We present a method for gradient computation in quantum algorithms implemented on linear optical quantum computing platforms. While parameter-shift rules have become a staple in qubit gate-based quantum computing for calculating gradients, their direct application to photonic platforms has been hindered by the infinite dimensionality of phase-shift operators in Fock space. We introduce a photonic parameter-shift rule that overcomes this limitation, providing an exact formula for gradient computation in linear optical quantum processors. Our method scales linearly with the number of input photons and utilizes the same parametrized photonic circuit with shifted parameters for each evaluation. This advancement bridges a crucial gap in photonic quantum computing, enabling efficient gradient-based optimization for variational quantum algorithms on near-term photonic quantum processors. We demonstrate the efficacy of our approach through numerical simulations in quantum chemistry and generative modeling tasks, showing superior optimization performance as well as robustness to noise from finite sampling and photon distinguishability compared to other gradient-based and gradient-free methods.

Continuous-time quantum walks are typically effected by either the discrete Laplacian or the adjacency matrix. In this paper, we explore a third option: the signless Laplacian, which has applications in algebraic graph theory and may arise in layered antiferromagnetic materials. We explore spatial search on the complete bipartite graph, which is generally irregular and breaks the equivalence of the three quantum walks for regular graphs, and where the search oracle breaks the equivalence of the Laplacian and signless Laplacian quantum walks on bipartite graphs without the oracle. We prove that a uniform superposition over all the vertices of the graph partially evolves to the marked vertices in one partite set, with the choice of set depending on the jumping rate of the quantum walk. We boost this success probability to 1 by proving that a particular nonuniform initial state completely evolves to the marked vertices in one partite set, again depending on the jumping rate. For some parameter regimes, the signless Laplacian yields the fastest search algorithm of the three, suggesting that it could be a new tool for developing faster quantum algorithms.

A quantum flipping device is a theoretical apparatus designed to transform an input quantum state, represented by the density operator $\rho$ acting on a $d$-dimensional Hilbert space $\mathcal{H}$, into an output state $\sigma$ residing within the subspace orthogonal to $\rho$. While the no-flipping theorem establishes the impossibility of such a device for qubits (two-dimensional systems), its extension to higher-dimensional systems ($d>2$) allows for the possibility of such devices due to the increased space available for the output state. In this paper, we derive an impossibility theorem for generalized flipping devices, applicable to higher-dimensional systems, based on a causal principle, namely, commutation of spacelike operations. Given a bipartite quantum state shared between two parties Alice and Bob, this principle prohibits the resulting state from depending on the time order of Alice's and Bob's spacelike separated local operations applied on the respective parts of the bipartite systems. Importantly, unlike the argument applied to qubits, our approach does not rely on the unitary dynamics postulate of quantum theory. Furthermore, we investigate the implications of violating the principle of commutation of spacelike operations and demonstrate that such violations do not necessarily entail a violation of the no-signaling principle.

We demonstrate that in stimulated Raman transitions introducing one or two simple phase shifts to the control fields significantly enhances the fidelity of state manipulation while simultaneously reducing leakage to the intermediate excited state. Our approach achieves high-fidelity quantum gate operations between the two target states under arbitrary detuning conditions. Notably, the average population in the intermediate excited state is approximately halved, without extending the overall evolution time. Additionally, our method exhibits greater robustness to static amplitude and detuning errors compared to conventional adiabatic elimination techniques, and maintains higher fidelity even in the presence of dissipation.

