This paper discusses quantum algorithms for the generator coordinate method (GCM) that can be used to benchmark molecular systems. The GCM formalism defined by exponential operators with exponents defined through generators of the fermionic $U\left(N\right)$ Lie algebra (Thouless theorem) offers a possibility of probing large subspaces using low-depth quantum circuits. In the present study, we illustrate the performance of the quantum algorithm for constructing a discretized form of the Hill-Wheeler equation for ground- and excited-state energies. We also generalize the standard GCM formulation to multiproduct extension that when collective paths are properly probed can systematically introduce higher rank effects and provide elementary mechanisms for symmetry purification when generator states break the spatial or spin symmetries. The GCM quantum algorithms also can be viewed as an alternative to existing variational quantum eigensolvers, where multistep classical optimization algorithms are replaced by a single-step procedure for solving the Hill-Wheeler eigenvalue problem.

Quantum computers offer the potential to efficiently simulate the dynamics of quantum systems, a task whose difficulty scales exponentially with system size on classical devices. To assess the potential for near-term quantum computers to simulate many-body systems we develop a formalism to straightforwardly compute bounds on the number of Trotter steps needed to accurately simulate the time evolution of fermionic lattice models based on the first-order commutator scaling. We apply this formalism to two closely related many-body models prominent in condensed matter physics, the Hubbard and t-J models. We find that, while a naive comparison of the Trotter depth first seems to favor the Hubbard model, careful consideration of the model parameters and the allowable error for accurate simulation leads to a substantial advantage in favor of the t-J model. These results and formalism set the stage for significant improvements in quantum simulation costs.

Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model and thus gives an approximate solution of the Hubbard model from the solution of a simpler quantum impurity model. Accurate solutions to the Anderson impurity model nonetheless become intractable for large systems. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models by preparing and evolving the ground state under the impurity Hamiltonian on a quantum computer that is assumed to have the scalability and accuracy far beyond the current state-of-the-art quantum hardware. As a proof of principle demonstration targeting the Anderson impurity model we, for the first time, close the DMFT loop with current noisy hardware. With a highly optimized fast-forwarding quantum circuit and a noise-resilient spectral analysis we observe both the metallic and Mott-insulating phases. Based on a Cartan decomposition, our algorithm gives a fixed depth, fast-forwarding, quantum circuit that can evolve the initial state over arbitrarily long times without time-discretization errors typical of other product decomposition formulas such as Trotter decomposition. By exploiting the structure of the fast-forwarding circuits we reduce the gate count (to 77 cnots after optimization), simulate the dynamics, and extract frequencies from the Anderson impurity model on noisy quantum hardware. We then demonstrate the Mott transition by mapping both phases of the metal-insulator phase diagram. Near the Mott phase transition, our method maintains accuracy where the Trotter error would otherwise dominate due to the long-time evolution required to resolve quasiparticle resonance frequency extremely close to zero. This work presents the first computation on both sides of the Mott phase transition using noisy digital quantum hardware, made viable by a highly optimized computation in terms of gate depth, simulation error, and runtime on quantum hardware. To inform future computations we analyze the accuracy of our method versus a noisy Trotter evolution in the time domain. Both algebraic circuit decompositions and error mitigation techniques adopted could be applied in an attempt to solve other correlated electronic phenomena beyond DMFT on noisy quantum computers.

Controlling the motion of active matter is a central issue that has recently garnered significant attention in fields ranging from nonequilibrium physics to chemical engineering and biology. Distinct methods for controlling active matter have been developed, and physical confinement to limited space and active matter with broken rotational symmetry (chirality) are two prominent mechanisms. However, the interplay between pattern formation due to physical constraints and the ordering by chiral motion needs to be better understood. In this study, we conduct numerical simulations of chiral self-propelled particles under circular boundary confinement. The collective motion of confined self-propelled particles can take drastically different forms depending on their chirality. The balance of orientation changes between particle interaction and the boundary wall is essential for generating ordered collective motion. Our results clarify the role of the steric boundary effect in controlling chiral active matter.

