Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using simulations on modern-day devices. Therefore, the inherent physical limitations of the device on the parameters of the simulation must be understood. This paper examines the interplay of errors arising from simulation of approximate time evolution with those due to practical, real-world device constraints. These errors are studied in Heisenberg-type systems on analog quantum devices described by the Ising Hamiltonian. A general framework for quantifying these errors is introduced and applied to several proposed time evolution methods, including Trotter-like methods and Floquet-engineered constant-field approaches. The limitations placed on the accuracy of time evolution methods by current devices are discussed. Characterization of the scaling of coherent effects of different error sources provides a way to extend the presented Hamiltonian engineering methods to take advantage of forthcoming device capabilities.

We have applied a machine learning algorithm to predict the emergence of environment-induced spontaneous synchronization between two qubits in an open system setting. In particular, we have considered three different models, encompassing global and local dissipation regimes, to describe the open system dynamics of the qubits. We have utilized the $k$-nearest-neighbor algorithm to estimate the long-time synchronization behavior of the qubits only using the early time expectation values of qubit observables in these three distinct models. Our findings clearly demonstrate the possibility of determining the occurrence of different synchronization phenomena with high precision even at the early stages of the dynamics using a machine learning-based approach. Moreover, we show the robustness of our approach against potential measurement errors in experiments by considering random errors in the qubit expectation values, initialization errors, as well as deviations in the environment temperature. We believe that the presented results can prove to be useful in experimental studies on the determination of quantum synchronization.

Boson sampling is a sampling task proven to be hard to simulate efficiently using classical computers under plausible assumptions, which makes it an appealing candidate for quantum advantage. However, due to a large noise rate for near-term quantum devices, it is still unclear whether those noisy devices maintain the quantum advantage for much larger quantum systems. Since the noise rate typically grows with the circuit depth, an alternative is to find evidence of simulation hardness at the shallow-depth quantum circuit. To find the evidence, one way is to identify the minimum depth required for the average-case hardness of approximating output probabilities, which is considered a necessary condition for the state-of-the-art technique to prove the simulation hardness of boson sampling. In this work, we analyze the output probability distribution of shallow-depth boson sampling for Fock states and Gaussian states and examine the limitation of the average-case hardness argument at this shallow-depth regime for geometrically local architectures. We propose a shallow-depth linear optical circuit architecture that can overcome the problems associated with geometrically local architectures. Our numerical results suggest that this architecture demonstrates possibilities of average-case hardness properties in a shallow-depth regime through its resemblance to the global Haar-random boson sampling circuit. This result implies that the corresponding architecture has the potential to be utilized for scalable quantum advantage with its shallow-depth boson sampling.

We derive analytically the leading beyond-mean-field contributions to the zero-temperature equation of state and to the fermionic quasiparticle residue and effective mass of a dilute Bose-Fermi mixture in two dimensions. In the repulsive case, we perform quantum Monte Carlo simulations for two representative bosonic concentrations and equal masses, extending a method for correcting finite-size effects in fermionic gases to Bose-Fermi mixtures. We find good agreement between analytic expressions and numerical results for weak interactions, while significant discrepancies appear in the regime close to mechanical instability, above which we provide evidence of phase separation of the bosonic component.

The Gottesman-Kitaev-Preskill (GKP) code offers the possibility to encode higher-dimensional qudits into individual bosonic modes with, for instance, photonic excitations. Since photons enable the reliable transmission of quantum information over long distances and since GKP states subject to photon loss can be recovered to some extent, the GKP code has found recent applications in theoretical investigations of quantum communication protocols. While previous studies have primarily focused on GKP qubits, the possible practical benefits of higher-dimensional GKP qudits are hitherto widely unexplored. In this paper, we carry out performance analyses for three quantum repeater protocols based on GKP qudits including concatenations with a multiqudit quantum polynomial code. We find that the potential data transmission gains for qudits are often hampered by their decreased GKP error-correcting capabilities. However, we also identify parameter regimes in which having access to an increased number of quantum levels per mode can enhance the theoretically achievable secret-key rate of the quantum repeater. Some of our protocols share the attractive feature that local processing and complete error syndrome identification are realizable without online squeezing. Provided a supply of suitable multimode GKP states is available, this can be realized with a minimal set of passive linear optical operations, even when the logical qudits are composed of many physical qudits.

