Large-scale quantum devices provide insights beyond the reach of classical simulations. However, for a reliable and verifiable quantum simulation, the building blocks of the quantum device require exquisite benchmarking. This benchmarking of large-scale dynamical quantum systems represents a major challenge due to lack of efficient tools for their simulation. Here, we present a scalable algorithm based on neural networks for Hamiltonian tomography in out-of-equilibrium quantum systems. We illustrate our approach using a model for a forefront quantum simulation platform: ultracold atoms in optical lattices. Specifically, we show that our algorithm is able to reconstruct the Hamiltonian of an arbitrary sized bosonic ladder system using an accessible amount of experimental measurements. We are able to significantly increase the previously known parameter precision.

We present a proposal to test the Bell inequality in the emerging field of cavity optomagnonics, where a sphere of ferromagnetic crystal supports two optical whispering gallery modes and one magnon mode. The two optical modes are driven by two laser pulses, respectively. Entanglement between the magnon mode and one of the two optical modes will be generated by the first pulse, and the state of the magnon mode is subsequently mapped into another optical mode via the second pulse. Hence correlated photon-photon pairs are created out of the cavity. A Bell test can be implemented by using these pairs, which enables us to test the local hidden-variable models at macroscopic scales. Our results show that a significant violation of the Bell inequality can be obtained in the weak-coupling regime. The violation of the Bell inequality not only verifies the entanglement between magnons and photons, but also implies that cavity optomagnonics is a promising platform for quantum information processing tasks.

By employing the spin-boson model in a dense limit of environmental modes, quantum entanglement and correlation of sub-Ohmic and Ohmic baths for dissipative quantum phase transitions are numerically investigated based on the variational principle. With several measures borrowed from quantum information theory, three different types of singularities are found for the first-order, second-order, and Kosterlitz-Thouless phase transitions, respectively, and the values of transition points and critical exponents are accurately determined. Besides, the scaling form of the quantum discord in the Ohmic case is identified, quite different from that in the sub-Ohmic regime. In a two-spin model, two distinct behaviors of the quantum discord are uncovered: one is related to the quantum entanglement between two spins and the other is decided by the correlation function in the position space rather than the entanglement.

Recent experimental studies have shown that the relaxation time $T_1$ and the dephasing time $T_2$ of superconducting qubits fluctuate considerably over time. Time-varying quantum channel (TVQC) models have been proposed in order to consider the time-varying nature of the parameters that define qubit decoherence. This dynamic nature of quantum channels causes a degradation of the performance of quantum error correction codes (QECCs) that is portrayed as a flattening of their error rate curves. In this article we introduce the concepts of quantum outage probability and quantum hashing outage probability as asymptotically achievable error rates by a QECC with the quantum rate $R_Q$ operating over a TVQC. We derive closed-form expressions for the family of time-varying amplitude damping channels and study their behavior for different scenarios. We quantify the impact of time variation as a function of the relative variation of $T_1$ around its mean. We conclude that the performance of QECCs is limited in many cases by the inherent fluctuations of their decoherence parameters and corroborate that parameter stability is crucial to maintain the excellent performance observed over static quantum channels.

In this work we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schrödinger-type, Hamiltonian partial differential equations (PDEs), using space-efficient variational circuits, including the symmetries of the problem, and global and gradient-based optimizers. We use this algorithm to benchmark the performance of the representation techniques by means of the computation of the ground state in three PDEs, i.e., the one-dimensional quantum harmonic oscillator and the transmon and flux qubits, studying how they would perform in ideal and near-term quantum computers. With the Fourier methods developed here, we obtain low infidelities of order ${10}^{-4}–{10}^{-5}$ using only three to four qubits, demonstrating the high compression of information in a quantum computer. Practical fidelities are limited by the noise and the errors of the evaluation of the cost function in real computers, but they can also be improved through error mitigation techniques.

To employ a quantum device, the performance of the quantum gates in the device needs to be evaluated first. Since the dimensionality of a quantum gate grows exponentially with the number of qubits, evaluating the performance of a quantum gate is a challenging task. Recently, a scheme called quantum gate verification (QGV) has been proposed, which can verifies quantum gates with near-optimal efficiency. In this paper, we implement a proof-of-principle optical experiment to demonstrate this QGV scheme. We show that for a single-qubit quantum gate, only $\sim 300$ samples are needed to confirm the fidelity of the quantum gate to be, at least, 97% with a 99% confidence level using the QGV method, whereas, at least, $\sim 3000$ samples are needed to achieve the same result using the standard quantum process tomography method. The QGV method validated by this paper has the potential to be widely used for the evaluation of quantum devices in various quantum information applications.

