Over the past few decades, quantum information processing research has focused heavily on error-mitigation schemes and error-correcting codes. However, while many proposed schemes have been successful in mitigating errors, most of them are perturbative and assume deterministic systematic errors, leaving studies of the problem considering the full noise and errors distribution scarce. In this work we introduce an error-mitigation scheme for robust single-qubit unitary gates based on a composite segmented design that accounts for the full distribution of the physical noise and errors in the system. We provide two optimization approaches to construct these robust segmented gates, perturbative and nonperturbative, which address all orders of errors. We demonstrate the effectiveness of our scheme in the photonics realm for the realization of dual-rail directional couplers. Specifically, we show that the three-segment composite design for the fundamental single-qubit unitary operations reduces the error by an order of magnitude for a realistic distribution of errors. Moreover, we demonstrate that the two approaches are compatible for small errors and significantly reduce the overhead of modern error-correction codes. Our methods are rather general and can be applied to other realizations of quantum information processing units.

We develop a resource theory for non-absolutely-separable states (non-AS) in which absolutely separable states (AS) that cannot be entangled by any global unitaries are recognized as free states and any convex mixture of global unitary operations can be performed without incurring any costs. We employ two approaches to quantify nonabsolute separability (NAS)—one based on distance measures and the other one through the use of a witness operator. We prove that both of the NAS measures obey all the conditions that should be followed by a “good” NAS measure. We demonstrate that NAS content is equal and maximal in all pure states for a fixed dimension. We then establish a connection between the distance-based NAS measure and the entanglement quantifier. We illustrate our results with a class of non-AS states, namely Werner states.

The application of quantum annealing to the optimization of continuous-variable functions is a relatively unexplored area of research. We test the performance of quantum annealing applied to a one-dimensional continuous-variable function with a rugged energy landscape. After domain-wall encoding to map a continuous variable to discrete Ising variables, we first benchmark the performance of the real hardware, the D-Wave 2000Q, against several state-of-the-art classical optimization algorithms designed for continuous-variable problems to find that the D-Wave 2000Q matches the classical algorithms in a limited domain of computation time. Beyond this domain, classical global optimization algorithms outperform the quantum device. Next we examine several optimization algorithms that are applicable to the Ising formulation of the problem, such as the time-evolving block decimation (TEBD) to simulate ideal coherent quantum annealing, simulated annealing, simulated quantum annealing, and spin-vector Monte Carlo. The data show that TEBD's coherent quantum annealing achieves far better results than the other approaches, demonstrating the effectiveness of coherent tunneling. From these two types of benchmarks, we conclude that the hardware realization of quantum annealing has the potential to significantly outperform the best classical algorithms if thermal noise and other imperfections are sufficiently suppressed and the device operates coherently, as demonstrated in recent short-time quantum simulations.

The expectation value of the product of two noncommuting observables (POTNO) can be used to test the commutation relation and dig out the correlation between two observables. However, since a POTNO is generally a non-Hermitian operator, its average cannot be measured directly according to standard quantum mechanics. Recently, a theoretical scheme has been proposed to obtain POTNOs, but the observables are limited to projection operators. In this paper, we present a scheme that employs weak measurement to directly measure the expectation value of the POTNO, where the observables are arbitrary operators. Our scheme transforms the measurement of this expectation value into the measurements of several single observable weak values. Experimentally we demonstrate our scheme by measuring the expectation value of the product of two Pauli operators and verify their commutation and anticommutation relations in a trapped-ion system. Moreover, our scheme is applicable to the cases with more than two observables.

We present the coherent enhancement of the frequency comb via high-order harmonic generation (HHG) in a train of infrared laser pulses combined with terahertz (THz) laser fields. The HHG spectra are obtained by solving the three-dimensional time-dependent Schrödinger equation by means of the time-dependent generalized pseudospectral method. We find that the structure of the frequency comb via HHG becomes much smoother and more regular, and the yield of the comb is increased by nearly two orders of magnitude. By analyzing the phase coherence of HHG spectra, we demonstrate that the THz laser fields are responsible for the optimization of the structure and yield of the frequency comb since the constructive phase coherence of the HHG spectra is modulated by the THz field. The physical origin of the constructive phase coherence is thanks to the uniform ionization efficiency induced by the THz laser field for each laser pulse, which greatly improves the synchronization of the harmonic emission. Our finding provides a promising method for the enhancement of the frequency comb via HHG.

