Quantum computing can be used to speed up the simulation time (more precisely, the number of queries of the algorithm) for physical systems; one such promising approach is the Hamiltonian simulation (HS) algorithm. Recently, it was proven that the quantum singular-value transformation (QSVT) achieves the minimum simulation time for HS. An important subroutine of the QSVT-based HS algorithm is the amplitude amplification operation, which can be realized via the oblivious amplitude amplification or the fixed-point amplitude amplification in the QSVT framework. In this work we execute a detailed analysis of the error and number of queries of the QSVT-based HS and show that the oblivious method is better than the fixed-point one in the sense of simulation time. Based on this finding, we apply the QSVT-based HS to the one-dimensional linearized Vlasov-Poisson equation and demonstrate that the linear Landau damping can be successfully simulated.

Quantum simulation of dynamics is an important goal in the noisy intermediate-scale quantum era, within which quantum error mitigation may be a viable path towards modifying or eliminating the effects of noise. Most studies on quantum error mitigation have focused on the resource cost due to its exponential scaling in the circuit depth. Methods such as probabilistic error cancellation rely on discretizing the evolution into finite time steps and applying the mitigation layer after each time step, modifying only the noise part without any Hamiltonian dependence. This may lead to Trotter-like errors in the simulation results even if the error mitigation is implemented ideally, which means that the number of samples is taken as infinite. Here we analyze the aforementioned errors which have been largely neglected before. We show that they are determined by the commutating relations between the superoperators of the unitary part, the device noise part, and the noise part of the open dynamics to be simulated. We include both digital quantum simulation and analog quantum simulation setups and consider defining the ideal error mitigation map both by exactly inverting the noise channel and by approximating it to first order in the time step. We use single-qubit toy models to numerically demonstrate our findings. Our results illustrate fundamental limitations of applying probabilistic error cancellation in a stepwise manner to continuous dynamics, thus motivating the investigations of truly time-continuous error cancellation methods.

The dissipative quantum Fisher information (DQFI) for a dynamic map with a general parameter in an open quantum system is investigated, which can be regarded as an analog of the quantum Fisher information in the Liouville space. We first derive a general dissipative generator in the Liouville space, and based on its decomposition form, find the DQFI stems from two parts. One is the dependence of eigenvalues of the Liouvillian supermatrix on the estimated parameter, which shows a linear dependence on time. The other is the variation of the eigenvectors with the estimated parameter. The relationship between this part and time presents rich characteristics, including harmonic oscillation, pure exponential gain and attenuation, as well as exponential gain and attenuation of oscillatory type, which depend specifically on the properties of the Liouville spectrum. This is in contrast to that of the conventional generator, where only oscillatory dependencies are seen. Particularly, we find that the nonunitary parameter encoding process induced by the dissipative generator can be transformed into two unitary encoding processes plus the contribution of the commutator between the two. Further, we illustrate the theory through a toy model: a two-level system with spin-flip noise. Especially, by using the DQFI, we demonstrated that the exceptional estimation precision cannot be obtained for this model at the Liouvillian exceptional point.

We reexamine the long-range interaction between two atoms placed in an equilibrium thermal radiation environment. Employing the formalism of quantum electrodynamics at finite temperatures, we derive an expression for the thermal correction to the interaction potential and explore various asymptotic behaviors. The numerical calculations of temperature-dependent dispersion coefficients for both the ground and highly excited states of the hydrogen atom are performed. We proceed from the first principles of the theory to derive the dipole-dipole interaction at finite temperature. The analysis presented in this work reveals that the expressions established earlier in the context of phenomenological extrapolation from zero- to finite-temperature scenarios exhibit disparate asymptotic behavior and lead to overestimated results compared to those of the rigorous quantum electrodynamics approach.

