Wigner functions help visualize quantum states and dynamics while supporting quantitative analysis in quantum information. In the discrete setting, many inequivalent constructions coexist for each Hilbert-space dimension. This fragmentation obscures which features are fundamental and which are artifacts of representation. We introduce a stencil-based framework that exhausts all possible $d\times d$ discrete Wigner functions for a single $d$-dimensional quantum system (including a novel one for even $d$), subsuming known forms. We also give explicit invertible linear maps between definitions within the same $d$, enabling direct comparison of operational properties and exposing representation dependence.

The realization of quantum networks that exploit multiqubit entanglement opens avenues for transformative applications in the realm of quantum communication. In the paper, we present a set of heralded deterministic protocols designed for the generation of two-qubit, three-qubit, and $N$-qubit Knill-Laflamme-Milburn (KLM) states by the photon scattering property in one-dimensional waveguide-emitter system. In each protocol, the auxiliary single photon functions as a universal interface to bridge all stationary qubits. Our proposed protocols allow for the conversion of irregular scattering incidents occasioned by nonideal coupling and frequency detuning into detectable events by triggering the detectors, which means that our protocols are effective for the generation of arbitrary KLM states with the predictive operational character and high fidelity. Owing to the significant breakthroughs in the integration of quantum emitters with nanophotonic waveguides, our protocols possess ideal features that position them as the promising candidates for deployment in long-range multiqubit quantum network systems.

Designing quantum error correcting codes that promise a high error threshold, low resource overhead, and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming code is one of the potential candidates that allows for constant space overhead and efficient decoding. We study the concatenation of surface codes with quantum Hamming codes as a quantum memory, and estimate its error threshold, resource overhead, and decoding time. A high error threshold is achieved, which can in principle be pushed up to the threshold of the surface code. Furthermore, the concatenated codes can suppress logical errors to a much lower level than the surface codes, under the assumption of comparable amount of resource overhead. The advantage in suppressing errors starts to show for a quantum memory of intermediate scale. Concatenating surface codes with quantum Hamming codes therefore provides a promising avenue to demonstrate small-scale fault-tolerant quantum circuits in the near future, and also paves a way for large-scale fault-tolerant quantum computation.

Computing eigenvalues is a computationally intensive task central to many applications in the natural sciences, particularly in quantum physics and chemistry, where determining low-lying energy spectra is key to characterizing physical and chemical properties. Toward this end, we present and investigate the quantum block Krylov subspace projector (QBKSP) algorithm—a multireference quantum Lanczos method—to accurately compute low-lying eigenenergies, including degenerate ones. We propose three compact quantum circuits, each suited to different problem settings, for evaluating the necessary expectation values. In contrast to previous multireference quantum Krylov methods, QBKSP achieves linear scaling with respect to the number of Krylov iterations instead of a quadratic one, and furthermore reduces the scaling with respect to the number of references by half for real Hamiltonians and reference states. To assess the impact of the number and fidelity of the initial reference states, as well as the QBKSP performance in different parameter regimes, we perform both error-free and sampling noise-limited simulations. Our results demonstrate that employing multiple reference states significantly improves convergence, particularly in noisy scenarios or when a single reference fails to capture all target eigenstates. Moreover, the QBKSP algorithm allows for the determination of degenerate eigenstates and their multiplicities through appropriate convergence conditions.

Forthcoming quantum devices will require high-fidelity information transfer across a many-body system. We formulate the criterion for lossless signal propagation and show that a single qubit can play the role of an antenna, collecting large amounts of information from a complex system. We derive the condition under which the antenna, far from the source and embedded in a many-body interacting medium, can still collect the complete information. A striking feature of this setup is that a single-qubit antenna can receive even the full signal amplified by the entanglement of the source. As a consequence, the recovery of this information can be performed with simple single-qubit operations on the antenna (which we fully characterize) rather than with multiqubit measurements of the source. Finally, we discuss the control of the system parameters necessary for lossless signal propagation. A method discussed here could improve the precision of quantum devices and simplify metrological protocols.