With the development of the quantum many-body simulator, Hamiltonian tomography has become an increasingly important technique for verification of quantum devices. Here we investigate recovering the generic Hamiltonians of two spin chains with two-local interactions and three-local interactions by measuring local observables. For these two models, we show that, when the chain length reaches a certain critical number, we can recover the generic local Hamiltonian from its one steady state by solving the homogeneous operator equation (HOE) developed by Bairey, Arad, and Lindner [Phys. Rev. Lett. 122, 020504 (2019)]. To explain the existence of such a critical chain length, we develop an alternative method to recover the Hamiltonian by solving the energy eigenvalue equations (EEE). By using the EEE method, we completely recovered the numerical results from the HOE method. Then we theoretically prove the equivalence between the HOE method and the EEE method. In particular, we obtain the analytical expression of the rank of the constraint matrix in the HOE method by using the EEE method, which can be used to determine the correct critical chain length in all the cases.

Applying optimal control algorithms on realistic quantum systems confronts two key challenges: to efficiently adopt physical constraints in the optimization and to minimize the variables for the convenience of experimental tuneups. To resolve these issues, we propose an algorithm by incorporating multiple constraints into the gradient optimization over piecewise pulse constant values, which are transformed to contained numbers of the finite Fourier basis for bandwidth control. Such complex constraints and variable transformation involved in the optimization introduce extreme difficulty in calculating gradients. We resolve this issue efficiently utilizing autodifferentiation on the machine learning platform TensorFlow. We test our algorithm by finding smooth control pulses to implement single-qubit and two-qubit gates for superconducting transmon qubits with always-on interaction, which remains a challenge of quantum control in various qubit systems. Our algorithm provides a promising optimal quantum control approach that is friendly to complex and optional physical constraints.

The parity-violating energy difference (PVED) between two enantiomers of a chiral molecule is caused by the weak interaction. Because of the smallness of the PVED, nonzero PVED is yet to be discovered in experimental searches. To detect the PVED, the search for molecules with large PVED values is important. Previously, one of the authors proposed that the PVED may be significantly enhanced in ionized or excited states. The significant enhancement of the PVED in some electronic excited states is proven in this study using ${\mathrm{H}}_2{X}_2$ ($X$ = O, S, Se, Te) molecules as examples. The maximum enhancement was an about 360-fold increase for ${\mathrm{H}}_2{\mathrm{Se}}_2$. For the PVED calculation, we employ the finite-field perturbation theory (FFPT) within the equation-of-motion coupled-cluster theory based on the exact two-component molecular mean-field Hamiltonian. The relation between the enhancement of the PVED and the contribution to the PVED from the highest occupied molecular orbital is also examined. The effects of computational elements, such as parameters related to the electron correlation and FFPT on PVED values in excited states of ${\mathrm{H}}_2{X}_2$ molecules, are studied.

Predicting magic wavelengths accurately requires precise knowledge of electric dipole matrix elements of nearby atomic transitions. As a result, measurements of magic wavelengths allow us to test theoretical predictions for the matrix elements that frequently cannot be probed by any other methods. Here, we calculate and measure a magic wavelength near 473 nm of the $5s^2{}^1{S}_0-5s5p{}^3{P}_1$ intercombination transition of ${}^{88}\mathrm{Sr}$. Experimentally, we find 473.371(6) nm for $\mathrm{\Delta }m=0$ ($\pi$ transition) and 473.117(15) nm for $\mathrm{\Delta }m=-1$ (${\sigma }^{-}$ transition). Theoretical calculations yield 473.375(22) and 473.145(20) nm, respectively. Determining magic wavelengths nearby the dominant 461-nm probe transition of ${}^{88}\mathrm{Sr}$ holds promise for state insensitive interfacing of strontium atoms and nanophotonic devices with a narrow band of operating wavelengths. Furthermore, the ${}^3{P}_1$ polarizability is dominated by the contributions to the $5p^2{}^{3}P$ levels, and excellent agreement of theory and experiment validates both theoretical values of these matrix elements and estimates of their uncertainties.

