Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic circuits designed for generating approximate solutions to combinatorial optimization problems constructed using two-bit stochastic matrices. Through a numerical study, we investigate the performance of our proposed variational circuits in solving the Max-Cut problem on various graphs of increasing sizes. Our classical algorithm demonstrates improved performance for several graph types to the quantum approximate optimization algorithm. Our findings suggest that evaluating the performance of quantum variational circuits against variational circuits with subuniversal gate sets is a valuable benchmark for identifying areas where quantum variational circuits can excel.

We introduce a class of bosonic quantum error-correcting codes, termed extended binomial codes, which generalize the structure of one-mode binomial codes by incorporating ideas from high-rate qubit stabilizer codes. These codes are constructed in close analogy to $\left[\right[n,k,d\left]\right]$ qubit codes, where the parameter $n$ corresponds to the total excitation budget rather than the number of physical qubits. Our construction achieves a significant reduction in average excitation per mode while preserving error-correcting capabilities, offering improved compatibility with hardware constraints in the strong-dispersive regime. We demonstrate that extended binomial codes not only reduce the mean excitation required for encoding but also simplify syndrome extraction and logical gate implementation, particularly the logical $\overline{X}$ operation. These advantages suggest that extended binomial codes offer a scalable and resource-efficient approach for bosonic quantum error correction.

We have measured momenta of electrons and recoil ions in triple coincidence with neutralized projectiles for slow collisions between various anions and target atoms. From the data we extracted triple differential momentum and angular distributions of electrons ejected in detachment, in detachment with simultaneous target ionization (DI), and in detachment with simultaneous target excitation (DE). The DI rates relative to the DE rates depend sensitively on the projectile speed and on the properties of the target.

We systematically investigate the ground state and dynamics of spinor Bose-Einstein condensates subject to a position-dependent detuning. This detuning induces three related quantities (a synthetic magnetic field, an angular velocity, and an angular momentum), which, due to trap anisotropy, may point in different directions. When the dipole frequencies along the three symmetric axes of the harmonic trap are degenerate, the dipole motion can decompose into two coupled transverse modes in the plane perpendicular to the synthetic magnetic field, and another decoupled longitudinal mode, enabling controllable Foucault-like precession or biconical trajectories depending on the excitation protocol. Furthermore, quenching the orientation of the synthetic magnetic field excites multiple coupled quadrupole modes. We develop a hydrodynamic theory whose predictions match well with Gross-Pitaevskii simulations. This study contributes to a deeper understanding of the effects of the synthetic magnetic field and the excitations of the collective mode in quantum fluids, providing a foundation for future developments in quantum simulation and high-precision sensing technologies.

We study the long-time dynamics of a dissipative Ising chain with varying quantum correlation. Invoking an ensemble-average formalism and assuming spatial translation symmetry, we show that the dynamics can be described by a Lindblad master equation with an interpolated coherent Hamiltonian. In the classical limit, the interpolation Hamiltonian leads to a set of nonlinear equations of motion, where limit cycles can emerge in the long-time dynamics. In the quantum limit, by contrast, the system approaches a ferromagnetic steady state at long times. In between the two extremes, the discrete spatial translation symmetry can be spontaneously broken, as an antiferromagnetic steady state emerges, bridging the classical and quantum regimes. In particular, we illustrate how the classical limit-cycle behavior gradually disappears with the increase of quantum correlation. Since our model in the two extremes respectively applies to a dissipative Rydberg gas in the high- and zero-temperature limits, we expect it to provide a qualitatively correct description of dissipative Rydberg gases at interim temperatures and shed light on the fate of limit cycles in a quantum open system.

Pulse splitting, which results from the excessive accumulation of nonlinear phase shifts, enables multipulse emission with an identical spectrum in mode-locked fiber lasers. However, spectral splitting was rarely observed owing to the limited gain bandwidth and gain competition effect. We demonstrate the spectral splitting of mode-locked pulses ubiquitously existed in birefringence-managed normal-dispersion fiber lasers, where a single-spectrum pulse evolves into multispectrum pulses with different group velocities by increasing the pump intensity. Theoretical analysis and numerical simulations fully reproduce the experimental observations, confirming that the periodic linear and nonlinear coupling of vector modes split the pulse in the frequency domain. This study presents a simple yet efficient method for generating controllable multispectrum mode-locked pulses without the use of spectral filters, which has significant implications for exploring multicolor pulse interactions and facilitating practical applications such as absolute distance measurement.