The molecular anion ${{\mathrm{C}}_2}^{-}$ has been of interest in the past few years as a candidate for laser cooling due to its electronic structure and favorable branching ratios to the ground electronic and vibrational states. Molecular hydrogen has been used by the Wester group at Innsbruck as a buffer gas to cool the molecule's internal rovibrational motion. In the present work we generate a five-dimensional (5D) interaction potential for the system by considering the ${\mathrm{H}}_2$ as a rigid rotor and the ${{\mathrm{C}}_2}^{-}$ as a rotating-vibrating diatomic molecule. We then calculate the cross sections and rate coefficients for rovibrational inelastic collisions of ${{\mathrm{C}}_2}^{-}$ with both para- and ortho-${\mathrm{H}}_2$ on this 5D ab initio potential energy surface using quantum scattering theory for the dynamics. The rates for vibrational quenching are obtained over a range of temperatures that covers the single point measured by the experiments. A comparison is also made with earlier results which had used a simpler 3D interaction potential. Para-${\mathrm{H}}_2$ is found to be more efficient than ortho-${\mathrm{H}}_2$ (with or without also undergoing rotational excitation) in cooling ${{\mathrm{C}}_2}^{-}$. The rate coefficients for cooling the anions have been computed by appropriately weighting the ortho- and para-${\mathrm{H}}_2$ and compared with the available experimental result at 20 K. The computed results are nearly two orders of magnitude larger than the single experimental point. When the vibrational deexcitation rate coefficients are employed without any concurrent rotational excitations in the final ${{\mathrm{C}}_2}^{-}$ anions (a situation considered to be nonphysical under the present experimental setup), the properly averaged results are found to get smaller and to become very close to the existing experimental measurements. The robustness of the present results is tested and confirmed. The implications of these results for laser cooling of ${{\mathrm{C}}_2}^{-}$ are analyzed and discussed.

Improving the bandwidth of Rydberg-atom-based receivers is an ongoing challenge owing to the long-lived Rydberg state lifetimes that limit the refresh rate of ground-state atoms. In particular, the local-oscillator-based Rydberg mixer approach allows for bandwidths into the few-megahertz range. Here we use heterodyne detection of the Rydberg-atom receiver probe laser to separate the negative and positive sidebands that originate from distinct six-wave-mixing processes, in order to investigate their individual bandwidths. We experimentally confirm the prediction that the negative sideband exhibits a higher bandwidth than the positive sideband. We further explore the effect of coupling and probe laser Rabi frequency on the bandwidth, which we find to be in close agreement with our model. We achieve maximum experimental (and theoretical) bandwidths of $10.5\pm 0.4$ (11.6) and $3.4\pm 0.2$ (5.4) MHz for the negative and positive sidebands, respectively, from the $-3$ dB roll-off point for optimized field parameters. This work provides insight into the bandwidth-limiting features of Rydberg-atom receivers and points the way towards further optimization of their response.

A three-dimensional (3D) photonic waveguide array is proposed to simulate the concept of reservoir-engineering-induced nonreciprocal transmission. The reservoir is offered by coupling two optical modes simultaneously to an additional mode with loss, yielding a jump operator, which is a coherent superposition of annihilation operators of these two modes. The waveguides are helically curved, leading to a synthetic gauge field for the propagating photons and consequently an adjustable phase factor for the jump operator. The unidirectional coupling is derived analytically and verified numerically, and an intuitive interpretation is provided. Furthermore, the model is extended to a periodic lattice, where asymmetric hopping arises and unidirectional hopping appears for certain Bloch wave vectors. Our design is based on real-experiment parameters, which can be readily implemented by femtosecond laser direct writing of 3D waveguides in silica.

Gaussian states are ubiquitous in quantum optics and information processing, and it is essential to have effective tools for their characterization. One such tool is a photon-number-resolving detector, and the simplest configuration involves counting the total number of photons in the state to be characterized. This motivates the following question: What properties of a multimode Gaussian state are determined by the signal from one detector that measures the total number of photons up to some bound? We find that if the Gaussian state occupies $S$ modes and the probabilities of $n$ photons for all $n\le 8S$ are known, then we can determine the spectrum of the Gaussian covariance matrix and the magnitude of the displacements in each eigenspace of the covariance matrix. Nothing more can be learned, even if all photon-number probabilities are known. When the state is pure, the covariance matrix spectrum determines the squeezing parameters of the state.

Improving the number and number density of cold molecules is a longstanding goal in cold molecule research. Stark deceleration provides an important access to taming polar molecules and makes the collision and high-resolution spectroscopy a reality. However, the full deceleration efficiency of the traditional Stark decelerator has been impeded by its intrinsic loss mechanisms, which significantly limit its applications. In this paper, we introduce an interspersed guiding deceleration strategy that surpasses the periodic phase stability limitations of traditional Stark decelerator. Our approach is theoretically and experimentally validated using the $\mathrm{N}{\mathrm{D}}_3$ molecule, achieving significant gains of $3\sim 8$ for all final velocity ranges. Additionally, our method requires a lower operation number of switching that is beneficial for reducing the consumption of the high-voltage switches and suitable for controlling a large number of deceleration stages. This method is applicable to any traditional crossed-pin Stark decelerator and can stop a wider variety of molecular species with higher densities, including those with a small Stark shift-to-mass ratio. It is anticipated to become an essential tool for producing cold and dense molecular samples, offering promising prospects for cold collision studies and precision measurements.

