We use quantum imaginary-time evolution (QITE) to solve polynomial unconstrained binary optimization (PUBO) problems. We show that a linear ansatz yields good results for a wide range of PUBO problems, often outperforming standard classical methods, such as the Goemans-Williamson (GW) algorithm. We obtain numerical results for the low-autocorrelation binary sequences (LABS) and weighted MaxCut combinatorial optimization problems, thus extending an earlier demonstration of successful application of QITE on MaxCut for unweighted graphs. We find the performance of QITE on the LABS problem with a separable ansatz comparable to QAOA at level 10 for up to 18 vertices and do not see a significant advantage with an entangling ansatz. On weighted MaxCut, QITE with a separable ansatz often outperforms the GW algorithm on graphs with up to 150 vertices.

One of the main problems in computational physics is predicting the low-energy behavior of many-body quantum systems. The computational complexity of this problem, however, is relatively poorly understood. A recent major progress in this direction has been the no low-energy trivial states (NLTS) theorem; it gives a family of qubit Hamiltonians whose low-energy states cannot be reached by shallow quantum circuits. In this work we provide a fermionic counterpart to this theorem, constructing local fermionic Hamiltonians with no low-energy trivial states. Distinct from the qubit case, we define trivial states via finite-depth fermionic quantum circuits. We further strengthen the result, allowing free access to (generally, deep) Gaussian fermionic circuits into our notion of a trivial state. The desired fermionic Hamiltonian can be constructed using any qubit Hamiltonian which has the NLTS property via well-spread distributions over bitstrings. We also define a fermionic analog of quantum probabilistically checkable proofs (PCPs) and explore the relation of fermionic PCP class with the qubit version.

We investigate how vibration affects molecular photoemission dynamics, through simulations on two-dimensional asymmetric model molecules including the electronic and nuclear motions in a fully correlated way. We show that a slight anisotropy in the electron-ion momentum sharing is sufficient to prevent one from unambiguously characterizing the vibrationally averaged photoemission dynamics in terms of stereo Wigner delays. We further show that vibrational resolution can be retrieved in fixed-nuclei simulations, using effective molecular conformations that are specific to each vibrational channel. The optimal internuclear distances found empirically in one-photon processes can be identified a priori using simple physical arguments. They also turn out to be efficient to simulate vibrationally resolved interferometric measurements and to account for interchannel coherences in broadband one-photon ionization.

The Stiefel-Whitney insultor is a two-dimensional topological insulator protected by parity-time ($\mathcal{PT}$) symmetry. With a vanishing Chern number, the topology in this system is characterized by second Stiefel-Whitney class. We propose a feasible scheme to realize a four-band Stiefel-Whitney insultor with spin-orbit coupled ultracold atoms in an optical Raman lattice. Four selected spin states are coupled by carefully designed Raman lasers to generate the desired spin-orbit interactions with spacetime inversion symmetry. We map out a phase diagram with respect to the experimental parameters, where a large topological phase region exists. We further present two distinct detection methods to resolve the non-Abelian band topology, in both equilibrium and dynamical ways. The detection relies on the spin textures extracted from the time-of-flight imaging, showing the tomographic signatures in the ground states and long-time averaged patterns on certain submanifolds via a bulk-surface duality. Our work paves a realistic way to explore novel topology inside real Berry bundles with quantum matters.

We propose a scheme for implementing nonreciprocal transmission and a nonreciprocal photon blockade (PB) in a whispering-gallery-mode optomechanical resonator. By decoupling the mechanical degree of freedom under the Born-Oppenheimer approximation, the system is reduced to one incorporating Kerr-type nonlinearities induced by optomechanical coupling, including self-Kerr nonlinearities of the clockwise (CW) and counterclockwise (CCW) modes and cross-Kerr nonlinearity between these two modes, thereby strong nonreciprocal PB and transmission can be implemented. We demonstrate that the nonreciprocal PB and transmission are sensitive to the relative phase $\theta$ between CW and CCW modes, allowing for switching between reciprocity and nonreciprocity of PB and transmission through engineering the relative phase of external driving lasers. Numerical results obtained with experimental parameters validate the feasibility of achieving perfect nonreciprocal PB and transmission. Our paper presents a viable mechanism for the implementation of perfect nonreciprocal PB and transmission, along with a versatile approach of phase modulation, which holds great promise in serving as a chiral single-photon source in unidirectional quantum communications based on quantum nonreciprocal devices.

