The variational quantum eigensolver (VQE) is considered one of the most powerful alternative approaches for near-term noisy intermediate-scale quantum devices. However, the successful implementation of the VQE is quite challenging, as the ansatz must be sufficiently expressive, yet, if it is overly expressive, it may hinder the optimization process of the VQE in finding the global minimum. To address this challenge of the VQE, a commonly used approach is to apply the symmetries of the system, which reduces the dimensionality of the parameter space for the VQE. Here, we propose a quantum circuit that can be used for systems with mirror symmetry and occupation-number-inversion symmetry. We demonstrate its usefulness by applying it to find the eigenenergies of the Anderson impurity model, a representative fundamental model for various quantum simulations. In addition, we demonstrate the usability of our quantum circuit by applying it to a quantum algorithm for Green's function, which plays a crucial role in understanding quantum systems of condensed matter physics.

We investigate the recent multiphoton extension [Alsing et al., Phys. Rev. A 105, 013712 (2022)] of the celebrated two-photon Hong-Ou-Mandel (HOM) effect [Hong, Ou, and Mandel, Phys. Rev. Lett. 59, 2044 (1987)] for the quantum interference of amplitudes that lead to complete destructive interference for coincident counts for the output of a balanced, lossless 50:50 beam splitter (BS). We examine the extended HOM (eHOM) effect by first investigating diagrammatically the multiphoton scattering of photons from the two input ports to the two output ports for Fock number basis states (FS) ${|n,m\rangle }_{12}$, and show that destructive interference occurs pairwise within the quantum amplitudes with many scattering components, generalizing the two-photon HOM effect. This analysis leads us to a general, simple analytical derivation of the eHOM effect for FS/FS inputs, which has profound implications for arbitrary bipartite photonic input states constructed from such basis states: if the input state to one input port of the BS is of odd parity, i.e., constructed only of odd numbers of photons, then regardless of the input state to the second 50:50 BS port, there will be a central nodal line (CNL) of zeros in the joint output probability distribution along the main diagonal for coincidence detection. We further examine the case of a single photon interacting with a coherent state (an idealized laser) and consider prospects for experimental detection by including additional effects such as imperfect detection efficiency and time delay between the detected output photons. This work highlights the importance of the nonclassicality of light, and in particular the interference effects stemming from the discreteness of photon quanta.

We revisit the coalescence behavior of the atomic Schrödinger wave functions from the angle of an operator-product expansion (OPE) within the nonrelativistic Coulomb-Schrödinger effective-field theory. We take the electron-nucleus coalescence as an explicit example to demonstrate our formalism, by proving an exact OPE relation to all orders in perturbation theory. As a consequence, the celebrated Kato's cusp condition can be readily reproduced. Our approach can be readily extended to ascertain the multiparticle coalescence behaviors of atomic wave functions, which are otherwise difficult to achieve from the conventional Schrödinger equation approach. Moreover, by incorporating relativistic effects, our OPE approach appears to be able to provide key insight for solving a 90-year-old puzzle concerning the peculiar coalescence behavior of the wave function for a Dirac hydrogen atom.

We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semiclassical approximation. The calculation benefits from the use of generalized coherent states for a basis. We find that the form of the semiclassical approximation remains valid to first order in the anharmonic perturbation, but that phase differences arise because the trajectory of a quantum wave packet will generally deviate from that of a classical particle. The quantum correction to the phase is a factor ${\ell }^2/A^2$ smaller than the semiclassical perturbation itself, where $\ell$ is the quantum harmonic-oscillator lengthscale, and $A$ is the classical amplitude of the motion. We provide analytical results for one-dimensional perturbations of power 3 through 6 in the position coordinate.

We explore the dynamics of qubit-state purity in the presence of transverse noise that is anisotropically distributed in the Bloch-sphere $XY$ plane. We perform Ramsey experiments with noise injected along a fixed laboratory-frame axis and observe oscillations in the purity at twice the qubit frequency arising from the intrinsic qubit Larmor precession. We probe the oscillation dependence on the noise anisotropy, orientation, and power spectral density, using a low-frequency fluxonium qubit. Our results elucidate the impact of transverse noise anisotropy on qubit decoherence and may be useful for disentangling charge and flux noise in superconducting quantum circuits.

In the quantum optimization paradigm, variational quantum algorithms face challenges with hardware-specific and instance-dependent parameter tuning, which can lead to computational inefficiencies. The promising potential of parameter transferability across problem instances with similar local structures has been demonstrated in the context of the quantum approximate optimization algorithm. In this paper we build on these advancements by extending the concept to annealing-based protocols, employing Bayesian optimization to design robust quasiadiabatic schedules. Our study reveals that, for maximum independent set problems on graph families with shared geometries, optimal parameters naturally concentrate, enabling efficient transferability between similar instances and from smaller to larger ones. Experimental results on the Orion Alpha platform validate the effectiveness of our approach, scaling to problems with up to 100 qubits. We apply this method to address a smart-charging optimization problem on a real dataset. These findings highlight a scalable, resource-efficient path for hybrid optimization strategies applicable in real-world scenarios.