The long-range electrostatic interactions between molecules depend strongly on their relative orientation, which manifests as a rotational-state dependence. Interactions between molecules in the same rotational quantum state are well-known attractive rotational van der Waals interactions. Interactions in rotational states that differ by one quantum show resonant dipole-dipole interactions. We show that where molecules are in rotational states that differ by more than one quantum, they exhibit repulsive van der Waals interactions. At temperatures below a millikelvin, this effect can reduce collisional loss by multiple orders of magnitude. These repulsive interactions lead to applications in quantum simulation and impurity physics with ultracold polar molecules.

Time-periodic systems allow engineering new effective Hamiltonians from limited physical interactions. For example, the inverted position of the Kapitza pendulum emerges as a stable equilibrium with rapid drive of its pivot point. In this work we propose the Kapitzonium: a Floquet qubit that is the superconducting circuit analog of a mechanical Kapitza pendulum. Under periodic driving, the bit- and phase-flip rates of the emerging qubit states are exponentially suppressed with respect to the ratio of the effective Josephson energy to charging energy. However, we find that dissipation causes leakage out of the Floquet qubit subspace. We engineer a passive cooling scheme to stabilize the qubit subspace, which is crucial for high-fidelity quantum control under dissipation. Furthermore, we introduce a hardware-efficient fluorescence-based method for qubit measurement and discuss the experimental implementation of the Floquet qubit. Our work provides the fundamental steps to develop more complex Floquet quantum systems from the ground up to realize large-scale protected engineered dynamics.

Recent advancements in abilities to create and manipulate the electron's transverse wave function within the transmission electron microscope (TEM) and scanning TEM have enabled vectorially resolved electron-energy-loss (EEL) and -gain (EEG) measurements of nanoscale and quantum material responses using pre- and postselected free-electron states. This newfound capability is prompting renewed theoretical interest in quantum-mechanical treatments of inelastic-electron-scattering observables and the information they contain. Here we present a quantum-mechanical treatment of the inelastic scattering of free electrons between pre- and postselected transverse states with fully retarded electron-sample interactions for both spontaneous EEL and continuous-wave laser-stimulated EEG measurements. General expressions for the state-resolved energy-loss and -gain rates are recast in forms amenable to numerical calculation using the method of coupled dipoles. We numerically implement our theory within the electron-driven discrete dipole approximation code and use it to investigate specific examples that highlight its versatility regarding the number, size, geometry, and material composition of the target specimen as well as its ability to describe matter-wave diffraction from finite nanoscopic targets.

Unless constrained by symmetry, measurement of an observable on an ensemble of identical quantum systems returns a distribution of values which are encoded in the full counting statistics. While the mean value of this distribution is important for determining certain properties of a system, the full distribution can also exhibit universal behavior. In this paper we study the full counting statistics of particle number in one-dimensional interacting Bose and Fermi gases which have been quenched far from equilibrium. In particular, we consider the time evolution of the Lieb-Liniger and Gaudin-Yang models quenched from a Bose-Einstein condensate initial state and calculate the full counting statistics of the particle number within a subsystem. We show that the scaled cumulants of the charge in the initial state and at long times are simply related and, in particular, the latter are independent of the model parameters. Using the quasiparticle picture we obtain the full time evolution of the cumulants and find that although their end points are fixed, the finite-time dynamics depends strongly on the model parameters. We go on to construct the scaled cumulant generating functions and from this determine the limiting charge probability distributions at long time which are shown to exhibit distinct, nontrivial, and non-Gaussian fluctuations and large deviations.

In classical optics, there is a well-known resolution limit called Rayleigh's curse in the separation of two incoherent optical sources in close proximity. Recently, Tsang et al. [Phys. Rev. X 6, 031033 (2016)] revealed that this difficulty may be circumvented in the framework of quantum theory. Following their work, various estimation methods have been proposed to overcome Rayleigh's curse, but none of them enables us to estimate the positions of two point sources simultaneously based on single-photon measurements with high accuracy. In this study, we propose a method to simultaneously estimate the positions of two point sources with the highest accuracy using an adaptive quantum state estimation scheme.

