Identifying necessary and sufficient conditions for universal quantum computing is a long-standing open problem for which contextuality is, perhaps, the only promising solution [Howard et al., Nature (London) 510, 351 (2014)]. To justify this conjecture, Howard et al. showed that contextuality is equivalent to Wigner negativity for qudits, and is therefore necessary and possibly sufficient for qudit magic state distillation. Here, we reformulate magic state distillation in the language of discrete phase space, to show that any finite qudit magic state distillation routine contains bound states outside the Wigner polytope; these states exhibit contextuality but are useless for magic state distillation.

Short-range correlations in bosonic Helium clusters, composed of ${}^4\mathrm{He}$ atoms, are studied utilizing the generalized contact formalism. The emergence of universal $n$-body short-range correlations is formulated and demonstrated numerically via Monte Carlo simulations. The values of the $n$-particle contacts are evaluated for $n\le 5$. In the thermodynamic limit, the two-body contact is extracted from available experimental measurements of the static structure factor of liquid ${}^4\mathrm{He}$ at high momenta, and found in a good agreement with the value extracted from our calculations.

The wave function is at the foundation of quantum theory, which is assumed to give a complete description of a quantum system. From early inception, the wave function was introduced as an abstract element of the theory and lacked any way to measure it directly. The situation, however, has somewhat changed with the reporting of the direct measurement of the quantum wave function via weak measurements, giving the wave function a clearly operational definition. The weak measurement method requires sequential measurements of conjugate observables position and momentum with the position measurement sufficiently weak. Surprisingly, recent research showed that performing sequential strong measurements realized the same object, in which case no approximation in weak measurements has to be made. Here, we report on experiments of direct measurements of the two-dimensional transverse wave function of photons via strong measurement, implying that an accurate and clear operational definition may be given to the wave function. We have measured the Gaussian and Laguerre–Gaussian of $l=1$ spatial wave functions of photons with fidelity of 0.93. As a potential important application, we show that this direct measurement of the wave function provides an alternative way to realize digital holography of three-dimensional objects. This realization of direct measurement of the wave function has significant consequences in quantum information processing and quantum imaging.

Superfluid helium's low-loss dielectric properties, excellent thermal conductivity, and unique collective excitations make it an attractive candidate to incorporate into superconducting qubit systems. We controllably immerse a three-dimensional superconducting transmon qubit in superfluid ${}^4\mathrm{He}$ and measure the spectroscopic and coherence properties of the system. We find that the cavity, the qubit, and their coupling are all modified by the superfluid, which we analyze within the framework of circuit quantum electrodynamics. At temperatures relevant to quantum computing experiments, the energy relaxation time of the qubit is not significantly changed by the presence of the superfluid, while the pure dephasing time modestly increases, which we attribute to improved thermalization of the microwave environment via the superfluid.

Provided that cavities are initially in a Greenberger-Horne-Zeilinger (GHZ) entangled state, we show that GHZ states of $N$-group qubits distributed in $N$ cavities can be created via a three-step operation. The GHZ states of the $N$-group qubits are generated by using $N$-group qutrits placed in the $N$ cavities. Here, “qutrit” refers to a three-level quantum system with the two lowest levels representing a qubit while the third level acting as an intermediate state necessary for the GHZ state creation. This proposal does not depend on the architecture of the cavity-based quantum network and the way for coupling the cavities. The operation time is independent of the number of qubits. The GHZ states are prepared deterministically because no measurement on the states of qutrits or cavities is needed. In addition, the third energy level of the qutrits during the entire operation is virtually excited and thus decoherence from higher energy levels is greatly suppressed. This proposal is quite general and can in principle be applied to create GHZ states of many qubits using different types of physical qutrits (e.g., atoms, quantum dots, NV centers, various superconducting qutrits, etc.) distributed in multiple cavities. As a specific example, we further discuss the experimental feasibility of preparing a GHZ state of four-group transmon qubits (each group consisting of three qubits) distributed in four one-dimensional transmission line resonators arranged in an array.