Obtaining exact solutions to combinatorial optimization problems using classical computing is computationally expensive. The current tenet in the field is that quantum computers can address these problems more efficiently. While promising algorithms require fault-tolerant quantum hardware, variational algorithms have emerged as viable candidates for near-term devices. The success of these algorithms hinges on multiple factors, with the design of the Ansatz being of the utmost importance. It is known that popular approaches such as the quantum approximate optimization algorithm (QAOA) and quantum annealing suffer from adiabatic bottlenecks, which lead to either larger circuit depth or evolution time. On the other hand, the evolution time of imaginary-time evolution is bounded by the inverse energy gap of the Hamiltonian, which is constant for most noncritical physical systems. In this work we propose an imaginary Hamiltonian variational Ansatz ($i\mathrm{HVA}$) inspired by quantum imaginary-time evolution to solve the MaxCut problem. We introduce a tree arrangement of the parametrized quantum gates, enabling the exact solution of arbitrary tree graphs using the one-round $i\mathrm{HVA}$. For randomly generated $D$-regular graphs, we numerically demonstrate that the $i\mathrm{HVA}$ solves the MaxCut problem with a small constant number of rounds and sublinear depth, outperforming the QAOA, which requires rounds increasing with the graph size. Furthermore, our Ansatz solves the MaxCut problem exactly for graphs with up to 24 nodes and $D\le 5$, whereas only approximate solutions can be derived by the classical near-optimal Goemans-Williamson algorithm. We validate our simulated results with hardware demonstrations on a graph with 67 nodes.

A $n^d\stackrel{p}{\to }1$ quantum random access code (QRAC) is a communication task where Alice encodes $n$ classical bits into quantum states of dimension $d$ and transmits them to Bob, who performs appropriate measurements to recover the required bit with probability $p$. In the presence of a noisy environment, the performance of a QRAC is degraded, losing the advantage over classical strategies. We propose a practical technique that enables noise tolerance in such scenarios, recovering the quantum advantage in retrieving the required bit. We perform a photonic implementation of a $2^2\stackrel{\text{p}}{\to }1$ QRAC using polarization-encoded qubits under an amplitude-damping channel, where simple operations allow for noise robustness showing the revival of the quantum advantage when the noisy channel degrades the performance of the QRAC. This revival can be observed by violating a suitable dimension witness, which is closely related to the average success probability of the QRAC. This technique can be extended to other applications in the so-called prepare-and-measure scenario, enhancing the semi-device-independent protocol implementations.

We investigate a square-lattice architecture of superconducting transmon qubits with interqubit interactions mediated by inductive couplers. Via periodically modulating the couplers, the Abelian gauge potential, termed effective magnetic flux, can be synthesized artificially, making the system an excellent platform for simulating two-dimensional topological physics. First, we focus on the three-leg ladder which only has three rows and investigate the chiral dynamics therein for the single-particle ground state when the effective magnetic flux varies. We find what we call the “staggered vortex-Meissner phase transition,” where the vortex number can typically stagger a few times between one (defined as “vortex phase”) and larger integers (defined as “Meissner phase”) when the effective magnetic flux changes between $-\pi$ and $\pi$. This phenomenon, actually not a phase transition by definition, is quite different from the vortex-Meissner phase transition in the two-leg ladder that, in contrast, possesses only two rows and is usually treated as the quasi-two-dimensional model. Also, we find that the chiral current relies on the effective magnetic flux according to a squeezed sinusoidal function. Both the staggering of the vortex number and squeezing of the chiral current can be controllable by the coupling ratio, which is defined by the coupling-strength ratio between the column direction and row direction. Second, we continue to increase the number of rows beyond three, and the topological band structure to be anticipated at an infinite number of rows begins to occur even for a relatively small number (10 or so for typical parameters) of rows. This heralds a small circuit scale enough to observe the topological band. The behavior of the edge state in the band gap can be interpreted by the topological Chern number, which can be calculated through integrating the Berry curvature with respect to the first Brillouin zone. Last, we present a systematic method on how to measure the topological band structure based on time- and space-domain Fourier transformation of the wave function after properly exciting the qubits, which should be helpful for comprehensively analyzing the topological physics since all the topological properties are mainly contained in the band structure. Our results offer an avenue for simulating two-dimensional topological physics on the state-of-the-art superconducting quantum chips.

