reflect the basic properties of the system. Symbolic regression methods are becoming more and more popular in the problems of structural-parametric identification of systems based on available observations and experimental data, which allow building regression models in the form of codes of mathematical expressions in a symbolic form. Among the known numerical evolutionary methods of symbolic regression, the universally acknowledged “favorite” is the method of genetic programming”, the application of which allows us to describe the search for solving a problem as the construction of a regression model by enumerating various arbitrary superpositions of functions from some predetermined set. In this case, the important indicators determining the quality of identification of the mathematical model of the system are the accuracy and complexity of the identified model. Often, the system model obtained as a result of solving identification problem is not accurate enough or excessively complex. As a result, the solution to the identification problem is inextricably linked to ensuring sufficient accuracy and simplicity of the identified model. In this connection, it is natural to adhere to the principle of balanced identification, which indicates the search for a compromise between the accuracy of reproduction and the measure of complexity of the identified model. The purpose of this paper, which develops the concept of balanced identification, is to analyze the trade-off between the accuracy and complexity of models of dynamic systems identified by genetic programming. In this paper we introduce a functional "accuracy-complexity", which allows us to balance the trade-off between these key indicators of the identified models when solving the identification problem. The effectiveness of the proposed functional is demonstrated on the example of computer identification by genetic programming of a Lorentz dynamical system.

The role of axial angular momentum in exact non-linear solutions of multipolar spherical and cylindrical vortices

The time-dependent acceleration of fluid particles in an arbitrary superposition of multipolar spherical and cylindrical vortices in presence of a background rotational rigid flow is the gradient of the difference between their kinetic energy and the product of their total axial angular momentum times the angular velocity of the background flow. If the potential energy is defined as the time-dependent field whose minus gradient equals the acceleration of the flow, then the total energy, defined as the sum of kinetic and potential energies, equals the total axial angular momentum times the angular velocity of the background flow. The total energy of a fluid particle has therefore a linear relationship with the azimuthal velocity field. The role of the axial angular momentum in these oscillating flows is explained also in the classical Lagrangian and Hamiltonian descriptions of motion. The linear relation between total energy and angular momentum makes possible that the free parameters of these flows may be obtained, in a way similar to that developed in the quantum mechanics description of motion, as the eigenvalues of linear operators acting on some components of the spherical modes. Beltrami flow solutions in prolate spheroidal geometry for axisymmetric flows are also discussed.

Coherent superposition of states in degenerate systems using zero-area pulses

The coherent superposition of states in degenerate quantum systems is investigated using detuned laser pulses in which the Rabi frequencies are time-dependent, and the pulse area is zero. In this study, a quantum system with an arbitrary number of degenerate states in the ground set as well as an arbitrary number of degenerate states in the exciting set is considered. We assume that all states in the ground set are coupled to the excited states using laser pulses such that the pulse area of Rabi frequency is zero, and all of them have the same time dependence. It is also assumed that all laser pulses are in a non-resonant condition with Bohr transitions, and all detunings are the same. We will show that by applying the appropriate temporal dependence for the pulses and the appropriate rate for the detunings, the population can be transferred from an arbitrary superposition from the ground states to a desired superposition from the excited states.

Quantum transport of high-dimensional spatial information with a nonlinear detector

Information exchange between two distant parties, where information is shared without physically transporting it, is a crucial resource in future quantum networks. Doing so with high-dimensional states offers the promise of higher information capacity and improved resilience to noise, but progress to date has been limited. Here we demonstrate how a nonlinear parametric process allows for arbitrary high-dimensional state projections in the spatial degree of freedom, where a strong coherent field enhances the probability of the process. This allows us to experimentally realise quantum transport of high-dimensional spatial information facilitated by a quantum channel with a single entangled pair and a nonlinear spatial mode detector. Using sum frequency generation we upconvert one of the photons from an entangled pair resulting in high-dimensional spatial information transported to the other. We realise a d = 15 quantum channel for arbitrary photonic spatial modes which we demonstrate by faithfully transferring information encoded into orbital angular momentum, Hermite-Gaussian and arbitrary spatial mode superpositions, without requiring knowledge of the state to be sent. Our demonstration merges the nascent fields of nonlinear control of structured light with quantum processes, offering a new approach to harnessing high-dimensional quantum states, and may be extended to other degrees of freedom too.

