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Using modulation transfer spectroscopy, we achieve the frequency stabilization of a high-power 3-W blue laser at the wavelength of 420 nm to the $\mathrm{Rb}$ $5S_{1/2}$–$6P_{3/2}$ transition. The in-loop frequency stability of this laser is $1.8\times {10}^{-11}/\sqrt{\tau }$, reaching $1.7\times {10}^{-12}$ at 100 s and $7\times {10}^{-13}$ at 1000 s. An external power feedback loop is established using an acousto-optic modulator, employing the zeroth-order diffracted light for power stabilization, achieving an in-loop power stability of $1.0\times {10}^{-6}$ at 1 s. Moreover, the continuous mode-hop free interval of this high-power laser can simultaneously cover the $5S_{1/2}$–$6P_{3/2}$ transitions of ${}^{85}\text{Rb}$ and ${}^{87}\text{Rb}$, with successful locking achieved for both isotopes, providing a comprehensive analysis of the $\mathrm{Rb}$ atomic transitions in the blue spectral region. As an application, this 3-W 420-nm laser with excellent power and frequency stabilities is used as a repumping source for diffuse laser cooling of ${}^{87}\text{Rb}$ atoms, realizing a one-meter-long cold-atom cloud. This paves the way for using blue-light cooling to realize a cold-$\mathrm{Rb}$-atom active optical clock. In addition, the ultrahigh-stability 420-nm laser also finds applications in various fields such as the Rydberg atom experiment, Bose-Einstein condensation, ultranarrow-bandwidth Faraday atomic filter, and so on.

Fluxonium qubits are recognized for their high coherence times and high operation fidelities. These are attributed to their unique design incorporating a superinductor, which is typically implemented using an array of over 100 Josephson junctions; however, this complexity poses significant fabrication challenges, particularly in achieving high yield and junction uniformity with traditional methods. Here, we introduce an overlap process for Josephson-junction fabrication that achieves nearly 100% yield and maintains uniformity across a 2-inch (50.8-mm) wafer with less than 5% variation for the phase-slip junction and less than 2% for the entire junction array. We use a compact junction array design that achieves state-of-the-art dielectric loss tangents and flux noise levels, as confirmed by multiple devices. This enables fluxonium qubits to reach energy relaxation times exceeding 1 ms at the flux-frustration point. This work paves the way for scalable, high-coherence fluxonium processors using processes compatible with complementary metal-oxide semiconductor manufacturing, marking a significant step toward practical quantum computing.

Realizing computationally complex quantum circuits in the presence of noise and imperfections is a challenging task. While fault-tolerant quantum computing provides a route to reducing noise, it requires a large overhead for generic algorithms. Here, we develop and analyze a hardware-efficient, fault-tolerant approach to realizing complex sampling circuits. We co-design the circuits with the appropriate quantum error-correcting codes for efficient implementation in a reconfigurable neutral atom-array architecture, constituting what we call a fault-tolerant compilation of the sampling algorithm. Specifically, we consider a family of $\text{⟦}{2}^D,D,2\text{⟧}$ quantum error-detecting codes whose transversal and permutation gate set can realize arbitrary degree-$D$ instantaneous quantum polynomial (IQP) circuits. Using native operations of the code and the atom-array hardware, we compile a fault-tolerant and fast-scrambling family of such IQP circuits in a hypercube geometry, realized recently in the experiments by Bluvstein et al. [Nature 626, 7997 (2024)]. We develop a theory of second-moment properties of degree-$D$ IQP circuits for analyzing hardness and verification of random sampling by mapping to a statistical mechanics model. We provide strong evidence that sampling from these hypercube IQP circuits is classically hard to simulate even at relatively low depths. We analyze the linear cross-entropy benchmark (XEB) in comparison to the average fidelity and, depending on the local noise rate, find two different asymptotic regimes. To realize a fully scalable approach, we first show that Bell sampling from degree-4 IQP circuits is classically intractable and can be efficiently validated. We further devise new families of $\text{⟦}O(d^D),D,d\text{⟧}$ color codes of increasing distance $d$, permitting exponential error suppression for transversal IQP sampling. Our results highlight fault-tolerant compiling as a powerful tool in co-designing algorithms with specific error-correcting codes and realistic hardware.