We perform a theoretical study of vacuum polarization corrections to the hyperfine structure in many-electron atoms. Calculations are performed for systems of interest for precision atomic tests of fundamental physics belonging to the alkali-metal atoms and singly ionized alkaline earths. The vacuum polarization is considered in the Uehling approximation, and we study the many-body effects core relaxation, core polarization, and valence-core correlations in the relativistic framework. We find that for $s$ states, the relative vacuum polarization correction may be well approximated by that for hydrogenlike ions, though for all other states an account of the many-body effects, in particular, the polarization of the core, is needed to obtain the correct sign and magnitude of the correction.

Measuring strong magnetic fields with atoms holds promise for various scientific applications, yet enhancing measurement resolution remains a challenge. This paper demonstrates strong magnetic-field measurement using the saturated absorption spectrum of a cesium micron-thick cell (MC), where the magnetic-field strength is indicated by the Zeeman shift of spectral lines and assessed via beat-frequency measurements with two stabilized lasers. Theoretical calculations have been refined to better interpret the clear splitting of experimental saturated absorption spectra of the MC in inhomogeneous strong magnetic fields with suppressed crossover spectral lines, which facilitates the magnetic-field measurements. Our approach achieves a measurement resolution of 0.36 G in an ambient magnetic field of 610 G and can effectively track time-varying magnetic fields. The measurement scheme provides high measurement resolution, which is valuable for remotely monitoring nuclear reactors, characterizing particle accelerator magnets, and mapping the magnetic fields of sunspots.

The saddle-point approximation (SPA) within the framework of strong-field approximation is extensively applied in strong-field physics because it offers clear physical insight into intense light-matter interactions. In this study, we introduce an $m$-resolved saddle-point approximation ($m$-SPA), where $m$ is the magnetic quantum number, to analyze the ionization dynamics of atoms initially in $p$ orbitals subjected to an intense laser field. Our results reveal that $m$ influences not only the prefactor of the ionization rate but also the saddle-point equation itself, an effect overlooked in prior studies. The accuracy of the $m$-SPA method is validated through comparisons with the backpropagation method and the strong-field approximation, showing its superiority over the conventional SPA approach. By employing the $m$-SPA approach, we are able to extract more accurate distributions of the initial tunneling exit energy and position, thereby allowing for a more precise determination of the asymptotic photoelectron characteristics. Additionally, we extend the conservation law for angular momentum and energy of photoelectrons from $s$ orbitals to $p$ orbitals and from circularly polarized to elliptically polarized laser fields, both at the tunnel exit and in the asymptotic region. This work facilitates future research on strong-field ionization from arbitrary atomic orbitals.

We investigate the nonequilibrium dynamics of a ground-state fermionic many-body gas subjected to a quench between parameter regimes of a topologically nontrivial Hamiltonian. By focusing on the role of the chiral edge states inherent in the system, we calculate the many-body overlap and show that the characteristic monotonic decay of the orthogonality catastrophe with increasing system size is notably altered. Specifically, we demonstrate that the dynamics are governed not solely by the total particle number but, rather, by the number of occupied single-particle edge states. This behavior is further explained through an analysis of the full work probability distribution, providing a deeper understanding of the system's dynamics.

We report on the development of a modular platform for programmable quantum simulation with atomic quantum gases. The platform is centered around exchangeable optical modules with versatile functionalities. The performance of each module is disentangled from all others, enabling individual validation and maintenance of its outputs. The relative spatial positioning of the modules with respect to the position of the atomic sample is set by a global reference frame. In this way, the platform simplifies reconfiguration and upgrading of existing setups and accelerates the design of new machines in a time- and cost-efficient manner. Furthermore, it facilitates collaborations between different experimental groups. This standardized hardware design framework, which we call Heidelberg Quantum Architecture, paves the way towards a new generation of on-demand and highly adaptable quantum simulation experiments.

Bound states in the continuum (BICs) in photonic crystal slabs are Bloch eigenstates with zero linewidth and infinite lifetimes, though practical devices exhibit quasi-BICs due to geometric imperfections and material losses. Despite these limitations, quasi-BICs still maintain high $Q$ factors, enabling applications in lasing, high harmonic generation, and biosensing. The selection of specific geometrical or material parameters is essential to achieve devices that sustain BICs. Our work presents a framework for generating BICs by driving the transfer matrix of a device to a singular point, where it becomes noninvertible, thus defining the BIC states. This method applies to nonhomogeneous, tessellated structures and is supported by closed-form analytical expressions, facilitating efficient parametric exploration. The proposed framework aligns with the conjecture that the most robust BICs are associated with topological defects in specific parameter spaces. We identify regions in parameter space supporting BICs and validate our theoretical predictions through full-wave numerical simulations. The framework extends to a wide range of photonic structures, enabling robust design and optimization of devices for diverse applications.