We report an experimental demonstration of generalized photonic spin splitting (PSS) using arbitrary linearly polarized higher-order orbital angular momentum (OAM) pointer states supported by a modified weak measurement model. The experimental findings show the dependence of longitudinal and transverse PSS on linear polarization angle, postselection angle, and azimuthal index ($l$) of OAM states. PSS rises as $l$ increases, reaching a maximum of roughly 300 $\mu \text{m}$ and 120 $\mu \text{m}$ for the transverse and longitudinal shift values, respectively. Considering $l=0$, 1, and 2, the polarization-controlled variation of both shifts at three distinct angles of incidence is investigated for a fixed postselection angle. All the experimental results agree well with the developed theoretical model, proving the model's accuracy. This model is valid for both external and internal reflection of arbitrary linearly polarized incident light reflecting from absorbing as well as nonabsorbing mediums, considering arbitrary coupling strength and a very small postselection angle. The manipulation of PSS using higher-order OAM light beams shown in this study will have a wide range of applications in wavefront manipulation, optical sensors, and nanophotonics.

One of the key issues in quantum discrimination problems is understanding the extent of the advantages in discrimination performance when using resource states compared to resourceless states. We show that in any resource theory of states, which may not be convex, the extent to which the maximum average success probability can be improved in quantum channel discrimination problems without using auxiliary systems can be precisely quantified by the robustness measure. This result offers an intuitive operational meaning of the robustness measure in any convex resource theory. Furthermore, we demonstrate that the robustness measure can also quantify the improvement in channel discrimination problems that use auxiliary systems. Using these findings, resources can be fully characterized to achieve higher success probabilities than any state without the given resource in channel discrimination problems.

In parity quantum computing, multiqubit logical gates are implemented by single-qubit rotations on a suitably encoded state involving auxiliary qubits. Consequently, there is a correspondence between qubit count and the size of the native gate set. One might then wonder, what is the smallest number of auxiliary qubits that still allows for universal parity computing? Here, we demonstrate that the answer is 1 if the number of logical qubits is even, and 2 otherwise. Furthermore, we present a sufficient condition for a given parity gate set to be universal. This leads to a variety of different universal parity gate sets corresponding to different numbers of auxiliary qubits and more generally contributes to the understanding of which entangling gates are required to augment the set of single-qubit unitaries to perform universal quantum computing. As a consequence, we obtain (i) minimal implementations of the parity framework on, e.g., a triangular lattice, (ii) hardware-specific implementations of the parity flow framework on, e.g., a heavy-hex lattice, and (iii) novel universal resources for measurement-based quantum computation.

The theory of open quantum systems is central to describing the dynamics and equilibration of dilute-gas Bose-Einstein condensates (BECs). We present an analysis of the linearized stochastic projected Gross-Pitaevskii equation (SPGPE) describing finite-temperature BECs. Our treatment provides an optimal choice for the cutoff that divides the Bose gas into the low-energy coherent region forming a classical wave and the high-energy thermal cloud treated as a reservoir. Moreover, it highlights the relevance of energy damping, the number-conserving scattering between thermal and coherent atoms. We analyze the equilibrium properties and near-equilibrium relaxation of a homogeneous BEC in one, two, and three dimensions at high phase-space density and calculate the autocorrelation function and power spectrum of the density and phase fluctuations. Simulations of the full nonlinear SPGPE are in close agreement and extend our arguments beyond the linear regime. Our work suggests the need for a reexamination of decay processes in BECs studied under the neglect of energy damping.