Sub-Doppler laser spectroscopy is crucial for laser-frequency stabilization, playing a significant role in atomic physics and precision measurement. However, despite decades of development, inefficient atomic utilization remains a widespread issue. Most existing methods rely on single-frequency lasers, and due to the Doppler effect, only a small fraction ($<1\mathrm{\%}$) of atoms with near-zero longitudinal velocities are utilized, severely limiting improvements in the spectral signal-to-noise ratio ($S/N$). Here, we propose a velocity-comb modulation transfer spectroscopy (VC-MTS) solution that leverages the velocity-selective resonance of modulated $N$-frequency lasers, seeming as an optical comb, to enhance the utilization of nonzero-velocity atoms, which optimizes the spectral amplitude and frequency instability by $N$ and $\sqrt{N}$ times, respectively. Unlike traditional MTS, in this work, each pair of counterpropagating lasers interacts with atoms from different longitudinal velocity groups, independently contributing to the amplitude and $S/N$. Preliminary proof-of-principle results show that the frequency stability of the triple-frequency laser is improved by $\sqrt{3}$ times compared to the single-frequency laser. With more frequency components, VC-MTS stabilized lasers are expected to achieve order-of-magnitude breakthroughs in frequency stability, taking an essential step toward next-generation compact optical clocks. This method also applies to quantum systems with wide velocity distributions, offering an innovative perspective on laser spectroscopy and inspiring further intriguing applications.

Demonstrating quantum advantage requires experimental implementation of a computational task that is hard to achieve using state-of-the-art classical systems. One approach is to perform sampling from a probability distribution associated with a certain class of highly entangled many-body wave functions. It has been suggested that such a quantum advantage can be certified with the linear cross-entropy benchmark (XEB). We critically examine this notion. First, we consider a “benign” setting, where an honest implementation of a noisy quantum circuit is assumed, and characterize the conditions under which the XEB approximates the fidelity of quantum dynamics. Second, we assume an “adversarial” setting, where all possible classical algorithms are considered for comparisons, and show that achieving relatively high XEB values does not imply faithful simulation of quantum dynamics. Specifically, we present an efficient classical algorithm that achieves high XEB values, namely 5–12% of those obtained in the state-of-the-art experiments, within just a few seconds using a single GPU machine. This is made possible by identifying and exploiting several vulnerabilities of the XEB, which allows us to achieve high XEB values without simulating a full quantum circuit. Remarkably, our algorithm features better scaling with the system size than a noisy quantum device for commonly studied random circuit ensembles in various architecture. We quantitatively explain the success of our algorithm and the limitations of the XEB by using a theoretical framework, in which the dynamics of the average XEB and fidelity are mapped to classical statistical mechanics models. Using this framework, we illustrate the relation between the XEB and the fidelity for quantum circuits in various architectures, with different choices of gate sets, and in the presence of noise. Taken together, our results demonstrate that XEB’s utility as a proxy for fidelity hinges on several conditions, which should be independently checked in the benign setting, but cannot be assumed in the general adversarial setting. Therefore, the XEB on its own has a limited utility as a benchmark for quantum advantage. We briefly discuss potential ways to overcome these limitations.

Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data. However, analytic results to date rely on assumptions and arguments from complexity theory. Because of this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold. Here, we study the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements. We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes. We use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality. In doing so, we demonstrate that our introduced quantum models are able to outperform state-of-the-art classical models even in practice.

To date, the laser cooling of rubidium atoms has inevitably relied on 780 nm cooling light corresponding to the first excited state $5{\mathrm{P}}_{3/2}$. Here, we demonstrate diffuse laser cooling of ${}^{87}\mathrm{Rb}$ atoms using the 420 nm $5{\mathrm{S}}_{1/2}\to 6{\mathrm{P}}_{3/2}$ transition without a preceding 780 nm cooling stage. A high-power $420\mathrm{nm}$ laser is used as the cooling light to produce cold atoms in a 1-m-long diffuse-cooling cell. Absorption spectroscopy yields a cold-atom density of approximately $1.4\times {10}^{11}{\mathrm{m}}^{-3}$. We compare the cooling performance of the 420 nm and conventional 780 nm diffuse-cooling schemes and verify the feasibility of using the high-excited-state transition as an independent cooling channel in this large-volume diffuse-cooling system. This approach provides an alternative cooling/pumping pathway for continuous cold-atom active optical clocks, where compatibility with the clock-lasing process and reduced cooling-light-induced perturbations are important. It is also expected to open up research directions and application prospects in frontier fields such as Rydberg atoms, quantum information, and so on.

We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g., the computational basis). Our approach is based upon the intuition that noise exponentially damps nonlocal correlations relative to local correlations. This enables one to classically simulate a noisy quantum circuit by keeping track of only the dynamics of local quantum information. Our algorithm also enables sampling from the output distribution of a circuit in quasipolynomial time, so long as the distribution anticoncentrates. A number of implications are discussed, including a fundamental limit on the efficacy of noise mitigation strategies: For constant noise rates, any quantum circuit for which error mitigation succeeds in polynomial-time on most input states can also be classically simulated in polynomial-time on most input states. Our algorithms scale exponentially in the inverse noise rate, which is fundamental and makes them impractical for current quantum devices.