Sympathetic cooling of ${\mathrm{Th}}^{3+}$ ions is demonstrated in an experiment where ${}^{229}\mathrm{Th}$ and ${}^{230}\mathrm{Th}$ are extracted from uranium recoil-ion sources and are confined in a linear Paul trap together with laser-cooled ${}^{88}\mathrm{Sr}^{+}$ ions. Because of their similar charge-to-mass ratios the ions are closely coupled and arrange themselves into two-species Coulomb crystals containing up to a few tens of ${\mathrm{Th}}^{3+}$ ions. To show the suitability of the sympathetically cooled ${\mathrm{Th}}^{3+}$ ions for high-resolution laser spectroscopy, the absolute frequencies and isotope shifts of $5F_{5/2}\to 6D_{5/2}$ and $5F_{7/2}\to 6D_{5/2}$ transitions of ${}^{230}\mathrm{Th}^{3+}$ are measured. The system is developed for hyperfine spectroscopy of electronic transitions of nuclear ground and isomeric states in ${}^{229}\mathrm{Th}^{3+}$.

In recent twenty years, the research on nuclear clocks based on Th nuclear transition has become increasingly intensive. Among them, solid-state nuclear clocks based on thorium-doped crystals are considered to have unique advantages in the detections of accurate energy and lifetime of nuclear isomers and the stability and miniaturization of optical clocks. In this work, The feasibility and potential of using Th:$\mathrm{BaLi}{\mathrm{F}}_3$ single crystal as a solid-state nuclear clock material was calculated and predicted by using density functional theory (DFT). The theoretical results showed that Th ions could be effectively doped in $\mathrm{BaLi}{\mathrm{F}}_3$ crystal through a suitable charge compensation mechanism, and only slightly decreased the transmittance of $\mathrm{BaLi}{\mathrm{F}}_3$ crystal in the nuclear transition band. On this basis, a Th:$\mathrm{BaLi}{\mathrm{F}}_3$ single crystal was successfully grown through experiments. Th concentration of the as-grown crystal can reach $3.13\times {10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$, and the transmittance can reach $T$ ∼ 50% at ∼150 nm. Compared with the pure $\mathrm{BaLi}{\mathrm{F}}_3$ crystal grown under similar conditions, it only slightly decreased. The Th:$\mathrm{BaLi}{\mathrm{F}}_3$ single crystal is expected to be a potential candidate for solid-state nuclear clock material.

We study the effect of electron-electron correlations on the quantum state of the light emitted from high-harmonic generation (HHG). The quantum state of the emitted light is obtained by using a fully quantum-mechanical description of both the optical modes as well as the electronic system. This is different from the usual semiclassical description of HHG, which only treats the electronic target system quantum mechanically. Using the generic Fermi-Hubbard model, the strength of the electron-electron correlation can be treated as a parameter enabling us to investigate the two limiting cases of a completely uncorrelated phase and a correlated Mott-insulating phase. In the completely uncorrelated phase, the model reduces to a single-band tight-binding model in which only intraband currents contribute to the spectrum. In this limit, we analytically find that the emitted light is in a classical coherent state. In the Mott-insulating phase, a consideration of the photon statistics and squeezing of the emitted photonic state shows that the inter-Hubbard-subband current generates nonclassical light. In this sense, we show that electron-electron correlation can induce the generation of nonclassical states of light.

We analyze the formation of three-dimensional spatiotemporal solitons in waveguides with a parabolic refractive index profile and pure quartic chromatic dispersion. We show, by applying both variational approaches and full three-dimensional numerical simulations, that fourth-order dispersion has a positive impact on soliton stabilization against spatiotemporal wave collapse. Specifically, pure quartic spatiotemporal solitons remain stable within a significantly larger energy range with respect to their second-order dispersion counterparts.

We demonstrate a method for determining the three-dimensional location of single atoms in a quantum gas microscopy system using a phase-only spatial light modulator to modify the point-spread function of the high-resolution imaging system. Here, the typical diffracted spot generated by a single atom as a point source is modified to a double spot that rotates as a function of the atom's distance from the focal plane of the imaging system. We present and numerically validate a simple model linking the rotation angle of the point-spread function with the distance to the focal plane. We show that, when aberrations in the system are carefully calibrated and compensated for, this method can be used to determine an atom's position to within a single lattice site in a single experimental image, extending quantum simulation with microscopy systems further into the regime of three dimensions.