We investigate theoretically the elliptically high-order harmonic generation from the ring-current state of the Ne atom by numerically solving the two-dimensional time-dependent Schrödinger equation in an orthogonally polarized two-color (OTC) laser fields. We find that the elliptically polarized harmonics can be generated by the ring-current state with nonzero angular momentum. A high-efficiency near-circularly-polarized single-atom radiation pulse can be obtained by adjusting the intensity ratio of the OTC laser fields. As the intensity ratio increases, the efficiency of the harmonics is enhanced and the ellipticity of the harmonics is increased, which is illustrated by the temporal evolution of the electronic density probability and the semiclassical three-step model. Moreover, we find that the ellipticity of a single-atom radiation pulse is sensitive to the relative phase of the OTC laser fields, which offers the possibility to control the polarization of extreme ultraviolet radiation.

We investigate the quantum phases of bosons in a two-chain-coupled ladder. This bosonic ladder is generally in a biased configuration, meaning that the two chains of the ladder can have dramatically different on-site interactions and potential energies. Adopting the numerical density-matrix renormalization-group method, we analyze the phase transitions in various parameter spaces. We find signatures of both insulating-to-superfluid and superfluid-to-insulating quantum phase transitions as the interchain tunneling is increased. Interestingly, tuning the interaction to some intermediate values, the system can exhibit a reentrant quantum phase transition between insulating and superfluid phases. We show that for infinite interaction bias the model is amenable to analytical treatment, predictions of which concerning the phase boundary are in great agreement with numerical results. We finally clarify some critical parameters which separate the system into regimes with distinct phase-transition behaviors, and we briefly compare typical properties of the biased and unbiased bosonic ladder systems. Our paper enriches Bose-Hubbard physics.

We study the dynamics of the matter-wave soliton interacting with a vibrating mirror created by an evanescent light and provide a quantum scattering picture for the time-domain diffraction of the matter-wave soliton. Under Kramers-Henneberger (KH) transformation, i.e., in a vibrating coordinate, the vibration of the mirror can be cast to an effective gauge field. We then can exploit the Dyson series and the quantum scattering theory to investigate the dynamics of the soliton that moves in the effective gauge field and is reflected by a static mirror. Our analytical theory can quantitatively deduce the locations and the relative weights of the scattered wave packets, which is consistent with our numerical simulations of directly solving a nonlinear Schrödinger equation. In particular, for a two-frequency vibrating case, our theory predicts some interesting multipeak sideband structures in the diffracted matter-wave distributions, which can be resorted to the resonance of two frequencies. Underlying mechanisms and possible applications are discussed.

Atomic arrays can exhibit collective light emission when the transition wavelength exceeds their lattice spacing. Subradiant states take advantage of this phenomenon to drastically reduce their overall decay rate, allowing for long-lived states in dissipative open systems. We build on previous work to investigate whether or not disorder can further decrease the decay rate of a singly excited atomic array. More specifically, we consider spatial disorder of varying strengths in a one-dimensional (1D) half waveguide and in 1D, two-dimensional (2D), and three-dimensional (3D) atomic arrays in free space and analyze the effect on the most subradiant modes. While we confirm that the dilute half waveguide exhibits an analog of Anderson localization, the dense half waveguide and free-space systems can be understood through the creation of close-packed, few-body subradiant states similar to those found in the Dicke limit. In general, we find that disorder provides little advantage in generating darker subradiant states in free space on average and will often accelerate decay. However, one could potentially change interatomic spacing within the array to engineer specific subradiant states.

Equioverlapping measurements, as a natural class of quantum measurements with the appealing property of equal overlap between any pair of measurement operators, generalize both the notions of equiangular tight frames (including von Neumann measurements) and symmetric informationally complete positive operator valued measures (SIC-POVMs). The structures of equioverlapping measurements in general dimensions are rather subtle and complicated. In this work, we reveal some structural properties of equioverlapping measurements which may be useful for constructing and classifying equioverlapping measurements. In particular, we obtain two bounds for the number of measurement operators in an equioverlapping measurement. We further illustrate how equioverlapping measurements go beyond SIC-POVMs in a nontrivial fashion with some illuminating examples in lower dimensions (two, three, and four). Finally, we present the challenging problem of fully classifying equioverlapping measurements and discuss some related perspectives.