The rate coefficients for dielectronic recombination and electron-impact excitation processes with H-like to Be-like silicon ions (${\mathrm{Si}}^{13+}\text{−}{\mathrm{Si}}^{10+}$) are calculated using relativistic distorted-wave approach. The prominent $▵n=1$ and the weaker $▵n=2$ and 3 dielectronic recombination (DR) resonances with $K$-shell excitations are presented, and compared with the existing DR experimental rate coefficients of ${\mathrm{Si}}^{13+}, {\mathrm{Si}}^{12+}$, and ${\mathrm{Si}}^{11+}$ ions, it is found that the theoretical DR rate coefficients are in very good agreement with the experimental results. With the same approach, the direct and resonant electron-impact excitation (EIE) cross sections associated with $1s-n^{\prime }{l}^{\prime }$ core excitations are calculated for the ground states of ${\mathrm{Si}}^{13+}\text{−}{\mathrm{Si}}^{10+}$ ions and found in excellent agreement with the available experiment. Finally, we present the synthesized DR and EIE rate coefficients for the sum of all detected $(13+\sim 10+)$ charge states of Si and these agree well with the experimental results.

Levitated nanodiamonds containing negatively charged nitrogen-vacancy centers $\left({\text{NV}}^{-}\right)$ have been proposed as a platform to generate macroscopic spatial superpositions. Requirements for this include having a long ${\text{NV}}^{-}$ spin coherence time, which necessitates formulating a dynamical decoupling strategy in which the regular spin flips do not cancel the growth of the superposition through the Stern-Gerlach effect in an inhomogeneous magnetic field. Here, we propose a scheme to place a $250\text{−}\mathrm{n}\mathrm{m}$-diameter diamond in a superposition with spatial separation of over $250\mathrm{n}\mathrm{m}$, while incorporating dynamical decoupling. We achieve this by letting a diamond fall for $2.4\mathrm{m}$ through a magnetic structure, including $1.13\mathrm{m}$ in an inhomogeneous region generated by magnetic teeth.

Accurate data on electric-dipole transition matrix elements (EDTMs) for bound-bound Rydberg-atom transitions have become increasingly important in science and technology. Here we compute radial EDTMs of rubidium in length, velocity, and acceleration forms for electric-dipole-allowed transitions between states with principal and angular-momentum quantum numbers $n$ and $\ell$ ranging from 15 to 100. Wave functions are computed based upon model potentials from [Phys. Rev. A 49, 982 (1994)]. Length-gauge EDTMs of strong low-$\ell$ Rydberg transitions, often employed in research and technology, are found to deviate from the fundamentally more accurate velocity-gauge form by approximately-$n$-independent and series-dependent shifts. The shift amount peaks at about $0.34e{a}_0$ for the Rb $nD\leftrightarrow (n+1)P$ series, a particularly strong Rydberg-transition series in Rb. The shift corresponds to relative EDTM corrections of up to $\approx {10}^{-3}$, which can be of concern in high-precision applications. We discuss the physical reasons for the observed gauge differences, explain the conditions for applicability of the velocity- and length-gauge forms for different transition series, and present a decision tree of how to choose EDTMs.

We theoretically study the attoclock using the Bohmian trajectory. The Bohmian trajectory includes a nonlocal quantum potential and the Coulomb potential, allowing us to separately study their effects on the attoclock. We show that the quantum potential has a significant effect on the photoelectron momentum spread while it only slightly affects the offset angle in the attoclock. We further show how the Coulomb potential affects the offset angle, revealing that the Coulomb force before the electron reaches the position of the classical tunnel exit has a significant contribution to the offset angle. Thus taking the full Coulomb effect into account during the tunneling ionization is a prerequisite for our understanding of the origin of the offset angle in the attoclock experiment. Our study also implies that there might be an inertia time for the initial wave function in response to the change of the laser electric field.

We present precise path-integral Monte Carlo results for the thermodynamics of a homogeneous dilute Bose gas. Pressure and energy are calculated as a function of temperature both below and above the Bose-Einstein transition. Specifically, we address interaction effects, focusing on deviations from the ideal-gas law in the thermodynamic limit. We also calculate the isothermal compressibility and the contact parameter, which provide a clear signature of the role played by interactions. In particular, we obtain indications of a discontinuity of the compressibility at the transition point. To gain physical insight, numerical results are systematically compared with the predictions of first-order Hartree-Fock and second-order Popov theories, both giving an approximate description of the gas thermodynamics. The comparison shows the extension of the critical region around the transition point, where the inaccuracies of the perturbative expansions are more pronounced.