We introduce a family of quantized field states that can perform exact (entanglement- and error-free) rotations of a two-level atom starting from a specific state on the Bloch sphere. We discuss the similarities and differences between these states and the recently introduced transcoherent states. Our field states have the property that they are left unchanged after the rotation, and we find they are the asymptotic states obtained when a field interacts with a succession of identically prepared ancillary atoms. Such a scheme was recently proposed [npj Quantum Inf. 3, 17 (2017)] as a way to “restore” a field state after its interaction with a two-level atom, so as to reuse it afterward, thus reducing the energy requirements for successive quantum logical operations. We generalize this scheme to find optimal pulses for arbitrary rotations and also study analytically what happens if the ancillas are in a mixed rather than a pure state. Consistent with the numerical results in the original proposal, we find that as long as the ancilla preparation error is small (of the order of $1/\overline{n}$, where $\overline{n}$ is the average number of atoms in the pulses considered) it will introduce only higher-order errors in the performance of the restored pulse.

Dipolar gases like erbium and dysprosium have a dense spectrum of resonant loss features associated with their strong anisotropic interaction potential. These resonances display various behaviors with density and temperature, implying diverse microscopic properties. Here we quantitatively investigate the low-field ($B<6\mathrm{G}$) loss features in ultracold thermal samples of ${}^{162}\mathrm{Dy}$. The atoms are spin polarized in their lowest internal state so that pure two-body losses due to spin relaxation are forbidden. However, our analysis reveals that some resonances lead to a two-body-like decay law, while others show the expected three-body decay. We present microscopic one-step and two-step models for these losses, investigate their temperature dependence, and detect a feature compatible with a $d$-wave Fano-Feshbach resonance that has not been observed before. We also report the variation of the scattering length around these resonances, inferred from the time-of-flight expansion of the condensate.

We demonstrate that the efficiency of effective-negative-temperature-based quantum Otto engines, already known to outperform their traditional counterparts operating with positive-temperature thermal reservoirs, can be further improved by terminating the isochoric strokes before the working substance reaches perfect equilibrium with its environment. Our investigation encompasses both Markovian and non-Markovian dynamics during these finite-time isochoric processes while considering a weak coupling between the working substance and the reservoirs. We assess the performance of these engines as they undergo a transition from the Markovian to the non-Markovian regime using two figures of merit: maximum achievable efficiency at a certain finite time during the isochoric heating stroke, and overall performance of the engine over an extended period during the transient phase of this stroke. We show that the maximum efficiency increases with the increase of non-Markovianity. However, the overall engine performance decreases as non-Markovianity increases. Additionally, we discover the existence of effective-negative-temperature-based necessarily transient quantum Otto engines. These engines operate within an extended operational domain, reaching into temperature ranges where conventional effective-negative-temperature-based quantum Otto engines, which rely on perfect thermalization during the isochoric strokes, are unable to function. Furthermore, this extended operational domain of an effective-negative- temperature-based necessarily transient quantum Otto engine increases as non-Markovianity becomes more pronounced.

When He is ionized by a chirped xuv pulse, additional peaks are identified in the joint energy spectra besides ordinary ionization peaks. Our results are based on the solution of the full-dimensional time-dependent Schrödinger equation of helium. Further numerical studies show that these additional structures are sensitive to both the pulse duration and the chirp parameter. To reveal the underlying mechanism, we have developed an analytical model based on the symmetric ionization assumption and the second-order time-dependent perturbation theory, which can qualitatively reproduce these additional structures. By systematic comparison studies, one can attribute the origin of these structures to the interference of two indistinguishable electrons and the diffraction in the time domain. In addition, we find that the interference effect is absent when one uses a negatively chirped laser pulse, while the diffraction in the time domain always persists.

Causal networks beyond that in the paradigmatic Bell's theorem can lead to new kinds and applications of nonclassical behavior. Their study, however, has been hindered by the fact that they define a nonconvex set of correlations and only very incomplete or approximated descriptions have been obtained so far, even for the simplest scenarios. Here we take a different stance on the problem and consider the relative volume of classical or nonclassical correlations a given network gives rise to, considering distances to sets of interest and how they distribute too. Among other results, we show instances where the inflation technique, arguably the most disseminated tool in the community, is unable to detect a significant portion of the nonclassical behaviors, up to three copies of each source, and that a concentration phenomenon of distances happens in one of them. Interestingly, we also show that the use of interventions, a central tool in causal inference, can enhance substantially our ability to witness nonclassicality.