We study a variety of Hofstadter ladders in order to probe the interplay between interactions, an applied magnetic field, and crystalline or quasiperiodic geometries. Motion will be induced on charged particles when a magnetic field is present, which can result in exotic distributions of current on a lattice. Typically, the geometry of a ladder lattice is assumed to be homogeneous. In this paper, however, we will study superlattice and quasicrystalline ladders that possess nonuniform bond lengths, in order to study the formation of localized currents. By using density matrix renormalization group (DMRG) to characterize the quantum phases, we confirm the presence of the usual vortex and Meissner distributions of current, in which particles circulate within the bulk and around the edge respectively. Furthermore, it is also possible to observe variations to these patterns; which combine both vortex and Meissner order, and the onset of incompressible domains for specific fillings of the lattice. If the bond lengths of a ladder fluctuate, we find substantial differences to the structure of currents. This is a consequence of an inhomogeneous, effective magnetic flux, resulting in preferential localization of currents throughout the lattice bulk, towards the smaller bond lengths. We then find that incompressible domains can significantly grow in size extent across the parameter space, with currents no longer possessing an extended structure across the longitudinal direction of the ladder.

The efficiency of particle acceleration at shock waves in relativistic, magnetized astrophysical outflows is a debated topic with far-reaching implications. Here, we study the impact of well-developed turbulence in the pre-shock plasma. Our simulations demonstrate that, for a mildly relativistic magnetized pair shock (Lorentz factor ${\gamma }_{\mathrm{sh}}\simeq 2.7$, magnetization level $\sigma \simeq 0.01$), strong turbulence can revive particle acceleration in a superluminal configuration that otherwise prohibits it. Depending on the initial plasma temperature and magnetization, shock-drift or diffusive-type acceleration governs particle energization, producing power-law spectra $dN/d\gamma \propto {\gamma }^{-s}$ with $s\approx 2.5–3.5$. At larger magnetization levels, stochastic acceleration within the preshock turbulence becomes competitive and can even take over shock acceleration.

We present a method to precisely determine the ${}^{2}D_{3/2}$ state lifetime of a single trapped ${}^{174}\mathrm{Yb}^{+}$ ion. This method is based on the detection of photons emitted from excited states, where a highly synchronized measurement sequence for laser control and an intensity-alternating sequence for atomic excitation and photon counting are used to minimize systematic errors. This method is easy to implement and is immune to fluctuations of magnetic field, laser intensity, and frequency detuning. Combined with the real-time approach of background photon correction, the radiative lifetime of the ${}^{2}D_{3/2}$ state is determined to be $54.83\pm 0.18$ ms, which represents an order of magnitude improvement in measurement precision. The accurately determined lifetime sets a benchmark for many-body atomic theories and is particularly useful to determine the coherence time limit of the optical clock.

Focused beams of electrons, which act as both sources and sensors of electric fields, can be used to characterize the electric response of complex photonic systems by locally probing the induced optical near fields. This functionality can be complemented by embracing the recently developed vortex electron beams (VEBs), made up of electrons with orbital angular momentum, which could, in addition, probe induced magnetic near fields. In this work we revisit the theoretical description of this technique, dubbed vortex electron energy-loss spectroscopy (v-EELS). We map the fundamental, quantum-mechanical picture of the scattering of the VEB electrons to the intuitive classical models, which treat the electron beams as a superposition of linear electric and magnetic currents. We then apply this formalism to characterize the optical response of dielectric nanoantennas with v-EELS. Our calculations reveal that VEB electrons probe electric or magnetic modes with different efficiency, which can be adjusted by changing either beam vorticity or acceleration voltage to determine the nature of the probed excitations. We also study a chirally arranged nanostructure, which in the interaction with electron vortices produces dichroism in electron-energy-loss spectra. Our theoretical work establishes VEBs as versatile probes that could provide information on optical excitations otherwise inaccessible with conventional electron beams.

