The time evolution of an open quantum system is governed by the Gorini-Kossakowski-Sudarshan-Lindblad equation for the reduced density operator of the system. This operator is obtained from the full density operator of the composite system involving the system itself, the bath, and the correlations between them, by performing a partial trace over the bath degrees of freedom. The entanglement between the system and the bath leads to a generalized Liouville evolution that involves, among other things, dissipation and decoherence of the system. In a similar fashion, the time evolution of a physical observable in a classically constrained dynamical system is governed by a generalization of the Liouville equation, in which the usual Poisson bracket is replaced by the so-called Dirac bracket. The generalization takes into account the reduction in the phase space of the system because of constraints that arise either because they are introduced by hand or because of singular Lagrangians. We derive an intriguing but precise classical-quantum correspondence between the aforementioned situations which connects the Lindblad operators to the constraints. The correspondence is illustrated in the ubiquitous example of coupled simple harmonic oscillators studied earlier in various contexts such as quantum optics, dissipative quantum systems, Brownian motion, and the area law for the entropy of black holes.

The local modes of trapped ions can be used to construct an analog quantum simulator and a digital quantum computer. However, the control of the phonon hopping remains difficult because it proceeds among all the local modes through the Coulomb coupling. We propose a method to cancel the phonon hopping among a given set of local modes by applying a sequence of phase shift gates implemented through the modulation of the trap potential. We analyze the error scaling in the algorithm to treat three or more modes and show that the error can be suppressed by repeating the pulse sequence. The duration of the phase shift gate in the present method can be as short as a few microseconds, which is an order of magnitude faster than the laser-based method. This short duration of the phase shift gate facilitates the suppression of the gate error. We finally show how the present method can be applied to the implementation of the beam splitter. The present method can also be applied to the simulation of bosonic systems as well as to the continuous variable encoding of quantum computing using trapped ions.

We consider non-Gaussian states generated by photon subtraction (PS) and photon addition (PA) on two-mode squeezed coherent (TMSC) states as resource states for continuous variable quantum teleportation. To this end, we derive the Wigner characteristic function for the family of photon-subtracted and photon-added TMSC states, which is then utilized to calculate the fidelity of teleporting a single-mode coherent state and a squeezed vacuum state. The analysis shows that, while symmetric PS enhances the fidelity of teleportation in an extensive range of squeezing, asymmetric PS enhances the performance marginally and only in the low squeezing regime. The addition operations, however, are less useful, symmetric three-PA leads to a marginal improvement while the other addition operations are useless. We consider the actual experimental setup for PS and PA operations and compute their success probabilities, which should be kept in mind while advocating the use of these operations. We could compute the fidelity of teleportation for a broad range of states because we analytically derive the Wigner characteristic function for these family of states, which we think will be useful for various other applications of these families of states.

When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography measurements of the quantum state. While full tomography measurement offers the most accurate reconstruction of the density matrix, limited measurements pose challenges for reconstruction algorithms, often resulting in nonphysical density matrices with negative eigenvalues. This is often remedied using maximum likelihood estimators, which have a high computing time or by other estimation methods that decrease the reconstructed fidelity. In this paper, we show that when restricting the measurement sample size, improvement over existing algorithms can be achieved. Our findings underline the multiplicity of solutions in the reconstruction problem, depending upon the generated state and measurement model utilized, thus motivating further research towards identifying optimal algorithms tailored to specific experimental contexts.

The formation of quantized vortices above a certain critical trap rotation frequency serves as a hallmark signature of superfluidity. Based on the beyond mean-field framework, crucial for the formation of exotic supersolid and droplet states, we investigate dynamical protocols for vortex nucleation in the superfluid and supersolid states of a dipolar Bose-Einstein condensate (BEC) at a trap rotation frequency lower than the conventional critical rotation frequency. We find that the critical rotation frequency depends not only on the dipole-dipole interaction strength, but also on the polarization direction of the external magnetic field. Interestingly, in the superfluid state, the critical rotation frequency increases with the tilt angle of the magnetic field, whereas in the supersolid state, increasing the tilt angle lowers the critical threshold. Leveraging these characteristics of dipolar BECs, along with the robustness of vortices with respect to changes in the polarization direction and $s$-wave scattering length, we demonstrate three dynamical protocols for vortex nucleation, even when rotating below the critical rotation frequency, viz., (i) varying the $s$-wave scattering length, (ii) changing the polarizing angle, and (iii) successive modulation of both the scattering length and polarizing angle. These dynamical vortex seeding protocols could serve as important benchmarks for future experimental studies.