We discuss the topology of Bogoliubov excitation bands from a Bose-Einstein condensate in an optical lattice. Since the Bogoliubov equation for a bosonic system is non-Hermitian, complex eigenvalues often appear and induce dynamical instability. As a function of momentum, the onset of appearance and disappearance of complex eigenvalues is an exceptional point (EP), which is a point where the Hamiltonian is not diagonalizable and hence the Berry connection and curvature are ill-defined, preventing defining topological invariants. In this paper, we propose a systematic procedure to avoid EPs in the Brillouin zone by introducing an imaginary part of the momentum. We then define the Berry phase for a one-dimensional bosonic Bogoliubov system. Extending the argument for Hermitian systems, the Berry phase for an inversion-symmetric system is shown to be ${\mathbb{Z}}_2$. As concrete examples, we numerically investigate two toy models and confirm the bulk-edge correspondence even in the presence of complex eigenvalues. The ${\mathbb{Z}}_2$ invariant associated with particle-hole symmetry and the winding number for a time-reversal-symmetric system are also discussed.

We present diffusion Monte Carlo (DMC) and path-integral Monte Carlo (PIMC) calculations of a one-dimensional Bose system with realistic interparticle interactions in a periodic external potential. Our main aim is to test the predictions of the Luttinger liquid (LL) theory, in particular with respect to the superfluid-Mott insulator transition at both zero and finite temperatures, in the predicted robust and fragile superfluid regimes. For that purpose, we present our results of the superfluid fraction ${\rho }_s/{\rho }_0$, the one-body density matrix, the two-body correlation functions, and the static structure factor. The DMC and PIMC results in the limit of very low temperature for ${\rho }_s/{\rho }_0$ agree, but the LL model for scaling ${\rho }_s/{\rho }_0$ does not fit the data well. The critical depth of the periodic potential is close to the values obtained for ultracold gases with different models of interaction, but with the same value of the bare LL parameter, demonstrating the universality of LL description. Algebraic decay of correlation functions is observed in the superfluid regime and exponential decay in the Mott-insulator one, as well as in all regimes at finite temperature for distances larger than a characteristic length.

We study the topological properties of an extended Bose-Hubbard model with cyclically modulated hopping and on-site potential parameters, which can be realized with ultracold bosonic atoms in a one-dimensional optical superlattice. We show that the interacting bosonic chain at half filling and in the deep Mott insulating regime can simulate bosonic Chern insulators with a topological phase diagram similar to that of the Haldane model of noninteracting fermions. Furthermore, we explore the topological properties of the ground state by calculating the many-body Chern number, the quasiparticle energy spectrum with gapless edge modes, the topological pumping of the interacting bosons, and the topological phase transition from normal (trivial) to topological Mott insulators. We also present the global phase diagram of the many-body ground state, which contains a superfluid phase and two Mott insulating phases with trivial (a zero Chern number) and nontrivial topologies (a nonzero Chern number), respectively.

We investigate the ground-state properties and excitations of Rydberg-dressed bosons in both three and two dimensions, using the hypernetted-chain Euler-Lagrange approximation, which accounts for correlations and thus goes beyond the mean-field approximation. The short-range behavior of the pair distribution function signals the instability of the homogeneous system with respect to the formation of droplet crystals at strong couplings and large soft-core radius. This tendency to spatial density modulation coexists with off-diagonal long-range order. The contribution of the correlation energy to the ground-state energy is significant at large coupling strengths and intermediate values of the soft-core radius while for a larger soft-core radius the ground-state energy is dominated by the mean-field (Hartree) energy. We have also performed path integral Monte Carlo simulations at selected system parameters to verify the performance of our hypernetted-chain Euler-Lagrange results in three dimensions. In the homogeneous phase, the two approaches are in very good agreement. Moreover, Monte Carlo simulations predict a first-order quantum phase transition from a homogeneous superfluid phase to the quantum droplet phase with face-centered cubic symmetry for Rydberg-dressed bosons in three dimensions.

