In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms addressing nonsquare matrices. Towards this kind of problems defined by $Ax=b$ where $A\in {\mathbb{R}}^{m\times n}$, we propose a quantum algorithm inspired by the classical multirow iteration method and provide an explicit quantum circuit based on the quantum comparator and quantum random access memory. The time complexity of our quantum multirow iteration algorithm is $O\left(K{log}_{2}m\right)$, with $K$ representing the number of iteration steps, which demonstrates an exponential speedup compared to the classical version.. Based on the convergence of the classical multirow iteration algorithm, we prove that our quantum algorithm converges faster than the quantum one-row iteration algorithm presented by Shao and Xiang [C. Shao and H. Xiang, Phys. Rev. A 101, 022322 (2020)]. Moreover, our algorithm places less demand on the coefficient matrix, making it suitable for solving inconsistent systems and quadratic optimization problems.

The natural gradient (NG) is an information-geometric optimization method that plays a crucial role, especially in the estimation of parameters for machine learning models like neural networks. To apply NG to quantum systems, the quantum natural gradient (QNG) was introduced and utilized for noisy intermediate-scale devices. Additionally, a mathematically equivalent approach to QNG, known as the stochastic reconfiguration method, has been implemented to enhance the performance of quantum Monte Carlo methods. It is worth noting that these methods are based on the symmetric logarithmic derivative (SLD) metric, which is one of the monotone metrics. So far, monotonicity has been believed to be a guiding principle to construct a geometry in physics. In this paper we propose generalized QNG by removing the condition of monotonicity. Initially, we demonstrate that monotonicity is a crucial condition for conventional QNG to be optimal. Subsequently, we provide analytical and numerical evidence showing that nonmonotone QNG outperforms conventional QNG based on the SLD metric in terms of convergence speed.

Quantum states of angular momentum and spin generally are not invariant under rotations of the reference frame. Therefore, they can be used as a resource of relative orientation, which is encoded in the asymmetry of the state under consideration. In this paper we introduce the analytical characterization of the rotational information by parametrizing the group characteristic function by polynomial functions. By doing so, we show that the set of states achievable through transformations lacking a reference frame (rotationally covariant ones) admits an analytical characterization and can be studied through the use of semidefinite optimization techniques. We demonstrate the developed methods via examples and provide a physical scenario in which a reference-independent operation performs a metrologically useful operation: the preparation of a state of light improving interferometer sensitivity, which equivalently can be realized as a postprocessing step.

The quantum approximate optimization algorithm (QAOA) is a promising quantum algorithm that can be used to approximately solve combinatorial optimization problems. The usual QAOA ansatz consists of an alternating application of the cost and mixer Hamiltonians. In this work, we study how using Hamiltonians other than the usual cost Hamiltonian, dubbed custom phase operators, can affect the performance of the QAOA. We derive an expected value formula for the QAOA with custom phase operators at $p=1$ and show numerically that some of these custom phase operators can achieve higher approximation ratios than the original algorithm implementation. Out of all the graphs tested at $p=1$, 0.036% of the random custom phase operators, 75.9% of the subgraph custom phase operators, 95.1% of the triangle-removed custom phase operators, and 93.9% of the maximal degree edge-removed custom phase operators have a higher approximation ratio than the original QAOA implementation. Furthermore, we numerically simulate these phase operators for $p=2$ and $p=3$ levels of QAOA and find that there exist a large number of subgraph, triangle-removed, and maximal degree edge-removed custom phase operators that have a higher approximation ratio than the QAOA at the same depth. These findings open up the question of whether better phase operators can be designed to further improve the performance of the QAOA.

