Quantum transport can be simulated with ultracold atoms by employing spin superpositions of fermions interacting with spin-dependent potentials. Here we first extend this scheme to an arbitrary number of spin components so as to allow simulating transport through a multiterminal quantum dot and derive a current formula in terms of a spin rotation matrix and potential phase shifts. We then show that a Fano resonance manifests itself in measuring a linear conductance at zero temperature in the case of two spin components. We also study how a weak interparticle interaction in bulk affects quantum transport in one dimension with the bosonization and renormalization techniques. In particular, we find that the conductance vanishes for an attractive interaction due to a bulk spin gap, while it is enhanced for a repulsive interaction by a power law with lowering the temperature or the chemical potential difference.

We compute the error threshold for the semion code, the companion of the Kitaev toric code with the same gauge symmetry group ${\mathbb{Z}}_2$. The application of statistical mechanical mapping methods is highly discouraged for the semion code, since the code is non-Pauli and non-Calderbank-Shor-Steane (CSS). Thus, we use machine learning methods, taking advantage of the near-optimal performance of some neural network decoders: multilayer perceptrons and convolutional neural networks (CNNs). We find the values $p_{\text{eff}}=9.5\%$ for uncorrelated bit-flip and phase-flip noise, and $p_{\text{eff}}=10.5\%$ for depolarizing noise. We contrast these values with a similar analysis of the Kitaev toric code on a hexagonal lattice with the same methods. For convolutional neural networks, we use the ResNet architecture, which allows us to implement very deep networks and results in better performance and scalability than the multilayer perceptron approach. We analyze and compare in detail both approaches and provide a clear argument favoring the CNN as the best suited numerical method for the semion code.

As a ubiquitous aspect of modern information technology, data compression has a wide range of applications. Therefore, a quantum autoencoder which can compress quantum information into a low-dimensional space is fundamentally important to achieve automatic data compression in the field of quantum information. Such a quantum autoencoder can be implemented through training the parameters of a quantum device using classical optimization algorithms. In this paper, we demonstrate the condition of achieving a perfect quantum autoencoder and theoretically prove that a quantum autoencoder can losslessly compress high-dimensional quantum information into a low-dimensional space (also called latent space) if the number of maximum linearly independent vectors from input states is no more than the dimension of the latent space. Also, we experimentally realize a universal two-qubit unitary gate and design a quantum autoencoder device by applying a machine learning method. Experimental results demonstrate that our quantum autoencoder is able to compress two two-qubit states into two one-qubit states. Besides compressing quantum information, the quantum autoencoder is used to experimentally discriminate two groups of nonorthogonal states.

Gauge theories appear broadly in physics, ranging from the standard model of particle physics to long-wavelength descriptions of topological systems in condensed matter. However, systems with sign problems are largely inaccessible to classical computations and also beyond the current limitations of digital quantum hardware. In this work, we develop an analog approach to simulating gauge theories with an experimental setup that employs dipolar spins (molecules or Rydberg atoms). We consider molecules fixed in space and interacting through dipole-dipole interactions, avoiding the need for itinerant degrees of freedom. Each molecule represents either a site or gauge degree of freedom, and Gauss's law is preserved by a direct and programmatic tuning of positions and internal state energies. This approach can be regarded as a form of analog systems programming and charts a path forward for near-term quantum simulation. As a first step, we numerically validate this scheme in a small-system study of $\mathrm{U}\left(1\right)$ quantum link models in ($1+1$) dimensions with link spin $S=1/2$ and $S=1$ and illustrate how dynamical phenomena such as string inversion and string breaking could be observed in near-term experiments. Our work brings together methods from atomic and molecular physics, condensed matter physics, high-energy physics, and quantum information science for the study of nonperturbative processes in gauge theories.

Probabilistic storage and retrieval (PSR) of unitary quantum dynamics is possible with exponentially small failure probability with respect to the number of systems used as a quantum memory [M. Sedlák, A. Bisio, and M. Ziman, Phys. Rev. Lett. 122, 170502 (2019)]. Here we study improvements due to a priori knowledge about the unitary transformation to be stored. In particular, we study $N\to 1$ PSR of qubit phase gates, i.e., qubit rotations around the $Z$ axis with an unknown angle, and show that if we access the gate only $N$ times the optimal probability of perfect retrieving of its single use is $N/(N+1)$. We propose a quantum circuit realization for the optimal protocol and show that a programmable phase gate [G. Vidal, L. Masanes, and J. I. Cirac, Phys. Rev. Lett. 88, 047905 (2002)] can be turned into a $(2^k-1)\to 1$ optimal PSR of phase gates and requires only $k$ controlled-not gates, while having exponentially small failure probability in $k$.