Two-photon interference underlies the functioning of many quantum photonics devices. It also serves as the prominent tool for testing the indistinguishability of distinct photons. However, as their time-spectral profile becomes more involved, extracting relevant parameters, foremost the central frequency difference, may become difficult. In a parametric approach, these arise from the need for an exhaustive model combined with limited count statistics. Here we discuss a solution to curtail these effects on the evaluation of frequency separation relying on a semiparametric method. The time trace of the quantum interference pattern of two photons from two independent solid-state emitters is preprocessed by means of singular spectral analysis before inspecting its spectral content. This approach allows one to single out the relevant oscillations from both the envelope and the noise, without resorting to fitting. This opens the way for robust and efficient on-line monitoring of quantum emitters.

During morphogenesis, epithelial monolayers actively alter their shape to create future body parts of the animal; this makes the epithelium one of the most active and critical structures in early animal development. While epithelia are often modeled as two-dimensional systems, real epithelia are not necessarily thin relative to cell cross section, and advances in 3D imaging have shown the possibility of substantial cell deformations in the third dimension, as well as differences in dynamics of the apical and basal surfaces indicative of three-dimensional coupling. With the importance of the third dimension in mind, we have developed a self-sculpting, three-dimensional model of epithelia whose dynamics are driven by active forces on its surface. We present a first, fundamental study for a reduced version of epithelia that investigates how surface forces affect its internal dynamics. Our model captures the 3D slab-like geometry of epithelia, viscoelasticity of tissue response, fluid surroundings, and driving from active surface forces. We represent epithelial tissue as a thick slab, a 3D continuum comprised of a Stokes fluid with an extra viscoelastic stress. Employing this model, we present both analytical and numerical solutions of the system and make quantitative predictions about cell shapes, cell dynamics, and the tissue's response to surface force in a three-dimensional setting. In particular, we investigate the implications of our model on the initiation of ventral furrow invagination and T1 transitions in Drosophila embryogenesis. In the former, we demonstrate the importance of fluid and geometric surroundings to drive invagination. In the latter, we show the limitations of surface forces alone to drive T1 transitions.

We propose and experimentally demonstrate the first example of Chern fractal insulators in an acoustic Sierpinski lattice. Through introducing fractality into the well-known Haldane model, we find that the topological phase diagram is significantly squeezed by about 0.5 times, compared with that of the original Haldane model. The energy spectra for different generations of a fractal lattice exhibits a hierarchy of self-similar energy bands in the form of a devil's staircase. With local acoustic measurements, we fabricate the sonic sample based on the theoretical model and experimentally confirm the fractality-induced squeezing and observe the one-way edge states that are protected by a robust mobility gap. Our work demonstrates the fundamental interplay between the fractality and topological Haldane insulator, and may provide new directions for the advanced control of sound waves.

We identify and describe unique early time behavior of a quantum system initially in a superposition, interacting with its environment. This behavior—the copycat process—occurs after the system begins to decohere, but before complete einselection. To illustrate this behavior analytic solutions for the system density matrix, its eigenvalues, and eigenstates a short time after system-environment interactions begin are provided. Features of the solutions and their connection to observables are discussed, including predictions for the continued evolution of the eigenstates towards einselection, time dependence of spin expectation values, and an estimate of the system's decoherence time. In particular we explore which aspects of the early stages of decoherence exhibit quadratic evolution to leading order, and which aspects exhibit more rapid linear behavior. Many features of our early time perturbative solutions are agnostic of the spectrum of the environment. We also extend our work beyond short time perturbation theory to compare with numerical work from a companion paper.