Recent progress in quantum computing and quantum simulation of many-body systems with arrays of neutral atoms using Rydberg excitation has provided unforeseen opportunities towards computational advantage in solving various optimization problems. The problem of a maximum-weight independent set of unit-disk graphs is an example of an NP-hard optimization problem. It involves finding the largest set of vertices with the maximum sum of their weights for a graph which has edges connecting all pairs of vertices within a unit distance. This problem can be solved using quantum annealing with an array of interacting Rydberg atoms. For a particular graph, a spatial arrangement of atoms represents vertices of the graph, while the detuning from resonance at Rydberg excitation defines the weights of these vertices. The edges of the graph can be drawn according to the unit-disk criterion. Maximum-weight independent sets can be obtained by applying a variational quantum adiabatic algorithm. We consider driving the quantum system of interacting atoms to the many-body ground state using a nonlinear quasiadiabatic profile for sweeping the Rydberg detuning. We also propose using a quantum wire, which is a set of auxiliary atoms of a different chemical element, to mediate strong coupling between the remote vertices of the graph. We investigate this effect for different lengths of the quantum wire. We also investigate the quantum phases of matter realizing commensurate and incommensurate phases in one- and two-dimensional spatial arrangements of the atomic array.

Real photonic devices are subject to photon losses that can decohere quantum information encoded in the system. In the absence of full fault tolerance, quantum error mitigation techniques have been introduced to help manage errors in noisy quantum devices. In this paper, we introduce an error mitigation protocol inspired by probabilistic error cancellation (a popular error mitigation technique in discrete variable systems) for continuous variable systems. We show that our quantum error cancellation protocol can undo photon losses in expectation value estimation tasks. To do this, we analytically derive the (nonphysical) inverse photon loss channel and decompose it into a sum over physically realizable channels with potentially negative coefficients. The bias of our ideal expectation value estimator can be made arbitrarily small at the cost of increasing the sampling overhead. The protocol requires a noiseless amplification followed by a series of photon subtractions. While these operations can be implemented probabilistically, for certain classes of initial state one can avoid the burden of carrying out the amplification and photon subtractions by leveraging Monte Carlo methods to give an unbiased estimate of the ideal expectation value. We validate our proposed mitigation protocol by simulating the scheme on squeezed vacuum states, cat states, and entangled coherent states.

The calculations of the first and the second ionization potentials of lawrencium and lutetium and the electron affinity of lawrencium are performed within the relativistic coupled-cluster framework. These results are corrected by including the contributions of extrapolation to the complete basis set limit and higher-order contributions due to relativity and electron correlation. The excellent agreement between our predictions of the ionization potentials of Lu and Lr and experimental values supports the accuracy of our predictions of the second ionization potential and the electron affinity of Lr.

We have measured triple differential momentum distributions for electron detachment in collisions of 30- and 300-keV anions (${\mathrm{C}}^{-}$ and $\mathrm{S}{\mathrm{i}}^{-}$) with atoms and molecules (He, Ar, and ${\mathrm{N}}_2$). The entire angular range of the ejected electrons was covered. The binary encounter ring, well known from positive ion-atom collisions, was observed in most cases. In a quasifree-electron scattering model this structure represents elastic scattering of the active electron from the target. However, especially for the slowest projectiles, this model fails to reproduce the angular distributions. In this regime it is probably necessary to use quasimolecular models to describe the collision. Indications for a projectile cusp are observed, implying that excitation-induced dipole moments in the ion projectile may be important.

Coherent-population-trapping resonance in vapor cell is a quantum interference effect that appears in the two-photon transitions between the ground-state hyperfine levels of alkali-metal atoms and is often utilized in miniature and centimeter-scale clock devices. To quantitatively understand and predict the performance of this phenomenon, it is necessary to consider the transitions and relaxations between all hyperfine Zeeman sublevels involved in the different excitation processes of the atom. In this paper, we constructed a computational multilevel atomic model of the Liouville density-matrix equation for 32 Zeeman sublevels involved in the $D_1$ line of ${}^{133}\mathrm{Cs}$ irradiated by two frequencies with circularly polarized components and then simulated the amplitude and shape of the resonance spectrum of the transmitted light through centimeter-scale Cs-vapor cells. We show that the numerical solutions of the equation and analytical investigations adequately explain a variety of the characteristics observed in the experiment.