Utilizing exact diagonalization techniques, we investigate a one-dimensional, nonreciprocal, interacting hard-core boson model under a Stark potential with tail curvature. By employing the nonzero imaginary eigenenergies ratio, half-chain entanglement entropy, and eigenstate instability, we numerically confirm that the critical points of spectral real-complex (RC) transition and many-body localization (MBL) phase transition are not identical, and an examination of the phase diagrams reveals that the spectral RC transition arises before the MBL phase transition, which suggests the existence of a non-MBL-driven spectral RC transition. These findings are quite unexpected, and they are entirely different from observations in disorder-driven interacting non-Hermitian systems. This work provides a useful reference for further research on phase transitions in disorder-free interacting non-Hermitian systems.

We study the sensitivity of thermometric probes that are composed of $N$ spins coupled to a sample prepared at temperature $T$. Our analysis extends beyond the weak-coupling limit into the strong sample-probe coupling regime. In particular, sample-induced interactions between each of the spins are generated via strong coupling effects and are not fine-tuned among each body composing the probe. By employing the reaction-coordinate mapping to evaluate the noncanonical equilibrium state of the probe at finite coupling, we compute the thermometric sensitivity via the quantum Fisher information through the equilibrium state itself. We find that for single-spin probes $(N=1)$, temperature sensitivity decreases in the regime of weak-to-intermediate coupling strength, however, as the coupling increases we observe much higher sensitivity of the probe in the low-temperature regime. Furthermore, as long as $N>1$, there exist optimal values of the sample-probe interaction energy that allow one to attain enhanced thermometric sensitivity when compared to the maximum achieved precision obtained from thermal Gibbs states at weak coupling, particularly in the regime of low temperature. Finally, we show that this enhanced sensitivity may be observed from suboptimal measurements.

We study an entangled distributed quantum sensing scheme based on an array of $d$ Mach-Zehnder interferometers (MZIs) for the estimation of relative phase shifts. The scheme uses $d$ coherent states and a single squeezed-vacuum state that is distributed among the MZIs by a quantum circuit (QC). The protocol can be optimized analytically: it overcomes the shot-noise limit and reaches the Heisenberg limit with respect to the average total number of probe particles, ${\overline{n}}_T$, for the estimation of arbitrary linear combinations of the $d$ phases. We compare the entangled strategy with a separable one that uses $d$ coherent and $d$ squeezed-vacuum states and the same ${\overline{n}}_T$. The entangled strategy benefits for a substantial reduction of resource overhead and can achieve a maximum gain equal to $d$ when using the same total squeezed-light intensity as the separable strategy. Interestingly, the entangled strategy using a single squeezed-vacuum state can reach the same sensitivity as the separable strategy that uses $d$ copies of the same state. Finally, given a random choices of the QC, we identify the optimal linear combination of the phases that can be estimated with maximum sensitivity. Our scheme paves the ways for a variety of applications in distributed quantum sensing with photonic and atomic interferometers.

The achievement of a larger magneto-optical Kerr effect (MOKE) in nanoscale layered structures is extremely important for both theoretical understandings and practical applications. However, nanoscale layered structures may not always exhibit enhanced MOKE under certain geometries. In this paper, we present a scheme based on weak-value amplification (WVA) for simultaneously detecting and enhancing the Kerr signals in nanoscale layered structures. The Kerr signals can be effectively amplified as the parameters of the preselection in WVA. We numerically investigate the dependence of the thickness $d$ of Co in the sample ${\text{HfO}}_2\left(10\text{nm}\right)/\text{Co}\left(d\mathrm{nm}\right)/{\mathrm{HfO}}_2\left(30\mathrm{nm}\right)/\mathrm{Al}\left(40\mathrm{nm}\right)/\mathrm{Si}$ and the sample $\text{Co}\left(d\mathrm{nm}\right)/\mathrm{Si}$ in the range of 5 nm $<d<$ 50 nm. Our results indicate that the combination of the cavity and WVA can simultaneously amplify the MOKE signals when compared to the application of WVA on the sample $\text{Co}\left(d\mathrm{nm}\right)/\mathrm{Si}$ and the application of traditional MOKE setup (TMOKES) on the two samples. Importantly, our results highlight that WVA maintains its ability to amplify MOKE signals even in cases where the cavity in the TMOKES scheme fails to enhance the Kerr signals. This signifies the exceptional advantage of WVA in amplifying Kerr signals over TMOKES, regardless of the sample structures and specific MOKE geometries employed.