Elementary excitation in the presence of a bosonic superfluid vortex line includes a kelvon and a Bogoliubov phonon as Nambu-Goldstone bosons, associated with spontaneous breaking of translational and $\text{U}\left(1\right)$ symmetries, respectively. Using the Bogoliubov approximation, we construct an effective Hamiltonian to describe the interplay among kelvons and Bogoliubov phonons in a microscopic manner and apply it for the decay process of an excited kelvon with Bogoliubov-phonon emission. Such a decay process governs the late-time behavior of vortex-excitation dynamics observed in cold-atom experiments and also in follow-up numerical simulations using the time-dependent Gross-Pitaevskii equation. We show our numerical result of the decay process and compare it with these previous studies. Our formalism provides the interaction Hamiltonian in terms of wave functions and energy spectra of the elementary excitations, thus potentially being useful in the description of other low-energy phenomena caused by the kelvon–Bogoliubov-phonon interaction.

The interplay among interaction, non-Hermiticity, and disorder opens a new avenue for engineering novel phase transitions. We study here the spectral and localization features of two interacting bosons in one-dimensional nonreciprocal quasicrystals. Specifically, by considering a quasiperiodic Hubbard lattice with nonreciprocal hoppings, we show that the interaction can lead to a mobility edge, which arises from the fact that the bound states display a much lower threshold for spectral and extended-localized transitions than scattering states. The localization transition of bound or scattering states is accompanied by a complex-real spectrum transition. Moreover, while the two-particle localized states are robust to the boundary conditions, the two-particle extended states turn into skin modes under open boundary conditions. We also show the correlated dynamics to characterize these localization transitions. Finally, we reveal that the bound states can form a mobility edge on their own by introducing a dimerized nonreciprocal quasicrystal. Our paper may pave the way for the study of non-Hermitian few-body physics.

Future distributed quantum systems and networks are likely to rely, at least in part, on the existing fiber infrastructure for entanglement distribution; hence, a precise understanding of the adverse effects of imperfections in optical fibers on entanglement is essential to their operation. Here, we consider maximally entangled polarization qubits and study the decay of the entanglement caused by spatial fluctuations in the refractive index of optical fibers. We study this entanglement dynamics using the spin-boson model and numerically solve our system of equations using the hierarchical equations of motion (HEOM) formalism. We show that within the range of practically relevant system parameters, our developed model exhibits both Markovian and non-Markovian entanglement decay behavior. Further, to counter the observed entanglement decay, we propose the implementation of dynamical decoupling in optical fibers using spaced half waveplates. In particular, we numerically model the time-dependent Hamiltonians of the Carr-Purcell-Meiboom-Gill and Uhrig dynamical decoupling schemes and show a reduced rate of entanglement decay even with sparsely spaced half waveplates along the length of optical fiber. Finally, we evaluate the performance of these two schemes in multiple system configurations.

For isotropic media, the magnetic field applied across the light propagation direction affects their optical properties only in the second order, and its effect proves to be much weaker than in the longitudinal field. In this work, we show that, under resonant excitation well beyond the linear regime, the situation changes drastically: A small magnetic linear anisotropy considerably increases, and an even stronger new quadrupole dichroism emerges. The latter manifests itself as the ${90}^{\circ }$-periodic azimuthal dependence of the transmission and anisotropic rotation of the probe polarization plane. These effects are described microscopically in a toy model, and their symmetry analysis is presented. Both are observed experimentally on the $D2$ resonance of cesium vapor and agree with the theoretical predictions. The large magnitude of the quadrupole dichroism makes it promising for magnetometric applications and for studying the effects of anisotropic bleaching.

