We present a generic Markovian master equation inducing the gradual decoherence of a bosonic quantum field. It leads to the decay of quantum superpositions of field configurations, while leaving the Ehrenfest equations for both the field and the mode-variables invariant. We characterize the decoherence dynamics analytically and numerically, and show that the semiclassical field dynamics is described by a linear Boltzmann equation in the functional phase space of field configurations.

A key problem in financial mathematics is the forecasting of financial crashes: If we perturb asset prices, will financial institutions fail on a massive scale? This was recently shown to be a computationally intractable (NP-hard) problem. Financial crashes are inherently difficult to predict, even for a regulator which has complete information about the financial system. In this Rapid Communication, we show how this problem can be handled by quantum annealers. More specifically, we map the equilibrium condition of a toy-model financial network to the ground-state problem of a spin-1/2 quantum Hamiltonian with two-body interactions, i.e., a quadratic unconstrained binary optimization problem. The equilibrium market values of institutions after a sudden shock to the network can then be calculated via adiabatic quantum computation and, more generically, by quantum annealers. Our procedure could be implemented on near-term quantum processors, thus providing a potentially more efficient way to assess financial equilibrium and predict financial crashes.

Fermionic linear optics corresponds to the dynamics of free fermions and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and consider the dynamics of number-preserving, quadratic Hamiltonians on these operators. We show that any such deformation results in an anyonic linear-optical model which allows for universal quantum computation.

Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is replaced by the SU(2) quantum Schur transform—a global transformation which maps the computational basis to a basis defined by angular momenta. We show that the output distributions of these circuits can be approximately classically sampled in polynomial time if they are sufficiently close to being sparse, thus isolating a regime in which they could lead to algorithms with exponential computational advantages. Our paper is primarily motivated by a conjecture that underpinned the hardness of permutational quantum computing, a restricted quantum computational model that has the above circuit structure in one of its computationally interesting regimes. The conjecture stated that approximating transition amplitudes of permutational quantum computing model to inverse-polynomial precision on a classical computer is computationally hard in this case. We disprove the extended version of this conjecture—even in the case when the hardness of approximation originated from a difficulty of finding the large elements in the output probability distributions. Finally, we present some evidence that output of the above permutational quantum computing circuits could be efficiently approximately sampled from on a classical computer.

We present algorithms to estimate outcomes for qubit quantum circuits. Notably, these methods can simulate a Clifford circuit in linear time without ever writing down stabilizer states explicitly. These algorithms outperform previous noisy near-Clifford techniques for most circuits. We identify a large class of input states that can be efficiently simulated despite not being stabilizer states. The algorithms leverage probability distributions constructed from Bloch vectors, paralleling previously known algorithms that use the discrete Wigner function for qutrits.

Techniques developed for device-independent characterizations allow one to certify certain physical properties of quantum systems without assuming any knowledge of their internal workings. Such a certification, however, often relies on the employment of device-independent witnesses catered for the particular property of interest. In this work, we consider a one-parameter family of multipartite, two-setting, two-outcome Bell inequalities and demonstrate the extent to which they are suited for the device-independent certification of genuine many-body entanglement (and hence the entanglement depth) present in certain well-known multipartite quantum states, including the generalized Greenberger-Horne-Zeilinger (GHZ) states with unbalanced weights, the higher-dimensional generalizations of balanced GHZ states, and the $W$ states. As a by-product of our investigations, we have found that, in contrast with well-established results, provided trivial qubit measurements are allowed, full-correlation Bell inequalities can also be used to demonstrate the nonlocality of weakly entangled unbalanced-weight GHZ states. Besides, we also demonstrate how two-setting, two-outcome Bell inequalities can be constructed, based on the so-called GHZ paradox, to witness the entanglement depth of various graph states, including the ring graph states, the fully connected graph states, and some linear graph states, etc.

In the usual entanglement detection scenario the possible measurements and the corresponding data are assumed to be fully characterized. We consider the situation where the measurements are known, but the data is scrambled, meaning the assignment of the probabilities to the measurement outcomes is unknown. We investigate in detail the two-qubit scenario with local measurements in two mutually unbiased bases. First, we discuss the use of entropies to detect entanglement from scrambled data, showing that Tsallis and Rényi entropies can detect entanglement in our scenario, while the Shannon entropy cannot. Then, we introduce and discuss scrambling-invariant families of entanglement witnesses. Finally, we show that the set of nondetectable states in our scenario is nonconvex and therefore in general hard to characterize.