We present a theoretical study of a random laser (RL) formed by a scale-free photonic network (PN) with dissipative photon tunneling between microcavities (MCs) hosting two-level quantum systems (TLSs). Using the Gorini-Kossakowski-Sudarshan-Lindblad framework, we identify two distinct lasing regimes. The first is independent of the tunneling parameter and emerges when the steady-state frequency of the $n\mathrm{th}$ mode is resonant with the TLS transition. This resembles lasing in uncoupled MCs and relies on population inversion. The second scenario arises from the nonreciprocal nature of dissipative tunneling and enables lasing of nonresonant modes even at vanishingly small population inversion, owing to energy redistribution across the network. In the latter case, interference effects along graph paths induce node-dependent frequency shifts and nonreciprocal photon transmission. We further propose a renormalization-group hypothesis for the PN to explain the observed spectral features. We analyze the phase structure of photonic modes in the scale-free RL and discuss its relevance for photonic Ising machines operating under the minimum power dissipation principle.

The Pancharatnam-Berry (PB) phase is characterized by the simple application method and comprehensive theoretical framework, offering significant advantages in designing metasurfaces for hologram and nanoprinting. However, the PB phase relies heavily on an analyzer to enable nanoprinting. Additionally, designing a chiral metasurface by the PB phase poses significant challenges, limiting the application in multifunctional metasurfaces. This paper introduces a metamolecular Pancharatnam-Berry phase based on metamolecules to enable the design of chiral metasurfaces. Metamolecules can independently and arbitrarily adjust intensity and phase without the need for an analyzer. By introducing the chiral factor to metamolecules, the proposed chiral metasurface achieves polarization-sensitive nanoprinting and hologram without the use of an analyzer. This approach addresses the limitations of the traditional PB phase in near-field modulation and chiral research while providing a theoretical foundation for the miniaturization and advancement of intelligent metasurfaces.

In quantum optics, the postselection amplitude of a nondegenerate parametric down-conversion (PDC) process is linked to a beamsplitter (BS) via partial time reversal, up to a normalization coefficient which is related to the parametric gain [Proc. Natl. Acad. Sci. USA 117, 33107 (2020)]. A special example where the gain is low is reminiscent of Klyshko's advanced-wave picture in quantum imaging. Here we propose and prove a generalized duality for multiple spatial paths connecting a quantum nonlinear interference setup consisting of nondegenerate PDCs and linear optical systems to a linear one, where the PDCs are directly replaced by hypothetical wavelength-shifting BSs. This replacement preserves the geometry of the original setup, and cascaded PDCs become optical cavities whose calculation involves the Redheffer star product. Additional terms in the normalization coefficient are related to the contribution of looping photons inside the cavities. Then we discuss the case of coherent state input and postselection for $Q$-function calculation. This theorem will be helpful in the development of quantum photonic devices beyond the low-gain limit.

Optical down-conversion is widely used for generating photon pairs, squeezed and entangled states of light, making it an indispensable tool in quantum optics and quantum information. In the regime where the pump is much stronger than the generated field, the standard parametric approximation treats the pump amplitude as a fixed parameter of the model. This approximation has a limited domain of validity since it assumes a nondepleted and nonentangled pump. By finding an approximate solution to the Schrödinger equation of the down-conversion process, we obtain an improved analytical model beyond the parametric one, which accounts for pump depletion and pump-signal entanglement. Our model is advantageous, first, because it allows one to compute averages of field operators far beyond the domain of validity of the parametric approximation, and second, because it allows one to establish error-specific limits of the latter domain. For a given pump amplitude, we find a maximum squeezing parameter, up to which the approximation remains valid within a specified acceptable error. Our results confirm that recent experiments on Gaussian boson sampling, with a squeezing parameter of $r\approx 1.8$ and a coherent pump amplitude of $\alpha \approx 2\times {10}^6$, can still be accurately described by the standard parametric approximation. However, we observe a sharp decline in validity as the squeezing parameter increases. For pump amplitudes of $\alpha \approx 2\times {10}^6$, the parametric approximation breaks down when the squeezing parameter exceeds $r\approx 4.5$, whereas the new approximation remains valid up to $r\approx 6$ with an acceptable error of 1%.