We present a theoretical and experimental study of the electronic structure of $N$-methyltrifluoroacetamide (FNMA) and examine the resonant Auger (RA) decay upon site- and state-specific excitation at the C $1s$, N $1s$, and O $1s$ edges. Based on the calculated energies for cationic states of $1h$ and $2h\text{−}1p$ configurations, we assign the peaks of recorded VUV photoelectron and RA spectra. Specifically, we identify the spectral features associated with participator and spectator RA decay. To aid in a deeper understanding of previous observations of limited site-specific bond breaking in FNMA, the influence of the site-specific excitation and the character of the Auger decay on the fragmentation is investigated using Auger electron ion coincidence experiments. Moreover, to investigate the potentially different capacity for selective bond cleavage of participator and spectator Auger states, we apply this technique to the spectator Auger state with the main electronic configuration of ${\left(31a^{\prime }\right)}^{-1}{\left(32a^{″}\right)}^{-1}{\left(34a^{″}\right)}^1$, which is well resolved in the experimental spectrum. Finally, the influence of the molecular excess energy and the electronic character of the RA final states on fragmentation is addressed. Based on our findings, we argue that the excess energy the FNMA molecule gains upon RA decay is the dominant factor determining the fragmentation pattern.

Anderson localization is a single-particle localization phenomena in disordered media that is accompanied by an absence of diffusion. Spin-orbit coupling (SOC) describes an interaction between a particle's spin and its momentum that directly affects its energy dispersion, for example, creating dispersion relations with gaps and multiple local minima. We show theoretically that combining one-dimensional spin-orbit coupling with a transverse Zeeman field suppresses the effects of disorder, thereby increasing the localization length and conductivity. This increase results from a suppression of backscattering between states in the gap of the SOC dispersion relation. Here, we focus specifically on the interplay of disorder from an optical speckle potential and SOC generated by two-photon Raman processes in quasi-one-dimensional Bose-Einstein condensates. We first describe backscattering by using a Fermi golden rule approach, and then numerically confirm this picture by solving the time-dependent one-dimensional Gross–Pitaevskii equation for a weakly interacting Bose-Einstein condensate with SOC and disorder. We find that on the tens of millisecond timescale of typical cold atom experiments moving in harmonic traps, initial states with momentum in the zero-momentum SOC gap evolve with negligible backscattering, while without SOC these same states rapidly localize.

Strongly correlated phases of matter are often described in terms of straightforward electronic patterns. This has so far been the basis for studying the Fermi-Hubbard model realized with ultracold atoms. Here, we show that artificial intelligence (AI) can provide an unbiased alternative to this paradigm for phases with subtle, or even unknown, patterns. Long- and short-range spin correlations spontaneously emerge in filters of a convolutional neural network trained on snapshots of single atomic species. In the less well-understood strange metallic phase of the model, we find that a more complex network trained on snapshots of local moments produces an effective order parameter for the non-Fermi-liquid behavior. Our technique can be employed to characterize correlations unique to other phases with no obvious order parameters or signatures in projective measurements, and has implications for science discovery through AI beyond strongly correlated systems.

We present a method for measuring nonharmonic contributions to the trapping potential of a cold atomic gas by measuring the dynamics of the cloud. This method can be used to minimize the anharmonicity of a trap, or to tune the quartic anharmonicity to some desired level in a sufficiently tunable trap. We present an approximate solution to the dynamics of a classical noninteracting cloud of thermal atoms in a cigar-shaped harmonic trap with a quartic perturbation along the weakly confined axis which is analytical and closed form. We calculate the first and second moments of position along the weak axis as functions of time, which is sufficient to characterize the trap. The dynamics of the thermal cloud differ notably from those of a single particle, with an offset to the oscillation frequency that persists even as the oscillation amplitude approaches zero. We also present some numerical results that describe the effects of time of flight on the behavior of the cloud in order to better understand the results of a hypothetical experimental realization of this system.

Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second- or higher-order EPs have been proposed or realized. In contrast, quantum information studies of $\mathcal{PT}$-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here, by using a single-photon interferometry setup, we simulate the quantum dynamics of a four-dimensional $\mathcal{PT}$-symmetric system across a fourth-order exceptional point. By tracking the coherent, nonunitary evolution of the density matrix of the system in $\mathcal{PT}$-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional $\mathcal{PT}$-symmetric systems, and our results point towards the rich dynamics and critical properties.