We present a variant of the Caldeira-Leggett (CL) model of a harmonic oscillator coupled to an environment. The CL model is a standard tool for studying the physics of decoherence. Our “adapted Caldeira-Leggett” (ACL) model is built in a finite Hilbert space which makes it suitable for numerical studies. Taking a numerical approach allows us to avoid the limitations of standard approximation schemes used with the CL model. We are able to evolve the ACL model in a fully reversible unitary manner, without the built-in time asymmetry and other assumptions that come with the master equation methods typically used. We have used the ACL model to study topics in the field of decoherence and einselection where the full unitary evolution is essential to our work. Those results (reported in companion papers) include an examination of the relationship between einselection and the arrow of time, and studies of the very earliest stages of einselection. This paper provides details about the ACL model and our numerical methods. Our numerical approach makes it straightforward to explore and plot any property of the physical system. Thus we believe the examples and illustrations we present here may provide a helpful resource for those wishing to improve their familiarity with standard decoherence results, as well as those looking to probe the underpinnings of our companion papers. We expect the ACL model will be a useful tool for exploring additional phenomena that cannot be studied using traditional approximation schemes.

Machine learning (ML) methods such as artificial neural networks are rapidly becoming ubiquitous in modern science, technology, and industry. Despite their accuracy and sophistication, neural networks can be easily fooled by carefully designed malicious inputs known as adversarial attacks. While such vulnerabilities remain a serious challenge for classical neural networks, the extent of their existence is not fully understood in the quantum ML setting. In this paper, we benchmark the robustness of quantum ML networks, such as quantum variational classifiers (QVC), at scale by performing rigorous training for both simple and complex image datasets and through a variety of high-end adversarial attacks. Our results show that QVCs offer a notably enhanced robustness against classical adversarial attacks by learning features, which are not detected by the classical neural networks, indicating a possible quantum advantage for ML tasks. Contrarily, and remarkably, the converse is not true, with attacks on quantum networks also capable of deceiving classical neural networks. By combining quantum and classical network outcomes, we propose an adversarial attack detection technology. Traditionally quantum advantage in ML systems has been sought through increased accuracy or algorithmic speed-up, but our study has revealed the potential for a kind of quantum advantage through superior robustness of ML models, whose practical realization will address serious security concerns and reliability issues of ML algorithms employed in a myriad of applications including autonomous vehicles, cybersecurity, and surveillance robotic systems.

Ultracold atoms are an ideal platform for understanding system-reservoir dynamics of many-body systems. Here, we study quantum back-action in atomic Bose-Einstein condensates, weakly interacting with a far-from resonant, i.e., dispersively interacting, probe laser beam. The light scattered by the atoms can be considered as a part of quantum measurement process, whereby the change in the system state derives from measurement back-action. We experimentally quantify the resulting back-action in terms of the deposited energy. We model the interaction of the system and environment with a generalized measurement process, leading to a Markovian reservoir. Further, we identify two systematic sources of heating and loss: a stray optical lattice and probe-induced light-assisted collisions (an intrinsic atomic process). The observed heating and loss rates are larger for blue detuning than for red detuning, where they are oscillatory functions of detuning with increased loss at molecular resonances and reduced loss between molecular resonances.

We consider the magnetically tunable Feshbach resonances that may exist in ultracold mixtures of molecules in ${}^2\mathrm{\Sigma }$ states and alkali-metal atoms. We focus on $\mathrm{Rb}+\mathrm{CaF}$ as a prototype system. There are likely to be Feshbach resonances analogous to those between pairs of alkali-metal atoms. We investigate the patterns of near-threshold states and the resonances that they cause, using coupled-channel calculations of the bound states and low-energy scattering on model interaction potentials. We explore the dependence of the properties on as-yet-unknown potential parameters. There is a high probability that resonances will exist at magnetic fields below 1000 G, and that these will be broad enough to control collisions and form triatomic molecules by magnetoassociation. We consider the effects of CaF rotation and anisotropy of the interaction potential, and conclude that they may produce additional resonances but should not affect the existence of rotation-free resonances.