We investigate spatiotemporal chaos in Bose-Einstein condensate (BEC) confined by a one-dimensional harmonic trap using Gross-Pitaevskii equation simulations. The chaos arises from nonlinear mixing of ground and excited states, confirmed by positive Lyapunov exponents. By sampling the density field at intervals matching the center-of-mass oscillation period, we analyze the density structure function. Both spatial and temporal density structure functions reveal Kolmogorov-type scaling through extended self-similarity (ESS). Our findings suggest that ESS and density structure functions provide experimentally accessible tools to explore spatiotemporal chaos and turbulencelike behavior in BECs.

We study optical analogs of Bloch oscillations and Zener tunneling in binary waveguide arrays (BWAs) with the help of the wave-number-based approach. We analytically derive two very simple laws describing the evolution of the central wave numbers of beams in BWAs that help us analytically obtain the propagation distances where the Zener tunneling takes place due to the interband transition and the distances where beams reach the turning points and change direction. These distances just depend on the strength of the linear potential and the initial wave number of input beams. We also show that nonlinearity of the Kerr type has a detrimental influence on the Bloch-Zener oscillations.

Precision measurement of small angles is essential in both industrial applications and high-precision scientific research. Although a traditional angle interferometer is widely employed, its resolution is fundamentally constrained. In this paper, we introduce an innovative method for ultrahigh-resolution angle measurement based on the laser frequency measurement, directly converting angle measurement into frequency measurement, which can be traced to the most accurate frequency standards. The proposed scheme integrates a frequency selection element interference filter (IF) with a transparent solid or liquid medium, forming a highly sensitive measurement system. This system capitalizes on the sensitivity of laser frequency to changes in cavity length and the incidence angle of the IF. As a result, even minute angular rotations of the sensor induce detectable shifts in the laser's frequency. The angular displacement is inferred directly by analyzing the frequency difference between a test signal and a reference, with this difference arising from variations in the incident angle at the IF and the corresponding changes in cavity length due to medium rotation. Theoretical analysis suggests that this method can achieve a resolution better than ${10}^{-4}$ arcsecond (${10}^{-8}\mathrm{deg}$), representing an order of magnitude improvement over existing techniques.

Advances in research have sparked an increasing curiosity in understanding the plasmonic excitation properties of molecular-scale systems. Polycyclic aromatic hydrocarbons, as the fundamental building blocks of graphene, have been documented to possess plasmonic properties through experimental observations, making them prime candidates for investigation. By doping different elements, the conjugated structure of the molecule can be altered. In this study, the plasmonic excitation properties influenced by conjugated structures in peropyrene and its derivatives are investigated through first-principles calculations that combine the plasmonicity index, generalized plasmonicity index, and transition contribution map. For molecular plasmonic excitation, the conjugated structure can influence the oscillation modes of valence electrons, which is pivotal in yielding distinct field enhancement characteristics. Furthermore, charge doping can lead to a certain degree of alteration in the conjugated structures, and the doping of elements will result in varying degrees of such alteration, thereby initiating different trends in the evolution of plasmonic resonance. This further enhances the tunability of molecular plasmonic resonance. The results provide novel insights into the development and utilization of molecular plasmonic devices in practical applications.

In this paper, we propose a scalable scheme to prepare multipartite entanglement and collective steering of four magnons, which are placed into four separate transmission line resonators. When the four cavity modes are coupled to a common superconducting qubit, the strong coherent coupling between the magnons and qubit can be established through virtual photon exchange. In the dressed picture, it is of interest to explore two types of interaction under different frequency-matching conditions, being responsible for the continuous-variable quadripartite Greenberger-Horne-Zeilinger and cluster entanglement. Furthermore, the generation of collective steering originates from the dissipation channel of Bogoliubov mode rather than from the conventional asymmetry of the system parameters. The multipartite entanglement in this solid-state device may find potential applications in constructing macroscopic quantum networks and the collective steering may be useful in one-sided device-independent quantum secret sharing.