Among the many loopholes that might be invoked to reconcile local realism with the experimental violations of Bell inequalities, the space dependence of the correlation functions appears particularly relevant for its connections with the so-called cluster property, one of the basic ingredients of axiomatic quantum field theory. The property states that the expectation values of products of observables supported within spacelike separated space-time regions factorize. Actually, in some massive models the factorization is exponentially fast with respect to the distance between the systems possibly involved in actual experiments. It is then often argued that considering the space dependence of the quantities involved in the Bell-like inequalities would eventually not violate them and thus support the reproducibility of the quantum behavior by a suitable local hidden variable model. In this paper, we show when this is actually the case and how nonlocal effects can still be visible.

Preparing the ground state of a local Hamiltonian is a crucial problem in understanding quantum many-body systems, with applications in a variety of physics fields and connections to combinatorial optimization. While various quantum algorithms exist which can prepare the ground state with high precision and provable guarantees from an initial approximation, current devices are limited to shallow circuits. Here we consider the setting where Alice and Bob, in a distributed quantum computing architecture, want to prepare the same Hamiltonian eigenstate. We demonstrate that the circuit depth of the eigenstate preparation algorithm can be reduced when the devices can share entanglement via a coherent link. This is especially so in the case where one of them has a near-perfect eigenstate, which is more efficiently broadcast to the other device. Our approach requires only a single auxiliary qubit per device to be entangled with the outside. We show that, in the near-convergent regime, the average relative suppression of unwanted amplitudes is improved to $1/\left(2\sqrt{e}\right)\approx 0.30$ per run of the protocol, outperforming the average relative suppression of $1/e\approx 0.37$ achieved with a single device alone for the same protocol.

The study of the gauge field is an everlasting topic in modern physics. Spin-orbit coupling is a powerful tool in ultracold atomic systems, resulting in an artificial gauge field that can be easily manipulated and observed in a tabletop environment. Combining optical Raman lattices and atom-atom interactions, the artificial gauge field can be made density dependent. In this work we propose a straightforward way to engineer a one-dimensional density-dependent gauge field in a Bose-Hubbard model in spin-orbit-coupled Raman lattices. We study the model from two perspectives: few-body quantum-walk dynamics and the many-body ground state. From the first perspective, we show that large spin-flipped tunneling can lead to a deep two-body bound state. From the second perspective, mean-field and density-matrix renormalization-group calculations consistently reveal three different phases, i.e., the Mott insulator phase, the superfluid phase, and the magnetic superfluid phase. Finally, we discuss the experimental protocol with Raman lattices based on existing experimental platforms.

A method is presented for the separation of polarization-entangled, frequency-degenerate photon pairs based on inverse Hong-Ou-Mandel interference. Adjusting the phase between photon states is achieved by exploiting the wavelength dispersion of optical glass, for which process a complete mathematical description is given. To experimentally demonstrate the phenomenon, a custom photon pair source has been built using spontaneous parametric downconversion of type-0 phase matching and a Sagnac interferometer. The effect of phase tuning was characterized by the modulation of coincidence probability. The visibility of quantum interference was found to be 0.820 and 0.720 for photons being in purely horizontal or vertical polarization state. In case of polarization entanglement, the measured state fidelity with respect to the $|{\mathrm{\Phi }}^{-}\rangle$ Bell state was 0.914.

Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve performance with increasing the number of qubits involved. Here, we propose a resource-efficient scaling of a five-qubit perfect code with increasing-weight cyclic stabilizers for small distances on the ring architecture, which takes into account the topological features of the superconducting platform. We show an approach to construct the quantum circuit of a correction code with ancillas entangled with non-neighboring data qubits. Furthermore, we introduce a neural network-based decoding algorithm supported by an improved lookup table decoder and provide a numerical simulation of the proposed code, which demonstrates the exponential suppression of the logical error rate.

Several variational quantum circuits for machine learning have been proposed in recent years, with one promising class of variational algorithms involving tensor networks operating on states resulting from local feature maps. In contrast, a random feature approach known as quantum kitchen sinks (C. M. Wilson et al., Quantum kitchen sinks: An algorithm for machine learning on near-term quantum computers, arXiv:1806.08321) provides comparable performance, but leverages nonlocal feature maps. Here we combine these two approaches by proposing a circuit Ansatz where a tree tensor network coherently processes the nonlocal feature maps of quantum kitchen sinks and we run numerical experiments to evaluate the performance of the Ansatz on image classification. From the perspective of classification performance, we find that simply combining quantum kitchen sinks with tensor networks yields no qualitative improvements. However, the addition of feature optimization greatly boosts performance, leading to state-of-the-art quantum circuits for image classification, requiring only shallow circuits and a small number of qubits, both well within reach of near-term quantum devices.