Quantum fidelity estimation is essential for benchmarking quantum states and processes on noisy quantum devices. While stabilizer operations form the foundation of fault-tolerant quantum computing, nonstabilizer resources further enable universal quantum computation through state injection. In this work, we propose several efficient quantum fidelity estimation protocols for both quantum states and channels within the resource theory of nonstabilizerness, focusing on qudit systems with odd prime dimensions. Our fidelity estimation algorithms require measuring only a constant number of phase-space point operator expectation values, with operators selected randomly according to an importance weighting scheme tailored to the target state. Notably, we demonstrate that mathematically defined nonstabilizerness measures—such as Wigner rank and mana—quantify the sample complexity of the proposed protocols, thereby endowing them with a clear operational interpretation in the fidelity estimation task. This connection reveals a fundamental trade-off: while fidelity estimation for general quantum states and channels requires resources that scale exponentially with their nonstabilizerness, the task remains tractable for states and channels that admit efficient classical simulation.

Quantum frequency converters that enable the interface between the itinerant photons and qubits are indispensable for realizing long-distance quantum networks. However, the cascaded connection between converters and qubits usually brings additional insertion loss and intermediate noises. Here, we propose a cooperative quantum interface that integrates the converter and qubit coupling into a single device for efficient long-distance entanglement generation. Compared to traditional cascaded systems, our scheme offers several advantages, including compactness, reduced insertion loss, and suppression of noise from intermediate modes. We prove the excellent performance over the separated devices by about two orders of magnitude for the entangled infidelity of two remote nodes. Moreover, we discuss an extended scheme for multiple remote nodes, revealing an exponential advantage in performance as the number of nodes increases. The cooperative effect is universal that can be further applied to multifunctional integrated quantum devices. This work opens up novel prospects for quantum networks, distributed quantum computing, and sensing.

We present a quantum optimal control protocol to generate highly spin-squeezed states in Rydberg atom arrays coupled via Ising-type van der Waals interactions. Using gradient-based optimization techniques, we construct time-dependent pulse sequences that steer an initial product state toward highly entangled, spin-squeezed states with predefined magnetization and squeezing axes. We focus on the Wineland parameter ${\xi }_W^2$ to measure spin squeezing, and our approach achieves near-optimal spin squeezing in one-dimensional ring arrays of up to $N=8$ spins, significantly outperforming conventional quench dynamics for all system sizes studied. Remarkably, optimized pulse sequences can be directly scaled to larger arrays without additional optimization, achieving a squeezing parameter as low as ${\xi }_W^2=0.227$ in systems containing $N=50$ spins. This work demonstrates the potential of quantum optimal control methods for preparing highly spin-squeezed states, opening pathways to enhanced quantum metrology.

The existence of an autodetaching state of ${\mathrm{O}}^{-}$ with a lifetime on the scale of 100 ns is demonstrated both experimentally and theoretically. The ${\mathrm{O}}^{-}$ lifetime values are determined using two recently developed methods. The experimental approach is based on a derivation from measured electron-loss cross sections combined with time-of-flight spectrometry. For the theoretical approach, the continued Green's function within the formalism of Fano-Feshbach is applied. We present the measured lifetime value of $100\pm 10\text{ns}$. The calculated lifetime value is 75 ns, and is associated with the ($2p^{3}3s^2){}^{4}S$ state of ${\mathrm{O}}^{-}$. We discuss how the existence of a 100-ns-lifetime oxygen metastable anion can impact the modeling of oxygen-containing systems.