The responsivity of perturbation sensing can be effectively enhanced by using higher-order exceptional points (EPs) due to their nonlinear response to frequency perturbations. However, experimental realization can be difficult due to the stringent parameter conditions associated with these points. In this work we study an EP laser composed of two coupled nonlinear resonators that uses nonlinearity to simplify these tuning requirements. This system demonstrates a distinct cube-root response in the steady-state lasing frequency, with a constant of proportionality that depends on the distribution of linear and saturable gain and loss. This design freedom enables several orders of magnitude higher responsivity than systems with a single nonlinear resonator, which have been previously explored. Maximizing responsivity also improves the robustness of sensing performance against parametric errors. These features are derived from coupled-mode theory and further supported by steady-state ab initio laser theory results at several nonlinear EPs. Through linear stability analysis, we also identify regions of instability within the class-A regime that arise due to mode competition, which can be induced by asymmetric passive losses. In the class-B regime, we show that the interplay between gain dynamics and detuning can lead to restabilization at slow relaxation rates or higher interresonator coupling rates. This regime could be used to increase the maximum achievable responsivity of the system.

In this paper, we present a scheme for remotely generating large-size motional Schrödinger cat states in cavity optomechanical (OM) systems with non-Gaussian quantum steering of continuous variables. We consider that the output field from the OM cavity undergoes three typical kinds of multiphoton operations: multiphoton subtraction, multiphoton addition, or multiphoton catalysis, followed by homodyne detection. We first demonstrate that these multiphoton operations can lead to non-Gaussian OM quantum steerable correlations, which are unveiled by the subsequent homodyne detection with a Fisher-information-based steering criterion. It is found that the non-Gaussian steering is obviously enhanced with an increasing number $n$ of photons in the multiphoton operations, which, as we show, fails to be revealed with the well-known Reid's steering criterion. It therefore suggests that the Fisher-information-based criterion is more effective for witnessing non-Gaussian quantum steering. We next show that the strong OM steering enables the remote preparation of large-size Schrödinger odd or even cat states of the mechanical oscillator by the homodyne detection. Accordingly, the amplitudes of the cat states also increase significantly with the photon number $n$, particularly in the cases of multiphoton subtraction and addition. Our results reveal the properties of non-Gaussian steering generated by multiphoton operations, and the large cat states of macroscopic mechanical resonators hold promise for fundamental tests in quantum mechanics and practical applications in quantum science.

Nitrogen-vacancy (NV) centers in diamond have been successfully coupled to various optical structures to enhance their radiation by the Purcell effect. The participation of many NV centers in these studies may naturally lead to cooperative emission and superradiance, and our recent experimental study with a diamond membrane in a fiber-based ultranarrow optical cavity demonstrated nonlinear radiation and fast photon bunching as signatures of the collective effects. In this theoretical article, we go beyond the simple model used in the previous study to address more phenomena, such as the appearance of bunching shoulders in second-order correlation function, Rabi splitting in steady-state spectrum, and population dynamics on excited Dicke states, which for moderate pumping explains the observed collective effects. Overall, our results can guide further experiments with NV centers, and they are also relevant for other solid-state color centers, such as silicon-vacancy centers in diamond and silicon carbide, boron-vacancy centers, and carbon-related centers in hexagonal boron nitride.

We address the nature of the Thouless charge pumping for a non-Hermitian (NH) generalization of the one-dimensional (1D) Rice-Mele model, considering a variety which allows closed-form analytical solutions for the eigensystems. The two-band system is subjected to an “adiabatic” time-periodic drive, which effectively gives us a closed two-dimensional (2D) manifold in the momentum-frequency space, mimicking a 2D Brillouin zone (BZ) for periodic boundary conditions. For open boundary conditions, we formulate the non-Bloch generalized Brillouin zone (GBZ). All these allow us to compute the Chern numbers of the 2D manifolds emerging for various parameter values, using the BZ or GBZ, which are well-defined integers in the gapped regions of the spectra. If Thouless pumping still holds for NH situations, the expectation values of the net displacement for the particles occupying a given band within a cycle, calculated using the right and left eigenvectors of a biorthogonal basis for the complex Hamiltonians, would coincide with the Chern numbers. However, we find that there are deviations from the expected quantized values whenever the spectra exhibit strongly fluctuating magnitudes of the imaginary parts of the (generically) complex eigenvalues. This implies that we need to address the question of how to meaningfully define time evolution, as well as adiabaticity, in the context of NH systems.