Manipulating Coherent Exciton Dynamics in CsPbI3 Perovskite Quantum Dots Using Magnetic Field.

Lead halide perovskite quantum dots (QDs) have recently emerged as a promising material platform for quantum information processing owing to their strong light-matter interaction and relatively long-lived optical and spin coherences. In particular, the coherence of the fine-structure bright excitons is sustainable up to room temperature and can be observed even at an ensemble level. Here modulation of the polarization of these excitons in CsPbI3 QDs and manipulation of their time-domain coherent dynamics using a longitudinal magnetic field are demonstrated. The manipulation is realized using femtosecond quantum beat spectroscopy performed with both circularly- and linearly-polarized pulses. The results are well captured by the density of matrix simulation and are picturized using a Bloch sphere. This study forms the basis for preparing arbitrary coherent superpositions of excitons in perovskite QDs for an array of quantum technologies under near-ambient conditions.

Resource-efficient simulation of noisy quantum circuits and application to network-enabled QRAM optimization

Giovannetti, Lloyd, and Maccone (2008) proposed a quantum random access memory (QRAM) architecture to retrieve arbitrary superpositions of N (quantum) memory cells via quantum switches and O(log (N)) address qubits. Toward physical QRAM implementations, Chen et al. (2021) recently showed that QRAM maps natively onto optically connected quantum networks with O(log (N)) overhead and built-in error detection. However, modeling QRAM on large networks has been stymied by exponentially rising classical compute requirements. Here, we address this bottleneck by: (1) introducing a resource-efficient method for simulating large-scale noisy entanglement, allowing us to evaluate hundreds and even thousands of qubits under various noise channels; and (2) analyzing Chen et al.’s network-based QRAM as an application at the scale of quantum data centers or near-term quantum internet; and (3) introducing a modified network-based QRAM architecture to improve quantum fidelity and access rate. We conclude that network-based QRAM could be built with existing or near-term technologies leveraging photonic integrated circuits and atomic or atom-like quantum memories.

Analog Quantum Bit Based on Pancharatnam‐Berry Phase Metasurfaces

AbstractThe emergence of information metamaterials has spurred significant advances in the field of information sciences. However, the current studies are predominantly focused on classical bits as the fundamental information units, and the classical bit can only be located at two poles of Bloch sphere, resulting in limited information capacity. To break such limit, quantum bits (qubits) offer a promising solution since they have superposition states anywhere on the Bloch sphere. Here, a Pancharatnam‐Berry (PB) phase metasurface is used to emulate the qubits. Firstly, it proposes a theoretical concept of analog quantum bit and develops its mathematical and geometrical representations. Subsequently, a meta‐atom is designed as a physical platform to implement the concept of analog qubits. By manipulating the geometric configuration of the proposed meta‐atom, it achieves arbitrary superpositions of polarization states. A PB phase metasurface is experimentally fabricated to validate that the proposed analog qubit can be used to emulate the quantum bit in terms of both mathematical and geometrical representations. This work not only provides a theoretical foundation to go beyond the information limit of classical bits but also develops a feasible physics platform to investigate quantum information metasurfaces, which would complement and revolutionize classical information science.