We formulate a general hybrid quantum-classical technique to describe the interaction of diatomic molecules with XUV pulses. We demonstrate the accuracy of our model in the context of the interaction of the ${\mathrm{O}}_2$ molecule with an XUV pulse with photon energy ranging from 20–42 eV. We account for the electronic structure and electron ionization quantum mechanically employing accurate molecular continuum wave functions. We account for the motion of the nuclei using classical equations of motion. However, the force of the nuclei is computed by obtaining accurate potential-energy curves of ${\mathrm{O}}_2$ up to ${\mathrm{O}}_2^{2+}$, relevant to the 20–42 eV photon-energy range, using advanced quantum-chemistry techniques. We find the dissociation limits of these states and the resulting atomic fragments and employ the velocity-Verlet algorithm to compute the velocities of these fragments. We incorporate both electron ionization and nuclear motion in a stochastic Monte Carlo simulation and identify the ionization and dissociation pathways when ${\mathrm{O}}_2$ interacts with an XUV pulse. Focusing on the ${\mathrm{O}}^{+}+{\mathrm{O}}^{+}$ dissociation pathway, we obtain the kinetic-energy release (KER) distributions of the atomic fragments and find very good agreement with experimental results. Also, we explain the main features of the KER in terms of ionization sequences consisting of two sequential single-photon absorptions resulting in different ${\mathrm{O}}^{+}$ and ${\mathrm{O}}^{2+}$ electronic state configurations involved in the two transitions.

Taking ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ as examples, we theoretically study the postionization dynamics of molecules in strong laser fields using a density matrix method for open systems, focusing on the effect of ionization-produced coherence on the dynamics of residual ions. We apply the adiabatic strong-field approximation (ASFA) method to predict the coherences between ionic states resulting from multiorbital strong-field ionizations. Compared with the standard strong-field approximation, the ASFA method can be applied across a wide range of laser intensities due to the consideration of orbital distortion effects. Based on the ASFA, it is found that there are obvious coherences between ionic states in residual molecular ions. These coherences significantly influence the transitions between ionic states, which finally change the postionization dynamics of molecular ions. Our findings reveal the importance of the ionization-produced coherences in modulating postionization molecular dynamics.

We unravel the existence and stability properties of one-dimensional droplets arising in genuine two-component particle-imbalanced bosonic mixtures under the influence of a weak harmonic confinement. A plethora of miscible droplet phases is found with the majority component atoms in the vicinity of the minority ones assembling in a droplet configuration, while the remaining excess atoms are in the gas state. Our computations identify a transition from a bound to a trapped gas many-body state for increasing total atom number and fixed interactions, with the bound character being prolonged for stronger intercomponent attractions. The spectral stability of these two-component droplets is revealed by examining their underlying Bogoliubov–de Gennes excitation spectrum. Furthermore, the collective dynamics associated with the fundamental dipole and breathing modes of the system is monitored by suddenly shifting the trap's center or quenching the trap's frequency, respectively. There, a backaction of the significantly localized minority component is imprinted in the majority cloud. The present findings can be simulated in recent cold-atom experiments, thus setting the stage for probing the complex nonequilibrium dynamics of two-component droplets.

The inverse-scattering analysis of the nonlinear Schrödinger equation (NSE) is shown to provide powerful insights into a beam breakup and filamentation dynamics of high-power laser pulses. In the highly nonlinear regime, in which a laser beam tends to break up into multiple filaments as a part of its nonlinear dynamics, the scattering-space waves representing real-space NSE fields are shown to obey the scalar wave equation for the field in a fictitious waveguide with an index profile as dictated by the Kerr lens induced by the laser beam. Despite the drastic differences in the ways the inverse-scattering framework and the Bespalov-Talanov theory of beam filamentation treat nonlinear beam dynamics, the angular spectrum of beam instabilities and the transverse size of filaments in both frameworks can be understood on strikingly similar grounds—in terms of wave-vector matching, reflecting the wave-by-wave scattering nature of the emerging filamentary beam structure.