Engineering quantum phases with spontaneously broken symmetries is a major goal of research in different fields. Trapped ultracold Rydberg-excited atoms in optical lattices are a promising platform for realizing quantum phases with broken lattice translational symmetry since they are interacting over distances larger than the lattice constant. Although numerous theoretical works on trapped Rydberg-excited gases have predicted such phases, in particular, density wave or supersolid phases, their experimental observation proves to be difficult due to challenges such as scattering processes and the limited experimentally achievable coupling strength. Most of these previous studies have focused on isotropically interacting gases dressed with Rydberg $s$ states, while the effect of anisotropic interactions due to Rydberg-excited $p$ states in trapped quantum gases remains much less investigated. Additionally, it was shown that the excitation scheme used to excite Rydberg $p$ states possesses advantages regarding achievable coupling strengths and limitation of scattering processes compared to its $s$-state counterpart, which makes the investigation of Rydberg $p$-state dressed quantum gases even more interesting. In the present work we study the extended two-component Bose-Hubbard model, realized with a bosonic quantum gas with Rydberg-excited $p$ states trapped in an optical lattice, within the Gutzwiller mean-field theory. We compute the ground-state phase diagram and investigate its different regimes. By comparison to the phase diagram of the isotropic case, we find the anisotropic interaction to be more advantageous for the observation of supersolid phases.

We study a one-dimensional Bose gas with two internal states described by the Yang-Gaudin model and calculate analytically the dispersion relation of a polaron quasiparticle, which is the lowest excitation branch. We study the dispersion in the thermodynamic limit in the regimes of weak and strong interaction without limitations on the momentum. At weak interaction the polaron dispersion is in the vicinity of the dark soliton one; we calculate the leading deviation in the parametric form. At strong interaction we find an ansatz for the explicit form of the polaron dispersion. It has the form of a power series of the sine function of the momentum with interaction-dependent coefficients. By increasing the power of the series, the corresponding coefficients show faster decay and thus one practically needs only a few of them; we give the results for the first three. The coefficients of the series are connected to the Maclaurin series of the polaron dispersion and thus it is sufficient to calculate latter quantity to automatically find the power series result for the dispersion at all momenta. The derived results for the dispersion can be used to obtain explicit expressions for the exponents of the power-law singularities in the response functions at the spectral edge.

Spinful superfluids of ultracold atoms are ideal for investigating the intrinsic properties of spin current and texture because they are realized in an isolated, nondissipative system free from impurities, dislocations, and thermal fluctuations. This study theoretically reveals the impact of spin current on a magnetic domain wall in spinful superfluids. An exact wall solution is obtained in the ferromagnetic phase of a spin-1 Bose-Einstein condensate with easy-axis anisotropy at zero temperature. The bosonic-quasiparticle mechanics analytically show that the spin current along the wall becomes unstable if the velocity exceeds the critical spin-current velocities, leading to complicated situations because of the competition between transverse magnons and ripplons. Our direct numerical simulation reveals that this system has a mechanism to generate an eccentric fractional skyrmion, which has a fractional topological charge, but its texture is not similar to that of a meron. This mechanism is in contrast to the generation of conventional skyrmions in easy-axis magnets. The theoretical findings can be examined in the same situation as in a recent experiment on ultracold atoms. In terms of the universality of spontaneous symmetry breaking, unexplored similar phenomena are expected in different physical systems with the same broken symmetry.

Quantum imaging, one of the pillars of quantum technologies, is well suited to study sensitive samples which require low-light conditions, like biological tissues. In this context, interaction-free measurements (IFM) allow us to infer the presence of an opaque object without the photon interacting with the sample. Current IFM schemes are designed for single-pixel objects, while real-life samples are structured, multipixel objects. Here we extend the IFM imaging schemes to multipixel, semitransparent objects, by encoding the information about the pixels into an internal degree of freedom, namely orbital angular momentum. This allows us to image the pixels in parallel. Our solution exhibits a better theoretical efficiency than the single-pixel case. Our scheme can be extended to other degrees of freedom, like the photon radial quantum number, in order to image one-dimensional (1D) and 2D objects.

Narrowband biphotons from an atomic ensemble are an extraordinary source for quantum information science. The generation of biphotons in the warm atomic system has many applicable prospects for its simplicity, stability, and compactness. In this article we experimentally demonstrate the generation of biphotons from the spontaneous four-wave mixing (SFWM) process in a warm rubidium vapor cell. By performing high-dimensional Bell-type measurements and mutually unbiased measurements, we maximally obtain a three-dimensional orbital-angular-momentum discrete-variable (DV) entangled state. The violation of high-dimensional Bell inequalities shows the great potential of warm atomic systems in generating DV high-dimensional entanglement. Such narrowband photon pairs may find applications in quantum-memory-based quantum communication networks. Through integration with the continuous-variable (CV) entanglement already existing in the same SFWM platform, our results here pave the way to construct atomic-ensemble-based DV-CV hybrid quantum information protocols.