Ultracold atom-ion collisions are an emerging field of research that can ultimately lead to their precise quantum control. In collisions in which the ion is prepared in an excited state, previous studies showed that the dominant reaction pathway was charge exchange. Here, we explored the outcome products and the energy released from a single ultracold collision between a single ${}^{88}\mathrm{Sr}^{+}$ ion and a single ${}^{87}\mathrm{Rb}$ atom prepared in excited metastable and ground electronic states, respectively, with control over their relative spins. We found that the ion's long-lived $D_{5/2}$ and $D_{3/2}$ states quench after roughly three collisions, acquiring immense kinetic energy in the process. By performing single-shot thermometry on the ion after the collision, we identified two dominant reaction pathways: electronic excitation exchange and spin-orbit change. In contrast to previous experiments, we observed no charge-exchange events. These processes are theoretically understood to occur through Landau-Zener avoided crossings leading to the observed reaction pathways. We also found that spin orientation has almost no effect on the reaction pathways, due to strong Coriolis-spin mixing. Our results provide a deeper understanding of ultracold atom-ion inelastic collisions and offer additional quantum control tools for the cold chemistry field.

We consider the space of $n\times n$ non-Hermitian Hamiltonians ($n=2$, 3, ...) that are equivalent to a single $n\times n$ Jordan block. We focus on adiabatic transport around a closed path (i.e., a loop) within this space, in the limit as the time scale $T=1/\varepsilon$ taken to traverse the loop tends to infinity. We show that, for a certain class of loops and a choice of initial state, the state returns to itself and acquires a complex phase that is ${\varepsilon }^{-1}$ times an expansion in powers of ${\varepsilon }^{1/n}$. The exponential of the term of $n\mathrm{th}$ order (which is equivalent to the “geometric” or Berry phase modulo $2\pi$) is thus independent of $\varepsilon$ as $\varepsilon \to 0$; it depends only on the homotopy class of the loop and is an integer power of $e^{2\pi i/n}$. One of the conditions under which these results hold is that the state being transported is, for all points on the loop, that of slowest decay.

A model of a quantum measurement process is presented: a system consisting of a qubit in a superposition interacts with a measuring apparatus consisting of a $N$ qubit state. Looking at the emerging, effective description of the apparatus given by the action of a coarse-graining channel, we have been able to recover information about the superposition coefficients of the system. We have also been able to visualize the death of quantum correlations between system and apparatus and the death of quantum coherences in the apparatus' effective state, in the limit of a strong coarse-graining action—a situation akin to decoherence, although it is not necessary to evoke any interaction with the surrounding environment.

We obtain exact dynamics of a two-qubit central spin model (CSM) consisting of two interacting qubits homogeneously coupled to a spin bath via the $XXZ$-type coupling, with the bath initially prepared in linear superpositions of the symmetric Dicke states. Using the interaction picture Hamiltonian with respect to the non-spin-flipping part of the model, we derive a sequence of equations of motion within each magnetization sector satisfied by the probability amplitudes of the time-evolved state. These equations of motion admit analytical solutions for the single-qubit CSM in which one of the two central qubits decouples from the rest of the system. Based on this, we provide a quantitative interpretation to the observed collapse-revival phenomena in the single-qubit Rabi oscillations when the bath is prepared in the spin coherent state. We then study the disentanglement and coherence dynamics of two initially entangled noninteracting qubits when the two qubits interact with individual baths or with a common bath. For individual baths, the coherent dynamics is found to be positively correlated to the single-qubit purity dynamics, and entanglement sudden disappearance and revivals are observed in both cases. The entanglement creation of two initially separable qubits coupled to a common bath is also studied and collapse and revival behaviors in the entanglement dynamics are observed. Choosing the equally weighted state and the $W$-class states as the bath initial states, we finally study the dynamics of entanglement between two individual bath spins and demonstrate the entanglement sharing mechanism in such a system.

The correlation alignment algorithm (CORAL), a representative domain adaptation algorithm, decorrelates and aligns a labeled source domain dataset to an unlabeled target domain dataset to minimize the domain shift such that a classifier can be applied to predict the target domain labels. In this paper, we implement the CORAL on quantum devices by two different methods. One method utilizes quantum basic linear algebra subroutines to implement the CORAL with exponential speedup in the number and dimension of the given data samples. The other method is achieved through a variational hybrid quantum-classical procedure. In addition, the numerical experiments of the CORAL with three different types of data sets, namely, the synthetic data, the synthetic-Iris data, and the handwritten digit data, are presented to evaluate the performance of our paper. The simulation results prove that the variational quantum correlation alignment algorithm can achieve competitive performance compared with the classical CORAL.