We present three-dimensional Monte Carlo simulations of the capture of 1000 K ${}^7\mathrm{Li}$ or 500 K ${}^{87}\mathrm{Rb}$ atoms by a continuous supersonic ${}^4\mathrm{He}$ jet and show that intense, cold alkali-metal beams form. The simulations use differential cross sections obtained from quantum scattering calculations of ${}^7\mathrm{Li}$ or ${}^{87}\mathrm{Rb}$ atoms with ${}^4\mathrm{He}$ atoms for relative collision energies between $k\times 1$ mK and $k\times 3000$ K, where $k$ is the Boltzmann constant. For collision energies higher than approximately $k\times 4$ K the collisions favor forward scattering, deflecting the ${}^7\mathrm{Li}$ or ${}^{87}\mathrm{Rb}$ atoms by no more than a few degrees. From the simulations, we find that about 1% of the lithium atoms are seeded into the ${}^4\mathrm{He}$ jet, resulting in a lithium beam with a most probable velocity of about $210\mathrm{m}/\mathrm{s}$ and number densities on the order of ${10}^8{\mathrm{cm}}^{-3}$. Simulations predict narrow yet asymmetric velocity distributions which are verified by comparing to fluorescence measurements of the seeded ${}^7\mathrm{Li}$ atoms. We find agreement between simulated and experimentally measured seeded ${}^7\mathrm{Li}$ densities to be better than 50% across a range of ${}^4\mathrm{He}$ flow rates. We make predictions for seeding efficiency and cooling of ${}^{87}\mathrm{Rb}$ by a supersonic ${}^4\mathrm{He}$ jet. The seeding efficiency for ${}^{87}\mathrm{Rb}$ is expected to be similar to ${}^7\mathrm{Li}$.

We present a theoretical analysis of phase separations between two repulsively interacting components in an ultracold fermionic gas, occurring at the dimensional crossover in a harmonic trap with varying aspect ratios. A tailored kinetic energy functional is derived and combined with a density-potential functional approach to develop a framework that is benchmarked with the orbital-based method. We investigate the changes in the density profile of the phase-separated gas under different interaction strengths and geometries. The analysis reveals the existence of small, partially polarized domains in certain parameter regimes, which is similar to the purely two-dimensional limit. However, the density profile is further enriched by a shell structure found in anisotropic traps. We also track the transitions that can be driven by a change in either interaction strength or trap geometry. The developed framework is noted to have applications for other systems with repulsive interactions that combine continuous and discrete degrees of freedom.

We investigate the ground state of the $\mathrm{SU}\left(4\right)$ Heisenberg model on a square lattice with spatial anisotropy on each plaquette bond using the tensor-network method based on infinite projected entangled pair states. We find that the $\mathrm{SU}\left(4\right)$ singlet ground state appears in the strongly anisotropic limit, whereas Néel and valence-bond crystal orders coexist in the nearly isotropic limit. By examining the intermediate parameter region, we identify a phase transition between these phases. The nature of the phase transition is likely to be of first order, and the transition point is estimated to be around $J^{\prime }/J\approx 0.85\left(5\right)$, where $J$ and $J^{\prime }$ are the interaction strengths of intra- and interplaquette bonds, respectively. We also calculate the anisotropy dependence of singlet correlations on a plaquette bond, which will be useful for future experiments of ultracold atoms in optical lattices.

We present a generalization of the two-body contact interaction for nonrelativistic particles trapped in one dimension. The particles interact only when they are a distance $c$ apart. The competition of the interaction length scale with the oscillator length leads to three regimes identified from the energy spectra. When $c$ is less than the oscillator length, particles avoid each other, whereas in the opposite case bunching occurs. In the intermediate region where the oscillator length is comparable to $c$, both exclusion and bunching are manifested. All of these regions are separated by dark states, i.e., bosonic or fermionic states which are not affected by the interactions.