Because of the potential advantages in data processing over the electrical counterpart, recent strategies for optical computing have received much attention. However, the tradeoff between the depth of the structures for optical computing and universality of their capability is hard to balance. In this work, we propose an optical computing strategy which can implement universal optical computing by a one-layer structure of the operation units. The proposal is based on the KAK decomposition of unitary matrices. We also present experimental validation of our proposal, showing the implementation of several operations. Moreover, it is pointed out that the proposal enables a resource-efficient implementation for certain operations, advancing the capability of performing the computation by light.

Superposed photon-added and photon-subtracted squeezed-vacuum states exhibit sub-Planck phase-space structures and metrological potential similar to the original compass states (superposition of four coherent states), but are more closely tied to modern experiments. Here, we observe that these compasslike states are highly susceptible to loss of quantum coherence when placed in contact with a thermal reservoir; that is, the interaction with the thermal reservoir causes decoherence, which progressively suppresses the capacity of these states to exhibit interference traits. We focus on the sub-Planck structures of these states and find that decoherence effects on these features are stronger with increasing the average thermal photon number of the reservoir, the squeezing parameter, or the quantity of added (or subtracted) photons to the squeezed-vacuum states. Furthermore, we observe that the sub-Planck structures of the photon-subtracted case survive comparatively longer in the thermal reservoir than their counterparts in the photon-added case, and prolonged contact with the thermal reservoir converts these compasslike states into a classical state.

We propose a scheme based on femtosecond stimulated Raman spectroscopy (FSRS) for $N$ molecules in an optical cavity. With theoretical simulations, the scheme can access the collective dynamics of molecular polaritons and their coupling to vibrations, along with crosstalk between polariton and dark states. Through multidimensional projections of the FSRS signal, we identify clear signatures of the dark states, e.g., pathways and timescales that used to be invisible with resonant techniques. A microscopic theory is developed for the polaritonic FSRS, which reveals the interplay between polaritonic population and coherence dynamics. The resulting signal makes the dark states visible, thereby providing a technique for probing the dynamics of dark states and their correlation with polariton modes.

The classification of phases and the detection of phase transitions are central and challenging tasks in diverse fields. Within physics, these rely on the identification of order parameters and the analysis of singularities in the free energy and its derivatives. Here, we propose an alternative framework to identify quantum phase transitions. Using the axial next-nearest-neighbor Ising (ANNNI) model as a benchmark, we show how machine learning can detect three phases (ferromagnetic, paramagnetic, and a cluster of the antiphase with the floating phase). Employing supervised learning, we demonstrate the feasibility of transfer learning. Specifically, a machine trained only with nearest-neighbor interactions can learn to identify a new type of phase occurring when next-nearest-neighbor interactions are introduced. We also compare the performance of common classical machine learning methods with a version of the quantum nearest neighbors (QNN) algorithm.

Perturbative gadgets are a tool to encode part of a Hamiltonian, usually the low-energy subspace, into a different Hamiltonian with favorable properties, for instance, reduced locality. Many constructions of perturbative gadgets have been proposed over the years. Still, all of them are restricted in some ways: Either they apply to some specific classes of Hamiltonians, they involve recursion to reduce locality, or they are limited to studying time evolution under the gadget Hamiltonian, e.g., in the context of adiabatic quantum computing, and thus involve subspace restrictions. In this work, we fill the gap by introducing a versatile universal, nonrecursive, nonadiabatic perturbative gadget construction without subspace restrictions, that encodes an arbitrary many-body Hamiltonian into the low-energy subspace of a three-body Hamiltonian and is therefore applicable to gate-based quantum computing. Our construction requires $rk$ additional qubits for a $k$-body Hamiltonian comprising $r$ terms. Besides a specific gadget construction, we also provide a recipe for constructing similar gadgets, which can be tailored to different properties, which we discuss.