Parity ($\mathcal{P}$)–violating pseudoscalar or pseudovector cosmic fields are invoked in different models for cold dark matter or in the standard model extension that allows for Lorentz invariance violation. A direct detection of the timelike component of such fields requires a direct measurement of $\mathcal{P}$-odd potentials or their evolution over time. Herein, advantageous properties of chiral molecules, in which $\mathcal{P}$-odd potentials lead to resonance frequency differences between enantiomers, for direct detection of such $\mathcal{P}$-odd cosmic field interactions are demonstrated. Scaling behavior of electronic structure enhancements of such interactions with respect to nuclear charge number and the fine-structure constant is derived analytically. This allows a simple estimate of the effect sizes for arbitrary molecules. The analytical derivation is supported by quasirelativistic numerical calculations in the molecules ${\mathrm{H}}_2{X}_2$ and ${\mathrm{H}}_{2}X\mathrm{O}$ with $X =$ O, S, Se, Te, or Po. Parity-violating effects due to cosmic fields on the C–F stretching mode in CHBrClF are compared to electroweak parity violation and influences of nonseparable anharmonic vibrational corrections are discussed. On this basis, Gaul et al. [Phys. Rev. Lett. 125, 123004 (2020)] estimated from a 20-year-old experiment with CHBrClF that bounds on Lorentz invariance violation as characterized by the parameter $|b_0^{\mathrm{e}}|$ can be pushed down to the order of ${10}^{-17}\mathrm{GeV}$ in modern experiments with suitably selected molecular system, which will be an improvement of the current best limits by at least two orders of magnitude. This serves to highlight the particular opportunities that precision spectroscopy of chiral molecules provides in the search for new physics beyond the standard model.

Quantum optimal control (QOC) is the field devoted to the production of external control protocols that actively guide quantum dynamics. Solutions to QOC problems were shown to constitute continuous submanifolds of control space. A solution navigation method exploiting this property to achieve secondary features in the control protocols was proposed [Larocca, Calzetta, and Wisniacki, Phys. Rev. A 101, 023410 (2020)]. Here, we present a navigation-powered protocol postprocessing mechanism allowing naturally inflexible optimization algorithms to produce user-customized solutions, for example, in terms of a Fourier decomposition. We test the performance of the method in two inherently different models: the two-level Landau-Zener system and the quantum harmonic oscillator.

We explore high-order soliton evolution in a composite all-normal dispersion photonic crystal fiber with frequency-dependent doping nonlinearity that can vary from positive to negative and vanish at a specific wavelength, named the zero-nonlinearity wavelength (ZNW). The change in frequency dependence of doping nonlinearity dramatically adjusts the position of the ZNW and the nonlinear strength acting on the supercontinuum spectral component. As the negative (positive) frequency dependence decreases (increases), one of two generated fundamental solitons via the combined action of negative nonlinearity and normal dispersion first has a gradually boosting soliton self-frequency shift (SSFS), and then a more suppressed SSFS, but is finally limited within an increasingly small spectral range while the other has a gradually decreasing SSFS toward the ZNW and radiates a broader and stronger phase-matched dispersive wave (DW) in the nonsolitonic region. Note that the collision between two fundamental solitons plays a significant role in regulating their temporal and spectral shift as well as energy redistribution. Furthermore, the numeric sign of the frequency dependence of doping nonlinearity provides another potential tool in controlling the spectral shift direction of fundamental solitons and DWs.

This paper studies the existence of electromagnetic surface waves localized on a boundary of half-infinite periodic superlattices formed by an arbitrary periodic sequence of layers of homogeneous or functionally graded materials with generally anisotropic dielectric permittivity and magnetic permeability tensors. The geometry in question implies either two superlattices attached together to form a photonic bicrystal or else a superlattice in contact with vacuum or any other homogeneous dielectric or metal. Using the formalism of transfer and impedance matrices, a series of statements is proved on the maximum number of surface waves which may exist within a forbidden band at a fixed tangential wave number. This number embraces possible occurrences of surface waves in a given bicrystal and in its counterpart obtained by swapping the upper and lower superlattices. A maximum total number of surface waves in both these structures with an arbitrary arrangement of their unit cells is 2 in the lowest forbidden band (extending from zero frequency) and 4 in any upper forbidden band. The same statements apply to the case where one of the half spaces is occupied by a homogeneous material. A factor 2 smaller number of surface waves occur in a bicrystal composed of superlattices with a symmetric arrangement of unit cells. The existence considerations are further specialized for the surface waves with TE and TM polarizations.

Quantum mechanics allows the occurrence of events without having any definite causal order. We show that the application of two different thermal channels in causally inseparable order can enhance the potential to extract work, in contrast to any of their definite order of occurrence. Surprisingly, this enhancement is possible even without assigning any thermodynamic resource value to the input qubits. Further, we provide a nontrivial example of causal enhancement using nonunital pin maps, the realization of which, in the superposition of path framework, has not been clearly known. Hence, our result may be a potential candidate to accentuate the difference between superposition of time and superposition of paths frameworks.