Using symmetry considerations, we derive a unitary scattering matrix for a three-port optical Y coupler or Y branch. The result is shown to be unique up to external phase shifts. Unlike traditional passive linear-optical one-way splitters, coupling light into the conventional output ports of the Y coupler results in strong coherent back-reflections, making the device a hybrid between feed-forward devices like the beam splitter, which do not reverse the direction of light, and a recently considered class of directionally unbiased multiport scatterers (with dimension greater than two), which do. While the device could immediately find use as a novel scattering vertex for the implementation of quantum walks, we also design a few simple but nonetheless useful optical systems that can be constructed by taking advantage of the symmetry of the scattering process. This includes an interference-free, resource-efficient implementation of the Grover four-port and a higher-dimensional Fabry-Perot interferometer with tunable finesse. Symmetry-breaking generalizations are also considered.

Despite its non-Hermitian nature, the optical beam shift exhibits real eigenvalues and nonorthogonal eigenstates. To explore this unexpected similarity to typical $\mathcal{PT}$ (parity-time)-symmetric systems, we first categorize the entire parametric regime of optical beam shifts into Hermitian, $\mathcal{PT}$-unbroken, and $\mathcal{PT}$-broken phases. Besides experimentally unveiling the $\mathcal{PT}$-broken regime, crucially, we illustrate that the observed $\mathcal{PT}$ transition is rooted in the momentum-domain inhomogeneous polarization transformation of the beam. The correspondence with a typical non-Hermitian photonic system is further established. Our work not only resolves a fundamental issue in the field of optical beam shift but also puts forward the notion of non-Hermitian spin-orbit photonics: a new direction to study non-Hermitian physics through optical beam shifts.

Single-photon sources are necessary components for many prospective quantum technologies. One candidate for a single-photon source is spontaneous parametric down-conversion combined with a heralding photon detection. The heralded light pulse from such a source is typically treated as single mode; this treatment, however, is incomplete. We develop a full multimode description based on the exact Bogoliubov treatment of the down-conversion process. We then provide a perturbative and effective treatment, which illustrates the most important physical mechanisms and permits analytical estimates of the success probability and purity of single-photon states under practical heralding conditions, both without relying on the precise detection time of the heralding photon and when accepting photons only in a narrow window around the time of the detection. This permits us to characterize the emitted light under three different assumptions for the pump pulse. For spontaneous parametric down-conversion with a very short pump pulse, we find the single-mode description to be accurate, while for longer pump pulses and continuous pumping, a multimode description is necessary. Our findings can be used to guide the design of quantum information protocols based on heralded single-photon sources, as their performance may depend on the multimode nature of the sources.

Nondegenerate triple-photon parametric down-conversion (NTPD) is a potential source for unconditional tripartite non-Gaussian entangled states of continuous variables. Recent experiment has demonstrated strong third-order correlations among bright photon triplets via microwave NTPD in a superconducting cavity [C. W. Sandbo Cheng et al., Phys. Rev. X 10, 011011 (2020)]. Previous theoretic works have revealed that only short-time genuine tripartite non-Gaussian entanglement can be generated in NTPD even in the absence of dissipation. In this paper, we investigate the properties of tripartite non-Gaussian entanglement and steering in the cavity output field by taking into account the cavity dissipation. We first derive experimentally detectable criteria for fully inseparable and genuine tripartite non-Gaussian entanglement and steering. With the criteria, we then find that steady-state tripartite non-Gaussian entanglement and steering can be generated in the output field, although they merely exist in the short-time regime inside the cavity. We also find that the initial cavity-field coherent states can obviously enhance the steady-state and transient tripartite entanglement and steering, in comparison to the case of initial vacuum states. We finally show that the output tripartite non-Gaussian steerable correlations can be applied to the remote generation of negative Wigner-function quantum states by homodyne detection.