A number of composite pulse (CP) sequences for four basic quantum phase gates—the Z, S, T, and general phase gates—are presented. The CP sequences contain up to 18 pulses and can compensate up to eight orders of experimental errors in the pulse amplitude and duration. The short CP sequences (up to eight pulses) are calculated analytically and the longer ones numerically. The results demonstrate the remarkable flexibility of CPs accompanied by extreme accuracy and robustness to errors. These CP sequences, in particular the Z, S, and T gates, can be very useful quantum control tools in quantum information applications, because they provide a variety of options to find the optimal balance among ultrahigh fidelity, error range, and speed, which may be different in different physical applications.

We show that in presence of a local and uncorrelated dephasing noise, quantum advantage can be obtained in the Fisher information-based lower bound of the minimum uncertainty in estimating parameters of the system Hamiltonian. The quantum advantage refers here to the benefit of initiating with a maximally entangled state instead of a product one. This quantum advantage was known to vanish in the same noisy scenario for a frequency estimation protocol. Restoration of the better precision in frequency estimation with maximally entangled probes can be obtained by incorporating an interaction between the system particles. The interaction examined here is Ising in nature, and is considered with or without a transverse magnetic field. There are instances, e.g., where frequency estimation in presence of a transverse field is considered and quantum advantage is not restored. A quantum advantage can also be obtained while estimating the strength of the introduced magnetic field along the transverse direction, whereas for the instances considered, using uncorrelated probes is better in measuring the coupling parameter of the Ising interaction. We also investigate the dependence of measurement precision on the entanglement content, which is not necessarily maximal, of the initial state. The precision in estimation of coupling constant decreases monotonically with the increase of entanglement content of the initial state, while the same for frequency estimation is independent of the entanglement content of the inputs.

We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field $h$ and study all of the dynamical excitations related to density perturbation. By calculating the density dynamic structure factor, we find anisotropic dynamical excitations in both collective modes and single-particle excitations. Along the direction of center-of-mass momentum $p$, there are two obvious gapless collective modes with different speeds and two kinds of continuous regimes related to single-particle excitation. The lower collective modes are from the usual gauge symmetry breaking and have a larger speed than the one in the negative direction of $p$. The higher one is due to the direction spontaneous symmetry breaking of center-of-mass momentum $p$ and separates a gapless lower-branch single-particle excitation from the other gapped higher-branch single-particle excitation in the positive $p$ direction. However, this higher mode disappears in the opposite direction of $p$, where two single-particle excitations overlap with each other. These signals of dynamical excitations could help to distinguish a Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in future experiments.

We investigate the dependence of ${\mathrm{N}}_2{}^{+}$ lasing radiation on the polarization ellipticity of the pump laser with the 900- and 980-nm wavelengths. Our results show that the 391-nm lasing radiation is stronger with the elliptically polarized laser in the 900-nm pumping case, while the lasing signal decays monotonically with the increasing ellipticity in the 980-nm pumping case. In contrast, the strongest 428-nm lasing appears with the linear polarization laser for both pumping cases. The theoretical simulations reproduce key observations and reveal that the physical origin underlying the ellipticity-dependent behaviors is the sensitivity of photoexcitation of different channels on the wavelength and polarization of the pump laser. At the 900-nm pump wavelength, one-photon excitation from $X{{}^2\mathrm{\Sigma }}_{\mathrm{g}}^{+}$ to $A{}^2{\mathrm{\Pi }}_{\mathrm{u}}$ of ${\mathrm{N}}_2{}^{+}$ plays a dominant role in the population inversion. The elliptically polarized laser is beneficial to the perpendicular transition between the two states. In the 980-nm pumping case, the three-photon excitation from $X{{}^2\mathrm{\Sigma }}_{\mathrm{g}}^{+}$ to $B{{}^2\mathrm{\Sigma }}_{\mathrm{u}}^{+}$, which prefers linear polarization pumping, dominates the population inversion. The 428-nm lasing gain mainly depends on the population on the $B{{}^2\mathrm{\Sigma }}_{\mathrm{u}}^{+}$ state, thus the strongest radiation always occurs in the case of linear polarization. The polarization-dependent behaviors of ${\mathrm{N}}_2{}^{+}$ lasing reflect the complex population inversion mechanism in the strong-field-prepared ionic system.