Universal quantum control of an atomic spin qubit on a surface

Scanning tunneling microscopy (STM) enables the bottom-up fabrication of tailored spin systems on a surface that are engineered with atomic precision. When combining STM with electron spin resonance (ESR), these single atomic and molecular spins can be controlled quantum-coherently and utilized as electron-spin qubits. Here we demonstrate universal quantum control of such a spin qubit on a surface by employing coherent control along two distinct directions, achieved with two consecutive radio-frequency (RF) pulses with a well-defined phase difference. We first show transformations of each Cartesian component of a Bloch vector on the quantization axis, followed by ESR-STM detection. Then we demonstrate the ability to generate an arbitrary superposition state of a single spin qubit by using two-axis control schemes, in which experimental data show excellent agreement with simulations. Finally, we present an implementation of two-axis control in dynamical decoupling. Our work extends the scope of STM-based pulsed ESR, highlighting the potential of this technique for quantum gate operations of electron-spin qubits on a surface.

Vortex-frequency-comb generation assisted by PT -symmetric ring resonators

We study propagation of optical vortices (OVs) in coupled parity-time ($\mathcal{P}\mathcal{T}$) symmetric multimode fibers with equal gain and loss. We show that this system has two second-order exceptional points (EPs) of spectral branches confluence where the degenerate modes are odd and even Laguerre-Gaussian (LG) modes. We study the evolution of an arbitrary incoming superposition of LG modes with the same orbital index in such a coupler. We prove that if the loss parameter exceeds its value in the lowest-lying EP, in the limit of the large coupler's length the outcoming field tends to the same attractor state depicted on the orbital Poincar\'e sphere (PS) by the orbital ``black hole.'' We show that localization of such a ``black hole'' on the PS does not change with variations of loss parameter beyond its value at the lowest EP, which can be called the pinning of the orbital ``black hole.'' We also demonstrate that the fiber ring resonator based on such a coupler can generate an optical vortex frequency comb (FC) far from the EP. The mechanism of such generation is not connected with any nonlinearity in the system. We determine the coupler's parameters under which such generation is feasible. This property can be useful for optimizing fiber-based orbital angular momentum communications.

Measuring ultrafast time-bin qudits

Time-bin qudits have emerged as a promising encoding platform in many quantum photonic applications. However, the requirement for efficient single-shot measurement of time-bin qudits instead of reconstructive detection has restricted their widespread use in experiments. Here, we propose an efficient method to measure arbitrary superposition states of time-bin qudits and confirm it up to dimension 4. This method is based on encoding time bins at the picosecond time scale, also known as ultrafast time bins. By doing so, we enable the use of robust and phase-stable single spatial mode temporal interferometers to measure time-bin qudit in different measurement bases.

Analytic contact solutions of the Boussinesq and Cattaneo problems for an ellipsoidal power-law indenter

Based on Galin’s theorem for the indentation of an elastic half-space by a polynomial punch and Barber’s theorem for the determination of the contact area in elastic normal contact problems, an exact contact solution is developed for the frictionless indentation of an elastic half-space by an ellipsoidal power-law punch. Within the Cattaneo–Mindlin-approximation of tangential contacts, the tangential contact problem with friction can be reduced to the frictionless normal contact via the Ciavarella–Jäger principle, based on which also the tangential contact solution for the ellipsoidal power-law indenter is given. All known solutions for special cases (axisymmetric contact, elliptical Hertzian contact) are exactly recovered. A comparison of the pressure distribution obtained analytically for the 4-th power ellipsoidal indenter with a corresponding numerical solution based on the boundary element method shows no noticeable differences. The proposed solution procedure can also be used exactly for an arbitrary finite superposition of ellipsoidal power-law profiles, and, in an approximate sense, is applicable for arbitrary monotonous ellipsoidal profiles.

Natural parametrized quantum circuit

Noisy intermediate-scale quantum computers are useful for various tasks such as state preparation and variational quantum algorithms. However, the non-Euclidean quantum geometry of parameterized quantum circuits is detrimental for these applications. Here we introduce the natural parameterized quantum circuit (NPQC) that can be initialized with a Euclidean quantum geometry. The initial training of variational quantum algorithms is substantially sped up as the gradient is equivalent to the quantum natural gradient. Further, we show how to estimate the parameters of the NPQC by sampling the circuit, which could be used for benchmarking or calibrating NISQ hardware. For a general class of quantum circuits, the NPQC has the minimal quantum Cram\'er-Rao bound, which highlights its potential for quantum metrology. Finally, we show how to generate arbitrary superpositions of two states with the NPQCs for state preparation tasks. Our results can be used to enhance currently available quantum processors.