Numerical attoclock is a theoretical model of attosecond angular streaking driven by a very short, nearly a single oscillation, circularly polarized laser pulse. The reading of such an attoclock is readily obtained from a numerical solution of the time-dependent Schrödinger equation as well as a semiclassical trajectory simulation. By comparing the two approaches, we highlight the essential physics behind the attoclock measurements. In addition, we analyze the predictions of the Keldysh-Rutherford model of the attoclock [A. W. Bray et al., Phys. Rev. Lett. 121, 123201 (2018)]. In molecular hydrogen, we highlight a strong dependence of the width of the attoclock angular peak on the molecular orientation and attribute it to the two-center electron interference. This effect is further exemplified in the weakly bound neon dimer.

Recent experiments with ultracold Rydberg-excited atoms have shown that long-range interactions can give rise to spatially ordered structures. Observation of crystalline phases in a system with Rydberg atoms loaded into an optical lattice seems also within reach. Here we investigate a bosonic model on a triangular lattice suitable for description of such experiments. Numerical simulations based on bosonic dynamical mean-field theory reveal a rich phase diagram with different supersolid phases. Comparison with the results obtained for a square lattice geometry shows qualitatively similar results in a wide range of parameters; however, on a triangular lattice we do not observe the checkerboard supersolid. Moreover, unlike on a square lattice, we did not find a phase transition from uniform superfluid to supersolid induced by increase of the hopping amplitude on a triangular lattice. Based on our results, we propose an intuitive interpretation of the nature of different supersolid phases. We also propose parameters for the experimental realization.

The recent experimental creation of knotted solitons in spin-1 Bose-Einstein condensates opens an interesting avenue for exploring the stability and dynamics of knot solitons. Knotted and helical vortices can be accommodated in spin-orbit-coupled antiferromagnetic spin-1 Bose-Einstein condensates. We demonstrate the stability of these topological structures via numerical simulations of the corresponding Gross-Pitaevskii equation. By changing the strength of the spin-orbit coupling, we find that the ground state undergoes a change from a knotted spin texture to a helical spin texture. Our results reveal that these types of topological object are experimentally realizable in spin-1 Bose-Einstein condensates.

A damped and driven collective spin system is analyzed by using quantum state diffusion. This approach allows for a mostly analytical treatment of the investigated nonequilibrium quantum many-body dynamics, which features a phase transition in the thermodynamical limit. The exact results obtained in this work, which are free of any finite-size defects, provide a complete understanding of the model. Moreover, the trajectory framework gives an intuitive picture of the two phases occurring, revealing a spontaneously broken symmetry and allowing for a qualitative and quantitative characterization of the phases. We determine exact critical exponents, investigate finite-size scaling, and explain a remarkable nonalgebraic behavior at the transition in terms of torus hopping.

The atomic spectrum of neutral promethium has been studied extensively by laser resonance ionization spectroscopy. We report on more than 1000 atomic transitions in the blue and near infrared spectral ranges, most of them between high excited energy levels. As Rydberg convergences could not be assigned unambiguously in the dense spectrum at high excitation energies, the first ionization potential (IP) was determined via field ionization of weakly bound states within a static electric field. By applying the saddle-point model, a value of ${\mathrm{IP}}_{\left(\mathrm{Pm}\right)}=45020.8\left(3\right){\mathrm{cm}}^{-1} \left[5.58188\right(4\left)\mathrm{eV}\right]$ was derived, which confirms previous expectations of $45027\left(80\right)$ and $44985\left(140\right){\mathrm{cm}}^{-1}$, which were obtained indirectly from lanthanide IP systematics.

We probe electric-field noise near the metal surface of an ion-trap chip in the temperature range from 295 to 530 K. We observe a nontrivial temperature dependence with the noise amplitude at 1 MHz frequency saturating around 500 K. Measurements of the noise spectrum reveal a $1/f^{\alpha \approx 1}$ dependence and a small decrease in $\alpha$ between low and high temperatures. This behavior can be explained by considering noise from a distribution of thermally activated two-level fluctuators with activation energies between 0.35 and 0.65 eV. Processes in this energy range may be relevant to understanding electric-field noise in ion traps; for example, defect motion in the solid state and surface adsorbate binding energies. The study of these processes may aid in identification of the origin of excess electric-field noise in ion traps—a major source of ion motional decoherence limiting the performance of surface traps as quantum devices.

Emission of matter-wave jets has been recently observed in a Bose-Einstein condensate confined by a cylindrical box potential, induced by a periodically modulated interparticle interaction [L. W. Clark et al., Nature (London) 551, 356 (2017)]. In this paper we apply the time-dependent Bogoliubov theory to study the quantum dynamics and the correlation effects observed in this highly nonequilibrium phenomenon. Without any fitting parameter, our theoretical calculations on the number of ejected atoms and the angular density correlations are in excellent quantitative agreement with the experimental measurements. The exponential growth in time of the ejected atoms can be understood in terms of a dynamical instability associated with the modulation of the interaction. We interpret the angular density correlation of the jets as the Hanbury Brown–Twiss effect between the excited quasiparticles with different angular momenta, and our theory explains the puzzling observation of the asymmetric density correlations between the jets with the same and opposite momenta. Our theory can also identify the main factors that control the height and width of the peaks in the density correlation function, which can be directly verified in future experiments.