Atomic spectroscopy provides a sensitive tool for searching for new bosons that mediate exotic forces between elementary fermions. A comparison between a recent high-precision measurement [Bullis et al., Phys. Rev. Lett. 130, 203001 (2023)] of the hyperfine splitting of the $2S_{1/2}$ electronic level in hydrogen and up-to-date bound-state quantum electrodynamics calculations yields improved constraints on electron-proton exotic interactions. These are expressed in terms of the dimensionless coupling strengths $g_A{g}_A, g_p{g}_p$, and $g_V{g}_V$, corresponding to the exchange of axial-vector, pseudoscalar (axionlike), and vector bosons, respectively. Building on these results, our analysis highlights the importance of examining combinations of spin-dependent potentials that contribute to the same class of exotic interactions. In particular, we employ the combination $V_2+V_3$ for both axial-vector–axial-vector and vector-vector couplings. These findings motivate further precision measurements toward spin-dependent exotic interactions.

The linear intensity scaling of entangled two-photon absorption (ETPA) offers a fundamental mechanism to enable nonlinear optical spectroscopy and microscopy under a substantially lower excitation power than is currently feasible. However, the long data acquisition time and low signal-to-noise ratio in reported ETPA-based spectroscopic and microscopic studies prevent its widespread application. To gain the full potential of this novel quantum light approach, it is essential to optimize entangled photon generation for significantly enhanced ETPA responses. Here, we report a new quantum light source by combining entangled photon generation with free-space femtosecond pump-pulse shaping. Through measurements of singles and coincidence counts by varying the patterns applied to a spatial light modulator to control the spectral widths of the pump pulses, we reveal strong dependence of the singles and coincidence count rates as well as their ratios on the spectral widths of pump pulses. An optimal spectral width for the highest ratios between the coincidence photon and the signal or idler photon count rates is also determined. Identification of such optimal spectral widths for entangled photon generation in the presence of postgeneration spectral selection makes this quantum light source a promising choice for ETPA-based spectroscopy and imaging.

We study the steady-state behavior of the open Dicke model, which describes the collective interaction of $N$ spin-$1/2$ particles with a lossy, quantized cavity mode and exhibits a superradiant phase transition above a critical light-matter coupling. While the standard model conserves total spin, Kirton and Keeling [Phys. Rev. Lett. 118, 123602 (2017)] demonstrated that even infinitesimal homogeneous local dephasing destroys this phase transition and that local atomic decay can restore it. We analyze this interplay using degenerate perturbation theory across subspaces of fixed total spin, $S$. For coupling strengths above the threshold, there exists a critical spin value $S_c$ such that the superradiant phase transition occurs only for $S>S_c$. The perturbative approach captures how weak dephasing and decay induce mixing between different $S$ subspaces, yielding a steady-state spin distribution whose width scales as $1/\sqrt{N}$. This framework requires only the first and second moments and can be implemented via different methods that can yield these two moments (for example, the second-cumulant approach), circumventing the need for full density matrix calculations. These results bridge the quantum Rabi model and Dicke physics, elucidate the roles of dephasing and decay in collective quantum effects, and apply broadly to open quantum systems with degenerate steady states.

We study the classical mechanics and dynamics of particles that retain some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective classical manifold associated with two-particle bosonic and fermionic coherent states, we show how their exchange statistics is reflected in the symplectic form of the manifold. We demonstrate the classical analogs of exclusion or bunching behavior expected in such states by studying their trajectories in various quadratic potentials. Our examples are two-particle coherent states in one dimension and two-particle vortex motion in the lowest Landau level. We finally compare and contrast our results with previous simulations of the full quantum system, and with existing results on the geometric interpretations of quantum mechanics.

We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary $\mathrm{SU}\left(d\right)$ symmetries. It allows us to enhance a natural model of quantum computation—permutational quantum computing (PQC) [Jordan, Quantum Inf. Comput. 10, 470 (2010)]—and define a more powerful model: $\mathrm{PQC}+$. While PQC was shown to be efficiently classically simulatable, we exhibit a problem which can be efficiently solved on a $\mathrm{PQC}+$ machine, whereas no classical polynomial time algorithm is known, thus providing evidence against $\mathrm{PQC}+$ being classically simulatable. We further discuss practical quantum machine learning algorithms which can be carried out in the paradigm of $\mathrm{PQC}+$.