We show that excitation of a semiconductor nanocrystal with a short pulse of electromagnetic field can result in the generation of a unipolar electric pulse, which is the distribution of field with a nonzero electric pulse area. The effect is caused by the exciton nonlinearity in a nanocrystal. The microscopic theory of the effect is presented. We also discuss related proposals of unipolar pulse generation, including the optical rectification effect and electric field-induced interband ionization of a nanocrystal.

The time-stretched dispersive Fourier transform method (TS-DFT) has been widely used to analyze multisoliton structures in ultrafast lasers, featuring shot-by-shot access to their spectral interferograms. Most exemplary structures consist of two interacting solitons whose spacing and relative phase can be simply retrieved from their interferograms mapped in time domain by TS-DFT. However, such analysis has not been elaborated for structures with more solitons that could result in a complicated TS-DFT signal. Here we report our theoretical inference of a deterministic discrepancy when retrieving structures consisting of more than two solitons with their TS-DFT signal. We unveil the underlying source of these discrepancies as a result of the quadratic phase mismatch induced by TS-DFT and correspondingly propose an improved retrieval method. Our work may provide a theoretical guideline for conducting unambiguous analysis of complex multipulse structures using TS-DFT, particularly when the dispersive stretching ratio is limited.

Photonic bound states in the continuum (BICs) are nonradiating eigenmodes of structures with open scattering channels. Most often, BICs are studied in highly symmetric structures with one or two open scattering channels. In this simplest case, the so-called symmetry-protected BICs can be found by tuning a single parameter, which is the light frequency. Another kind of BIC—accidental BICs—can be obtained by tuning two parameters, e.g., the frequency and a wave-vector component. For more complex structures lacking certain symmetries or having many open scattering channels, more than two parameters might be required. In the present work, we propose an algebraic approach for computing the number of parameters required to obtain a BIC by expressing it through the dimension of the solution set of certain algebraic equations. Computing this dimension allows us to relate the required number of parameters to the number of open scattering channels without solving Maxwell's equations. We show that different relations take place when the scattering matrices describing the system are symmetric or asymmetric. The obtained theoretical results are confirmed by the results of rigorous electromagnetic simulations.

Cat states are maximally entangled states with applications in metrology and fault-tolerant quantum computation. Experiments have revealed that Rydberg collective avalanche decoherence acts as a bottleneck for cat creation with Rydberg atoms. This process initiates after the blackbody-radiation-induced decay of Rydberg atoms and sets a strong limit on the cat creation time. These findings necessitate the exploration of new ideas to accelerate current Rydberg cat schemes. To enhance the interaction-to-loss ratio, this paper delves into cat-state formation in the strong-Rydberg-dressing regime, uncovering the emergence of cat states despite the presence of complex orders of nonlinearities. This unexplored regime demonstrates the potential for rapid cat-state formation, which is particularly beneficial for operation in typical two-dimensional lattices in Rydberg laboratories. In an extreme case, this paper demonstrates that second-order nonlinearity could be isolated under resonant Rydberg driving if a large number of atoms are accommodated inside the blockade volume. The resonant model significantly enhances the interaction-to-loss ratio while circumventing the adiabaticity condition, allowing fast switching of lasers. In addition, this paper presents a method for generating multicomponent cat states, which are superpositions of $m$ coherent spin states ($|m\text{−}\text{CSS}\rangle$). The maximum value of $m$ is determined by the number of atoms within the blockade radius, where $m=\sqrt{N}$. The states with larger $m$ are more robust against the presence of multiple orders of nonlinearity in the strong-dressing Hamiltonian and are accessible in a much shorter time compared to traditional two-component cat states.