Image-enhancing optical cavities offer an intriguing platform for nonlinear optical processing of two-dimensional signals, with potential applications in optical information processing and optically implemented artificial neural networks. Here, we analyze the performance of a self-imaging degenerate cavity via numerical simulations and show the existence of a cavity-size-dependent minimum spread in the transverse-mode resonances. This nondegeneracy, in turn, leads to an inherent trade-off between the resonant enhancement and the fidelity of the intracavity image as the cavity finesse changes.

We demonstrate the experimental observation of loosely bound solitons and pulsations in a passively mode-locked fiber laser. The soliton amount inside one soliton bunch typically increases with the increment of pump power, while the average pulse-to-pulse separation in the regime of hundreds of picoseconds decreases in principle accordingly. Besides, by employing the real-time measurement based on the dispersive Fourier-transform technique, we find that some solitons in a single bunch are experiencing a simultaneous pulsating process with a period corresponding to 100 times longer than the cavity round-trip time. The experimental results can be beneficial for better understanding the formation of multiple solitons and pulsating solitons and enriching the nonlinear phenomena in complex soliton systems.

In this paper, we show that nonreciprocal unconventional photon blockade can be observed in a spinning cavity immersed in a degenerate optical parametric amplifier (OPA) driven by the laser driving with weak Kerr nonlinearities through the Fizeau drag. We analytically derive the optimal conditions for strong antibunching, which are in good agreement with those obtained by numerical simulations. Under the weak driving condition, we discuss the physical origins of the nonreciprocal unconventional photon blockade, which originates from the destructive interference between different paths from the ground state to two-photon states by driving the device from the left side. While the quantum interference paths are broken when the device is driven from the right side, which leads to the occurring of the photon bunching. Moreover, we extend the above results to the general non-Markovian regimes, in which the cavity couples with a thermal reservoir consisting of collection of infinite oscillators (bosonic photonic modes). We show nonreciprocal unconventional photon blockade exhibits a transition from the non-Markovian to Markovian regimes by controlling environmental spectral width regardless of the weakness of OPA gain and driving field.

We introduce a method to rotate arbitrarily the excitation profile of universal broadband composite pulse sequences for robust high-fidelity population inversion. These pulses compensate deviations in any experimental parameter (e.g., pulse amplitude, pulse duration, detuning from resonance, Stark shifts, unwanted frequency chirp, etc.) and are applicable with any pulse shape. The rotation allows one to achieve higher-order robustness to any combination of pulse area and detuning errors at no additional cost. The latter can be particularly useful, e.g., when detuning errors are due to Stark shifts that are correlated with the power of the applied field. We demonstrate the efficiency and universality of these composite pulses by experimental implementation for rephasing of atomic coherences in a ${\text{Pr}}^{3+}\text{:}{\text{Y}}_2{\text{SiO}}_5$ crystal.

We introduce a theoretical and computational method to design resonant objects, such as nanoantennas or meta-atoms, exhibiting tailored multipolar responses. In contrast with common approaches that rely on a multipolar analysis of the scattering response of an object upon specific excitations, we propose to engineer the intrinsic (i.e., excitation-independent) multipolar content and spectral characteristics of the natural resonances—or quasinormal modes—of the object. A rigorous numerical approach for the multipolar decomposition of resonances at complex frequencies is presented, along with an analytical model conveying a direct physical insight into the multipole moments induced in the resonator. Our design strategy is illustrated by designing a subwavelength optical resonator exhibiting a Janus resonance that provides side-dependent coupling to waveguides over the full linewidth of the resonance and on a wide angular range for linearly polarized incident plane waves. The method applies to all kinds of waves and may open new perspectives for subwavelength-scale manipulation of scattering and emission.