Existing quantum state tomography methods are limited in scalability due to their high computation and memory demands, making them impractical for the recovery of large quantum states. In this work, we address these limitations by reformulating the maximum likelihood estimation problem using the Burer–Monteiro factorization, resulting in a nonconvex but low-rank parametrization of the density matrix. We derive a fully unconstrained formulation by analytically eliminating the trace-one and positive-semidefinite constraints, thereby avoiding the need for projection steps during optimization. Furthermore, we determine the Lagrange multiplier associated with the unit-trace constraint a priori, reducing computational overhead. The resulting formulation is amenable to scalable first-order optimization, and we demonstrate its tractability using the limited-memory Broyden-Fletcher-Goldfarb-Shanno method. Importantly, we also propose a low-memory version of the above algorithm to fully recover certain large quantum states with Pauli-based positive-operator-value measurements. Our low-memory algorithm avoids explicitly forming any density matrix, and does not require the density matrix to have a matrix product state or other tensor structure. For a fixed number of measurements and fixed rank, our algorithm requires just $O\left(d{log}_{2}d\right)$ complexity per iteration to recover a $d\times d$ density matrix. Additionally, we derive a useful error bound that can be used to give a rigorous termination criterion. We numerically demonstrate that our method is competitive with state-of-the-art algorithms for moderately sized problems, and then demonstrate that our method can solve a 20-qubit problem on a laptop in under 5 hours.

High-dimensional hyperentangled states, serving as crucial physical resources in quantum communication, have attracted significant attention due to their exceptional properties (e.g., higher information density) compared to conventional two-dimensional single-degree-of-freedom entanglement. However, practical quantum entanglement systems inevitably suffer from environmental interactions, resulting in their degradation into partially entangled pure states or even mixed states, thereby significantly compromising the efficiency and security of quantum communication. Consequently, improving entanglement preservation in noisy systems emerges as a pivotal challenge in realizing fault-tolerant quantum networks. We propose two universal distillation schemes based on local positive-operator-valued measures (POVMs) for single-copy $(2\times 4\times 4)$-dimensional hyperentangled photons. These schemes effectively suppress photon vacuum errors induced by transmission losses and are constructed using spatial-mode and polarization-based POVM measurements, respectively. Our results demonstrate that the spatial-mode-based scheme outperforms its polarization-based counterpart in terms of fidelity and success probability. Remarkably, we discover that with appropriate POVM parameters, the fidelity range of amplitude-damped noisy states can be expanded to cover almost all parameter spaces. Due to the universal applicability of POVM measurements, which require neither auxiliary entanglement nor complex detectors and operate on single copies of imperfect states in each purification round, our scheme provides an experimentally feasible solution for distilling high-dimensional hyperentangled photonic states.

The increasing focus on long-term time series prediction across various fields has been significantly strengthened by advancements in quantum computation. In this paper we introduce a data-driven method designed for time series prediction with quantum dynamical embedding (QDE). This approach enables a trainable embedding of the data space into an extended state space, allowing for the recursive retrieval of time series information. Based on its independence of time series length, this method achieves depth-efficient quantum circuits that are crucial for near-term quantum computers. Numerical simulations demonstrate the model's capability to predict not only wave signals but also more complex signals such as NARMA. Prediction accuracy improves with model scaling, and notably, the model achieves better accuracy on wave signal tasks with fewer parameters compared to QRC. Additionally, the model shows promising potential for denoising classical noise in wave signals, and when combined with error mitigation techniques for typical quantum noise, it enables reliable long-term prediction of wave signals. We implement this model, restricted to two qubits, on the Origin “Wukong” superconducting quantum processor as a simple proof of concept on NISQ devices. Furthermore, we provide theoretical analysis of the QDE's dynamical properties for the two-qubit case and discuss its potential universality. Overall, this study represents our first step towards leveraging near-term quantum devices for time series forecasting, offering insights into integrating data-driven learning with quantum dynamical embeddings.