Unidirectional absorption, storage, and emission of single photons in a collectively responding bilayer atomic array

Two-dimensional regular arrays of atoms are a promising platform for quantum networks, with collective subradiant states providing long-lived storage and collimated emission allowing for natural coherent links between arrays in free space. However, a single-layer lattice can only efficiently absorb or emit light symmetrically in the forward and backward directions. Here we show how a bilayer lattice can absorb a single photon either incident from a single direction or an arbitrary superposition of forward and backward propagating components. The excitation can be stored in a subradiant state, transferred coherently between different subradiant states, and released, again in an arbitrary combination of highly collimated forward and backward propagating components. We explain the directionality of single and bilayer arrays by a symmetry analysis based on the scattering parities of different multipole radiation components of collective excitations. The collective modes may exhibit the conventional half-wave loss of fields near the array interface or completely eliminate it. The proposed directional control of absorption and emission paves the way for effective one-dimensional quantum communication between multiple arrays, with single-photons propagating backward and forward between quantum information-processing and storage stages.

Experimental preparation of generalized cat states for itinerant microwave photons

Generalized cat states represent arbitrary superpositions of coherent states, which are of great importance in various quantum information processing protocols. Here we demonstrate a versatile approach to creating generalized itinerant cat states in the microwave domain, by reflecting coherent-state photons from a microwave cavity containing a superconducting qubit. We show that with a coherent control of the qubit state, a full control over the coherent-state superposition can be realized. The prepared cat states are verified through quantum state tomography of the qubit-state-dependent reflection photon field. We further quantify quantum coherence in the prepared cat states based on the resource theory, revealing a good experimental control on the coherent-state superpositions. The photon number statistic and the squeezing properties are also analyzed. Remarkably, fourth-order squeezing is observed in the experimental states. Those results open up new possibilities of applying generalized cat states for the purpose of quantum information processing.

Arbitrary superposition of plasmonic orbital angular momentum states with nanostructures.

A kind of plasmonic nanostructure is proposed that can generate the arbitrary superposition of orbital angular momentum (OAM) states in surface plasmons (SPs), which is achieved by combining the segmented spirals with nanoslit pairs. The structures can independently modulate both the phase and amplitude of SP waves, and thus enable the superposition of two OAM states with arbitrary topological charges (TCs) as well as free control of their relative amplitudes. Superposed states distributed over the entire Bloch sphere and hybrid superposed states with different TCs were constructed and experimentally demonstrated. This work will offer more opportunities for multifunctional plasmonic devices.

Switchable selective interactions in a Dicke model with a driven biased term.

In this work, we propose a method to investigate controllable qubit-resonator interactions in a Dicke model with driven biased term. The nonlinearity of the spectrum, which can be induced by qubit-resonator interactions, plays an important role in such controllable interactions. To gain insight into the mechanism of the nonlinearity, we perform a unitary transformation of the Hamiltonian. The results show that the nonlinearity of the transformed Hamiltonian depends on the qubit-resonator coupling strength. The general forms of the effective Hamiltonians are discussed in detail based on the frequency modulation approach. The dynamical evolution can be switched on and off by adjusting the modulation parameters. By utilizing such controllable interactions, we discuss the creation of Dicke states and the arbitrary superposition of Dicke states. We also consider the nonlinearity of the energy level for the limit of large qubit numbers. In the thermodynamics limit, the Kerr type nonlinearity is induced from "magnon"-resonator coupling, and the selective preparation of "magnon" Fock states can be studied under a "magnon" scenario.