A symmetric magneto-optical resonance arising from the single two-quantum RF transition $|F_g=1,m_{F_g}=-1\rangle \leftrightarrows |F_g=1,m_{F_g}=1\rangle$ in an optically aligned atomic ensemble is studied in the case when the quadratic Zeeman shift exceeds the width of the resonance. It is shown that the signal-to-noise ratio of the resonance can be significantly increased by applying the phase modulation to the RF field at a frequency close to the value of quadratic Zeeman shift. This theoretical prediction is corroborated by the experimental results with ${}^{87}\mathrm{Rb}$ atoms. The proposed technique can be used in magnetometers based on atomic alignment or by utilizing multiquantum RF resonances in optically oriented atomic ensembles.

We investigate the impact of higher-order nonlinear and dispersive effects on the dynamics of a single soliton solution in the complex cubic-quintic Ginzburg-Landau equation. Operating in the regime of soliton explosions, we show how the splitting of explosion modes is affected by the interplay of the high-order effects (HOEs) resulting in the controllable selection of right- or left-side periodic explosions. In addition, we demonstrate that HOEs induce a series of pulsating instabilities, significantly reducing the stability region of the single soliton solution.

Microscopically conserving reduced models of many-body systems have a long, highly successful history. Established perturbative theories of this type are the random-phase approximation for Coulomb fluids and the particle-particle ladder model for nuclear matter. There are also more physically comprehensive diagrammatic approximations, such as the induced-interaction and parquet models. Notwithstanding their explanatory power, some theories have lacked an explicit Hamiltonian from which all significant system properties, static and dynamic, emerge canonically. This absence can complicate evaluation of the conserving sum rules, essential consistency checks on the validity of any theory. In a series of papers Kraichnan introduced a stochastic embedding procedure to generate explicit Hamiltonians for common approximations for the full many-body problem. Existence of a Hamiltonian greatly eases the task of securing fundamental identities in such studies. I revisit Kraichnan's method to apply it to correlation theories for which such a canonical framework has been missing. I exhibit Hamiltonians for more elaborate correlated models incorporating both long-range screening and short-range scattering phenomena. These are relevant to the study of strongly interacting electrons and condensed quantum systems broadly.

We examine, in correlated mixed states of qudit-qubit systems, the set of all conditional qubit states that can be reached after local measurements at the qudit based on rank-1 projectors. While for a similar measurement at the qubit the conditional postmeasurement qudit states lie on the surface of an ellipsoid, for a measurement at the qudit we show that the set of postmeasurement qubit states can form more complex solid regions. In particular, we show the emergence, for some classes of mixed states, of sets which are the convex hull of solid ellipsoids and which may lead to conelike and trianglelike shapes in limit cases. We also analyze the associated measurement-dependent conditional entropy, providing a full analytic determination of its minimum and of the minimizing local measurement at the qudit for the previous states. Separable rank-2 mixtures are also discussed.

Measurement-device-independent quantum key distribution (MDI-QKD) is the only known QKD scheme that can completely overcome the problem of detection side-channel attacks. Yet, despite its practical importance, there is no standard approach towards proving the security of MDI-QKD. Here, we present a simple numerical method that can efficiently compute almost-tight security bounds for any discretely modulated MDI-QKD protocol. To demonstrate the broad utility of our method, we use it to analyze the security of coherent-state MDI-QKD, decoy-state MDI-QKD with leaky sources, and a variant of twin-field QKD called phase-matching QKD. In all of the numerical simulations (using realistic detection models) we find that our method gives significantly higher secret key rates than those obtained with current security proof techniques. Interestingly, we also find that phase-matching QKD using only two coherent test states is enough to overcome the fundamental rate-distance limit of QKD. Taken together, these findings suggest that our security proof method enables a versatile, fast, and possibly optimal approach towards the security validation of practical MDI-QKD systems.

We present an experimental optical implementation of a parallel-in-time discrete model of quantum evolution, based on the entanglement between the quantum system and a finite-dimensional quantum clock. The setup is based on a programmable spatial light modulator which entangles the polarization and transverse spatial degrees of freedom of a single photon. It enables the simulation of a qubit history state containing the whole evolution of the system, capturing its main features in a simple and configurable scheme. We experimentally determine the associated system-time entanglement, which is a measure of distinguishable quantum evolution, and also the time average of observables, which in the present realization can be obtained through one single measurement.