The Kuramoto model serves as a paradigm for describing spontaneous synchronization in a system of classical interacting rotors. In this paper, we extend this model to the quantum domain by coupling quantum interacting rotors to external baths following the Caldeira-Leggett approach. Studying the mean-field model in the overdamped limit using Feynman-Vernon theory, we show how quantum mechanics modifies the phase diagram. Specifically, we demonstrate that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We examine the phase transition into the synchronized phase at various temperatures, revealing that classical results are recovered at high temperatures while a quantum phase transition occurs at zero temperature. Additionally, we derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters, and examine the differences between classical and quantum behavior.

Sharing entanglement across quantum interconnects is fundamental for quantum information processing. We discuss a practical setting where this interconnect, modeled by a quantum channel, is used once with the aim of sharing high-fidelity entanglement. For any channel, we provide methods to easily find both this maximum fidelity and optimal inputs that achieve it. Unlike most metrics for sharing entanglement, this maximum fidelity can be shown to be multiplicative. This ensures a complete understanding in the sense that the maximum fidelity and optimal inputs found in our one-shot setting extend even when the channel is used multiple times, possibly with other channels. Optimal inputs need not be fully entangled. We find that the minimum entanglement in these optimal inputs can even vary discontinuously with channel noise. Generally, noise parameters are hard to identify and remain unknown for most channels. However, for all qubit channels with qubit environments, we provide a rigorous noise parametrization, which we explain in terms of no cloning. This noise parametrization and a channel representation that we call the standard Kraus decomposition have pleasing properties that make them useful more generally.

We observe dark-state polariton collapses and revivals in a quantum memory based on electromagnetically induced transparency on a cloud of cold cesium atoms in a magnetic field. Using ${\sigma }^{+}$-polarized signal and control beams in the direction of the magnetic field, we suppress the dark-state polariton collapses by polarizing the atoms towards one of the stretched Zeeman states and optimizing the frequency detuning of the control beam. In this way, we demonstrate a quantum memory with only partial dark-state polariton collapses, making the memory usable at any storage time, not only at discretized times of revivals. We obtain a storage time of more than 400 $\mu \mathrm{s}$, which is ten times longer than what we can achieve by trying to annul the magnetic field.

Digital quantum computers have the potential to study the dynamics of many-body quantum systems. Nonequilibrium open quantum systems are, however, less straightforward to be implemented. Here we explore the feasibility of studying steady-state transport in strongly interacting many-body quantum systems on a digital quantum computer. To do so, we consider a collisional model representation of the nonequilibrium open dynamics for a boundary-driven $XXZ$ spin chain. More specifically, we investigate how the depth of the quantum circuit is affected by how close we want the steady state to be to the one expected from the underlying master equation. We study the simulation of a boundary-driven spin chain in regimes of weak and strong interactions, which would lead in large systems to diffusive and ballistic dynamics, considering also possible errors in the implementation of the protocol. Last, we analyze the effectiveness of digital simulation via the collisional model of current rectification when the $XXZ$ spin chains are subject to nonuniform magnetic fields and show that, although the circuit depths required to reach steady states are still prohibitive for today's hardware, few collisions are enough to suggest a strong rectifying power.

We characterize the set of optimal protocols for two-qubit entangling gates through a mechanism analysis based on quantum pathways, which allows us to compare and rank the different solutions. As an example of a flexible platform with a rich landscape of protocols, we consider trapped neutral atoms excited to Rydberg states by different pulse sequences that extend over several atomic sites, optimizing both the temporal and the spatial features of the pulses. Studying the rate of success of the algorithm under different constraints, we analyze the impact of the proximity of the atoms on the nature and quality of the optimal protocols. We characterize in detail the features of the solutions in parameter space, showing some striking correlations among the set of parameters. Together with the mechanism analysis, the spatiotemporal control allows us to select protocols that operate under mechanisms by design, like finding needles in a haystack.