The problem of simulatability of quantum processes using classical resources plays a cornerstone role for quantum computing. Quantum circuits can be simulated classically, e.g., using Monte Carlo sampling techniques applied to quasiprobability representations of circuits' basic elements, i.e., states, gates, and measurements. The effectiveness of the simulation is determined by the amount of the negativity in the representation of these basic elements. Here we develop an approach for minimizing the total negativity of a given quantum circuit with respect to quasiprobability representations, that are overcomplete, i.e., are such that the dimensionality of corresponding quasistochastic vectors and matrices is larger than the squared dimension of quantum states. Our approach includes both optimization over equivalent quasistochastic vectors and matrices, which appear due to the overcompleteness, and optimization over overcomplete frames. We demonstrate the performance of the developed approach on some illustrative cases, and show its significant advantage compared to the standard overcomplete quasistochastic representations. We also study the negativity minimization of noisy brick-wall random circuits via a combination of increasing frame dimension and applying gate merging technique. We demonstrate that the former approach appears to be more efficient in the case of a strong decoherence.

An alternative quantization rule, in which time becomes a self-adjoint operator and position is a parameter, was proposed by Dias and Parisio [Phys. Rev. A 95, 032133 (2017)]. In this approach, the authors derived a space-time-symmetric (STS) extension of quantum mechanics (QM) where a new quantum state (intrinsic to the particle) $\left|\varphi \right(x)\rangle$ is defined at each point in space. The quantum state $\left|\varphi \right(x)\rangle$ obeys a space-conditional (SC) Schrödinger equation and its projection on $|t\rangle , \langle t\left|\varphi \right(x)\rangle$, represents the probability amplitude of the particle's arrival time at $x$. In this work we provide an interpretation of the SC Schrödinger equation and the eigenstates of observables in the STS extension. Analogous to the usual QM, we propose that by knowing the initial state $\left|\varphi \right(x_0)\rangle$, which predicts any measurement on the particle performed by a detector localized at $x_0$, the SC Schrödinger equation provides $|\varphi \left(x\right)\rangle =\widehat{\mathbb{U}}(x,x_0)|\varphi \left(x_0\right)\rangle$, enabling us to predict measurements when the detector is at $x\lessgtr x_0$. We also verify that for space-dependent potentials, momentum eigenstates in the STS extension $|P_b\left(x\right)\rangle$ depend on position just as energy eigenstates in the usual QM depend on time for time-dependent potentials. In this context, whereas a particle in the momentum eigenstate in the standard QM, $|\psi \left(t\right)\rangle ={|P\rangle |}_t$, at time $t$, has momentum $P$ (and indefinite position), the same particle in the state $|\varphi \left(x\right)\rangle =|P_b\left(x\right)\rangle$ arrives at position $x$ with momentum $P_b\left(x\right)$ (and indefinite arrival time). By investigating the fact that $\left|\psi \right(t)\rangle$ and $\left|\varphi \right(x)\rangle$ describe experimental data of the same observables collected at $t$ and $x$, respectively, we conclude that they provide complementary information about the same particle. Finally, we solve the SC Schrödinger equation for an arbitrary space-dependent potential. We apply this solution to a potential barrier and compare it with a generalized Kijowski distribution, showing that they can predict distinct traversal times.

We introduce a relax-and-round approach embedding the quantum approximate optimization algorithm (QAOA) with $p\ge 1$ layers. We show for many problems, including Sherrington-Kirkpatrick spin glasses, that at $p=1$, it is as accurate as its classical counterpart, and maintains the infinite-depth optimal performance guarantee of the QAOA. Employing a different rounding scheme, we prove the method shares the performance of the Goemans-Williamson algorithm for the maximum cut problem on certain graphs. We pave the way for an overarching quantum relax-and-round framework with performance on par with some of the best classical algorithms.