The laser pulse reflected and focused by the relativistically moving curved plasma mirror can exceed the laser intensity obtained by focusing high-power laser pulses with conventional physical optics. In the ultrarelativistic limit where the Lorentz $\gamma$ factor is large ($\gamma \gg 1$), the general field configuration focused by the relativistic curved plasma mirror is calculated using the $4\pi$-spherical focusing scheme in the boosted frame of reference. The calculated field strength and distribution can be applied to investigate nonlinear quantum electrodynamic effect (electron-positron pair creation from the vacuum via the Schwinger mechanism) under the two-beam colliding scheme, in which a high-intensity laser pulse collides with a focused field by the relativistic mirror. The benefit of using the relativistic mirror has been discussed in terms of the invariant field. Taking advantage of the mathematical expression for the focused field, the spatial distributions of the pair creation rate have been calculated as functions of time and the carrier envelope phase of the laser pulse. The calculation predicts that creating $\approx 2.2\times {10}^6$ electron-positron pairs is possible by colliding a 25 PW laser pulse with a reflected and focused field by the relativistic mirror with $\gamma =100$. This attributes to the field enhancement by the double Doppler effect, a large geometrical factor of the relativistic mirror, and the increase in the reflectivity due to the oblique incidence.

We explore and extend the application of homological algebra to describe quantum entanglement, initiated by Mainiero [arXiv:1901.02011], focusing on the Hodge-theoretic structure of entanglement cohomology in finite-dimensional quantum systems. We construct analogs of the Hodge star operator, inner product, codifferential, and Laplacian for entanglement $k$-forms. We also prove that such $k$-forms obey versions of the Hodge isomorphism theorem and Hodge decomposition, and that they exhibit Hodge duality. As a corollary, we conclude that the dimensions of the $k\mathrm{th}$ and $(n-k)\text{−}\mathrm{th}$ cohomologies coincide for entanglement in $n$-partite pure states, which explains a symmetry property (“Poincaré duality”) of the associated Poincaré polynomials.

Quantifying multipartite entanglement poses a significant challenge in quantum information theory, prompting recent advancements in methodologies to assess it. We introduce the notion of “volume of assistance” (VoA), which computes the geometric mean of entanglement of assistance across all potential parties. We demonstrate the feasibility of VoA for three-qubit pure states and certain classes of pure tripartite qudit states. We have extended this measure to four-qubit states and general multipartite scenarios. We have done a comparative analysis to illustrate VoA's distinctiveness from established entanglement measures, notably showing it serves as an upper bound for the much celebrated generalized geometric measure. Remarkably, VoA excels in distinguishing a broad class of states that elude differentiation by the recently proposed Minimum Pairwise Concurrence measure. Finally, VoA is applied to quantify genuine entanglement in the ground states of a three-qubit Heisenberg $XY$ model, which highlights its practical utility in quantum information processing tasks.

Two-dimensional compass codes are a family of quantum error-correcting codes that contain the Bacon-Shor codes, the $X$-Shor and $Z$-Shor codes, and the rotated surface codes. Previous numerical results suggest that the surface code has a constant accuracy and coherence threshold under uniform coherent rotation. However, having analytical proof supporting a constant threshold is still an open problem. It is analytically proven that the toric code can exponentially suppress logical coherence in the code distance $L$. However, the current analytical lower bound on the threshold for the rotation angle $\theta$ is $|sin(\theta \left)\right|<1/L$, which linearly vanishes in $L$ instead of being constant. We show that this lower bound is achievable by the $Z$-Shor code, which does not have a threshold under stochastic noise. Compass codes provide a promising direction to improve on the previous bounds. We analytically determine thresholds for two new compass code families that provide upper and lower bounds to the rotated surface code's numerically established infidelity threshold. Furthermore, using a Majorana mode-based simulator, we use random families of compass codes to smoothly interpolate between the $Z$-Shor codes and the $X$-Shor codes.