Metastable states in an atomic energy-level structure greatly influence atomic processes in plasmas. In particular, high-energy long-lived metastable levels brought about by $5s$ and $4f$ electrons in multiply charged heavy ions often trigger anomalous emission and ionization processes in plasmas. Here, we present a theoretical and experimental study of the ionization processes between the moderate-charge-state barium ions ${\mathrm{Ba}}^{8+}, {\mathrm{Ba}}^{9+}$, and ${\mathrm{Ba}}^{10+}$ in an electron-beam ion-trap plasma. Indirect ionization processes through $5s$ and $4f$ metastable states in the low-density plasma induce production of higher-charge-state ions at electron energies well below the ionization potential. Remarkably, the observed intensity ratio of an emission line of ${\mathrm{Ba}}^{10+}$ to that of ${\mathrm{Ba}}^{9+}$ decreases with increasing electron energy in a particular energy region, implying there is a characteristic electron energy dependence of each ion abundance. We discuss the experimentally observed characteristic behavior by comparing it with a theoretical simulation based on fine-structure-resolved collisional-radiative modeling with ionization balance.

The time-dependent equation-of-motion coupled-cluster singles and doubles (TD-EOM-CCSD) and time-dependent coupled-cluster singles and doubles (TDCCSD) methods are compared by simulating Rabi oscillations for distant atoms in a classical electromagnetic field. While the TD-EOM-CCSD simulations are numerically stable, the oscillating time-dependent energy expectation value displays an incorrect scaling with the number of atoms resonant with the field. On the other hand, the TDCCSD simulations exhibit the correct scaling in the initial stages of the Rabi cycle but break down when the multiatom system approaches complete population inversion. The numerical stability of the TDCCSD simulations is shown to be very sensitive to any interactions between the atoms and to left amplitudes that do not participate in the expression for time-dependent expectation values for noninteracting atoms. Moreover, we introduce a general theoretical framework for describing the two methods, where the cluster amplitude time derivatives serve as auxiliary conditions related to a shift of the time-dependent Hamiltonian matrix. In this framework, time-dependent coupled-cluster methods exhibit a shifted Hamiltonian matrix with a block upper triangular structure in terms of the number of excited noninteracting subsystems, explaining the correct scaling properties of the TDCCSD method.

We demonstrate electromagnetic waves following a gravitational field using a photonic crystal. We introduce spatially distorted photonic crystals (DPCs) capable of deflecting light waves owing to their pseudogravity caused by lattice distortion. We experimentally verify the phenomenon in the terahertz range using a silicon DPC. Pseudogravity caused by lattice distortion reveals alternative approaches to achieve on-chip trajectory control of light propagation in PCs.

The spatial structure of the inhomogeneity in a disordered medium determines how waves scatter and propagate in it. We present a theoretical model of how the Fourier components of the disorder control wave scattering in a two-dimensional disordered medium, by analyzing the disordered Green's function for scalar waves. By selecting a set of Fourier components with the appropriate wave vectors, we can enhance or suppress wave scattering to filter out unwanted waves and allow the robust coherent transmission of waves at specific angles and wavelengths through the disordered medium. Based on this principle, we propose an approach for creating selective transparency, band gaps, and anisotropy in disordered media. This approach is validated by direct numerical simulations of coherent wave transmission over a wide range of incident angles and frequencies and can be experimentally realized in disordered photonic crystals. Our approach, which requires neither nontrivial topological wave properties nor a non-Hermitian medium, creates opportunities for exploring a broad range of wave phenomena in disordered systems.

We analyze a set of models frequently appearing in quantum optical settings by expressing their Hamiltonians in terms of Fock-state lattices (FSLs). The few degrees-of-freedom of such models, together with the system symmetries, make the emerging FSLs relatively simple such that they can be linked to known lattice models from the condensed-matter community. Thus, the FSLs may shed new light on known quantum optical systems. While we provide a rather long list of models and their corresponding FSLs, we pick a few to demonstrate the method's strength. The three-mode boson model, for example, is shown to display a fractal spectrum and chiral evolution in the FSL characterized by localized distributions traversing along symmetric trajectories. In a second example, we consider the central spin model, which generates an FSL reminiscent of the Su-Schrieffer-Heeger model hosting topological edge states. We further demonstrate how the phenomenon of flat bands in lattice models can manifest in related FSLs, which can be linked to so-called dark states.