The quantum harmonic oscillator is one of the most fundamental objects in physics. We consider the case where it is extended to an arbitrary number modes and includes all possible terms that are bilinear in the annihilation and creation operators, and we assume that we also have an arbitrary time-dependent drive term that is linear in those operators. Such a Hamiltonian is very general, covering a broad range of systems, including quantum optics, superconducting circuit QED, quantum error correcting codes, Bose-Einstein condensates, atomic wave packet transport beyond the adiabatic limit, and many others. We examine this situation from the point of view of quantum control, making use of optimal control theory to determine what can be accomplished, both when the controls are arbitrary and when they must minimize some cost function. In particular we develop a class of analytical pulses. We then apply our theory to a number of specific topical physical systems to illustrate its use and provide explicit control functions, including the case of the continuously driven conditional displacement gate.

We demonstrate a method to reduce the number of single-photon detectors (SPDs) required in multiparty quantum key distribution (QKD) networks by a factor of 2 by using detector time multiplexing (DTM). We implement the DTM scheme for an entanglement-based time-bin protocol and compare QKD results with and without DTM in our QKD network with four users. When small efficiency losses are acceptable, DTM enables cost-effective, scalable implementations of multiuser QKD networks.

Intensities in the Tm i emission series originating from a common upper level are measured using a Fourier transform spectrometer. The derived relative transition probabilities within each series are compared to the theoretical predictions obtained from large-scale calculations that combine configuration interaction with many-body perturbation theory. Moreover, the Tm i spectrum recorded in an external magnetic field is analyzed. Our theoretical results well describe the current measurements and show no more than a two-fold difference from previous experimental data on absolute transition probabilities. Additionally, Landé $g$ factors, hyperfine structure constants, and atomic electric quadrupole moments for several levels of interest are computed and compared to experimental observations, where available.

We investigate the ground state and dynamics of one-dimensional spin-orbit coupled (SOC) quantum droplets within the extended Gross–Pitaevskii approach. As the SOC wave number increases, stripe droplet patterns emerge, with a flat-top background, for larger particle numbers. The surface energy decays following a power-law with respect to the interactions. At small SOC wave numbers, a transition from Gaussian to flat-top droplets occurs for either a larger number of atoms or reduced intercomponent attraction. The excitation spectrum shows that droplets for relatively small SOC wave numbers are stable, otherwise stripe droplets feature instabilities as a function of the particle number or the interactions. We also witness rich droplet dynamical features using velocity imprinting and abrupt changes in the intercomponent interaction or the SOC parameters. Characteristic responses include breathing oscillations, expansion, symmetric and asymmetric droplet fragmentation, admixtures of single and stripe droplet branches, and erratic spatial distributions suggesting the triggering of relevant instabilities. Our results reveal the controlled dynamical generation and stability properties of stripe droplets that should be detectable in current cold-atom experiments.

We study oblique incident light absorption in opaque media with rough surfaces. An analytical approach with modified boundary conditions taking into account the surface roughness in metallic or dielectric films has been discussed. Our approach reveals interference-linked terms that modify the absorption dependence on different characteristics. We have discussed the limits of our approach that hold valid from the visible to the microwave region. Polarization and angular dependences of roughness-induced absorption are revealed. The existence of an incident angle or a wavelength for which the absorptance of a rough surface becomes equal to that of a flat surface is predicted. Based on this phenomenon a method of determining roughness correlation length is suggested.

Symmetry plays a key role in classifying topological phases, which can be enriched by the projective symmetry group in the presence of artificial gauge fields (AGFs). Here, we utilize two-dimensional (2D) photonic microring lattices to create three different topological states based on projective symmetry. By engineering link rings, we are able to flexibly manipulate the AGFs and coupling magnitude. As each plaquette carries a $\pi$ flux, the two translation symmetries of a rectangle microring lattice are projectively represented. By applying different types of dimerization, we tune the spatial space to break translation symmetry and achieve a Möbius topological insulator with twisted edge bands and a graphenelike topological semimetal with flat bands, which we reflect by unique excitation spectra and field distributions. Additionally, by changing the configuration of gauge flux, the mirror and translation operators become anticommutative, leading to the fractal translation of the Brillouin zone. As a result, the band structure of topological edge modes experiences twice the period in momentum space. All results are confirmed by full-wave simulation. Our study has the potential to construct unprecedented photonic topological insulators benefiting from gauge fields.