We analyze and generalize a construction method of Kochen-Specker (KS) sets given by Waegell and Aravind. In this method the bases that participate in a KS set are formed by modifying a seed basis using a vector space of shifts. We show that any real or generalized Hadamard matrix can be used as the seed basis, and that the space of shifts can be much smaller than originally proposed. Main benefits of these generalizations are a vastly extended set of available seed matrices, and significantly smaller KS sets produced. Analytical constructions of infinite families of Hadamard matrices combined with our generalized approach allow us to construct an infinite family of KS sets.

The density matrix yields probabilistic information about the outcome of measurements on a quantum system, but it does not distinguish between classical randomness in the preparation of the system and entanglement with its environment. Here we show that retrodiction, employing both prior and posterior knowledge, gives rise to conditional probabilities for measurements on a single system, that can witness if it is part of a larger composite system. The degree of certainty with which one can retrodict the outcomes of multiple measurements on a system can witness both the existence and the quantitative nature of its entanglement with the environment.

Efficient photon capture in optical cavities is essential for quantum networks and computing, yet single-pass methods suffer from uncaptured reflections due to finite capture windows and coupling strengths, precluding perfect transfer of arbitrary photonic states. We introduce a two-pass "pitch-and-catch" method that recycles initial reflections to achieve perfect capture of arbitrary pulses in the noiseless regime and enhances fidelity under intrinsic losses. The method extends to photon emission, enabling arbitrary pulse shaping. This advance offers significant improvements for quantum repeaters, memories, and transduction, enhancing the toolkit for quantum information processing.

This work analyzes quantum correlations of photon pairs initially prepared in a Bell state, where one photon undergoes Compton scattering from a stationary, unpolarized electron. The evolved two-photon density matrix is analytically derived and spectrally decomposed. Concurrence and the Clauser-Horne-Shimony-Holt (CHSH) inequality evaluations identify angular regions demonstrating quantum steering correlations, entanglement without steering, and complete separability. The Peres conjecture is applied to interpret regions of entanglement lacking steering, emphasizing their limited practicality for quantum-information tasks. These results provide details potentially useful for employing Compton-scattered annihilation photons in various quantum protocols.

The three-body fragmentation dynamics of pyridine trications ${\mathrm{C}}_5{\mathrm{H}}_5{\mathrm{N}}^{3+}$ produced by 200-eV electron-impact triple ionization are investigated using a reaction microscope. The three complete deprotonation fragmentation channels of ${\mathrm{H}}^{+}+{\mathrm{CH}}_2{\mathrm{N}}^{+}+{\mathrm{C}}_4{\mathrm{H}}_2^{+}, {\mathrm{H}}^{+}+{\mathrm{C}}_2{\mathrm{H}}_2^{+}+{\mathrm{C}}_3{\mathrm{H}}_2{\mathrm{N}}^{+}$, and ${\mathrm{H}}^{+}+{\mathrm{C}}_3{\mathrm{H}}_2^{+}+{\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{N}}^{+}$ are determined by multiparticle coincidence momentum imaging. By analyzing the correlation maps as a function of kinetic energy release and the angle $\theta$ between the conjugate momenta of the first and second breakup steps as well as the momentum correlation spectra of three fragment ions (Newton diagram) in these three channels, we separate two distinct sequential mechanisms involving proton emission in the first or second step of sequential fragmentation. Moreover, we determine the relative ratio of the two dissociation pathways for each channel. We find that proton emission in the first step of the sequential dissociation is the dominant process (94% branching ratio) for the channel involving the H migration of ${\mathrm{H}}^{+}+{\mathrm{CH}}_2{\mathrm{N}}^{+}+{\mathrm{C}}_4{\mathrm{H}}_2^{+}$. It can be explained by the pyridine trication undergoing ultrafast hydrogen migration and forming a more stable $\alpha$-isomeric ion, which attenuates the ring-opening reactions. Our study provides insight into the dynamics of deprotonation and ring-breaking reactions in the three-body fragmentation processes of heterocyclic molecules.