In a recent paper [Phys. Rev. Lett. 111, 100501 (2013)], a scheme was proposed where subsequent observers can extract unambiguous information about the initial state of a qubit, with finite joint probability of success. Here, we generalize the problem for arbitrary preparation probabilities (arbitrary priors). We discuss two different schemes: one where only the joint probability of success is maximized and another where, in addition, the joint probability of failure is also minimized. We also derive the mutual information for these schemes and show that there are some parameter regions for the scheme without minimizing the joint failure probability where, even though the joint success probability is maximum, no information is actually transmitted by Alice.

We investigate an optimal distance of two components in an entangled coherent state for quantum phase estimation in lossy interferometry. The optimal distance is obtained by an economical point, representing the quantum Fisher information that we can extract per input energy. Maximizing the formula of the quantum Fisher information over an input mean photon number, we show that, as the losses of the interferometer increase, it can be more beneficial to prepare an initially entangled coherent state that is less entangled. This represents that the optimal distance of the two-mode components decreases with more loss in the interferometry. Under the constraint of the input mean photon number, we obtain that the optimal entangled coherent state is more robust than a separable coherent state, even in a high photon loss rate. The optimal entangled coherent state preserves quantum advantage over the standard interferometric limit of the separable coherent state. We also show that the corresponding optimal measurement requires correlation measurement bases.

Extending the concept of steerability for quantum states, channel steerability is an ability to remotely control the given channel from a coherently extended party. Verification of channel steering can be understood as certifying coherence of the channel in a one-sided device-independent manner with respect to a bystander. Here we propose a method to verify channel steering in a measurement-device-independent way. To do this, we first obtain Choi matrices from given channels and use the canonical method of measurement-device-independent verification of quantum steering. As a consequence, exploiting channel-state duality which interconverts steerability of channels and that of states, channel steering is verified. We further analyze the effect of imperfect preparation of entangled states used in the verification protocol, and find that the threshold of the undesired noise that we can tolerate is bounded from below by steering robustness.

The direction of arrival (DOA) estimation in array signal processing is an important research area. The effectiveness of the direction of arrival greatly determines the performance of multi-input multi-output (MIMO) antennas. The multiple signal classification (MUSIC) algorithm, which is the most canonical and widely used subspace-based method for direction angle estimation, has a moderate estimation performance of DOA. In this article, we present a quantum algorithm for performing MUSIC. Compared with the best-known classical algorithm, quantum MUSIC can show a polynomial speedup. In our scheme, we first efficiently implement a non-Hermitian chain product subroutine for the matrix ${\widehat{R}}_{ss}\in R^{N\times N}$ with $L$ snapshots, where the method is different from that of Cong and Duan [I. Cong and L. Duan, New J. Phys. 18, 073011 (2016)]. In this subroutine, we perform amplitude transduction [Y. R. Sanders, G. H. Low, A. Scherer, and D. W. Berry, Phys. Rev. Lett. 122, 020502 (2019)] by testing an inequality to neglect the calculation of the approximate arcsine function. Second, a quantum labeling operation based on the principal eigenvalues is proposed for preparing the coherent state of the principal eigenvectors. Finally, we generalize our results to some quantum algorithms with quantum principal component analysis subroutines and some existing quantum algorithms where the covariance matrices occur in the non-Hermitian chain product form.

We study theoretically the effects of dissipation on the performances of a variational quantum algorithm used to approximately solve a combinatorial optimization problem, the maximum independent set, on a platform of neutral atoms. We take a realistic model of dissipation with spontaneous emission, and show numerically that the detrimental effects of these incoherent processes are spontaneously attenuated by the variational nature of the procedure. We furthermore implement an alternative optimization scheme recently proposed, where one uses the expected shortfall of the mean energy as the objective function.

A fully relativistic approach is applied to the evaluation of the nuclear recoil effect on the bound-electron $g$ factor in hydrogenlike ions to first order in the electron-to-nucleus mass ratio $m/M$ and to all orders in $\alpha Z$. The calculations are performed in the range $1\le Z\le 20$ for $g$ factors of the $1s$, $2s$, $2p_{1/2}$, and $2p_{3/2}$ states. The $\alpha Z$ dependence of the nontrivial QED recoil contribution as a function of $Z$ is studied.