Quantum generative models hold the promise of accelerating or improving machine learning tasks by leveraging the probabilistic nature of quantum states, but the successful optimization of these models remains a difficult challenge. To tackle this challenge, we present a new architecture for quantum generative modeling that combines insights from classical machine learning and quantum phases of matter. In particular, our model utilizes both many-body localized (MBL) dynamics and hidden units to improve the optimization of the model. We demonstrate the applicability of our model on a diverse set of classical and quantum tasks, including a toy version of MNIST handwritten digits, quantum data obtained from quantum many-body states, and nonlocal parity data. Our architecture and algorithm provide novel strategies of utilizing quantum many-body systems as learning resources and reveal a powerful connection between disorder, interaction, and learning in quantum many-body systems.

We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being nonuniversal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses. Equipped with the intrinsic single-instance-hardness property, a single fixed unitary evolution in our model is sufficient to produce classically intractable results, compared to several other models that rely on implementation of an ensemble of different unitaries (instances). We propose a feasible experimental scheme to implement our Hamiltonian model using cold atoms trapped in a square optical lattice. We formulate a procedure to certify the correct functioning of this quantum machine. The certification requires only a polynomial number of local measurements assuming measurement imperfections are sufficiently small.

Representation by neural networks, in particular by restricted Boltzmann machines (RBMs), has provided a powerful computational tool to solve quantum many-body problems. An important open question is how to characterize which class of quantum states can be efficiently represented with RBMs. Here, we show that RBMs can efficiently represent a wide class of many-body entangled states with rich exotic topological orders. This includes (1) ground states of double semion and twisted quantum double models with intrinsic topological orders, (2) states of the AKLT model and two-dimensional CZX model with symmetry protected topological orders, (3) states of stabilizer Fracton models with fracton topological order, and (4) (generalized) stabilizer states and hypergraph states that are important for quantum information protocols. One twisted quantum double model state considered here harbors non-Abelian anyon excitations. Our result shows that it is possible to study a variety of quantum models with exotic topological orders and rich physics using the RBM computational toolbox.

Hybrid quantum-classical variational algorithms are one of the most propitious implementations of quantum computing on near-term devices, offering classical machine-learning support to quantum scale solution spaces. However, numerous studies have demonstrated that the rate at which this space grows in qubit number could preclude learning in deep quantum circuits, a phenomenon known as barren plateaus. In this work, we implicate random entanglement, i.e., entanglement that is formed due to state evolution with random unitaries, as a source of barren plateaus and characterize them in terms of many-body entanglement dynamics, detailing their formation as a function of system size, circuit depth, and circuit connectivity. Using this comprehension of entanglement, we propose and demonstrate a number of barren plateau ameliorating techniques, including initial partitioning of cost function and non-cost function registers, meta-learning of low-entanglement circuit initializations, selective inter-register interaction, entanglement regularization, the addition of Langevin noise, and rotation into preferred cost function eigenbases. We find that entanglement limiting, both automatic and engineered, is a hallmark of high-accuracy training and emphasize that, because learning is an iterative organization process whereas barren plateaus are a consequence of randomization, they are not necessarily unavoidable or inescapable. Our work forms both a theoretical characterization and a practical toolbox; first defining barren plateaus in terms of random entanglement and then employing this expertise to strategically combat them.

The fluxonium qubits have emerged as a promising platform for gate-based quantum information processing. However, their extraordinary protection against charge fluctuations comes at a cost: when coupled capacitively, the qubit-qubit interactions are restricted to $XX$ interactions. Consequently, effective $ZZ$ or $XZ$ interactions are only constructed either by temporarily populating higher-energy states, or by exploiting perturbative effects under microwave driving. Instead, we propose and demonstrate an inductive coupling scheme, which offers a wide selection of native qubit-qubit interactions for fluxonium. In particular, we leverage a built-in, flux-controlled $ZZ$ interaction to perform qubit entanglement. To combat the increased flux-noise-induced dephasing away from the flux-insensitive position, we use a continuous version of the dynamical decoupling scheme to perform noise filtering. Combining these, we demonstrate a 20 ns controlled-z gate with a mean fidelity of 99.53%. More than confirming the efficacy of our gate scheme, this high-fidelity result also reveals a promising but rarely explored parameter space uniquely suitable for gate operations between fluxonium qubits.

Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations which are difficult to capture using classical models. We show theoretically that such quantum-inspired correlations provide a powerful resource for generative modeling. In particular, we provide an unconditional proof of separation in expressive power between a class of widely used generative models, known as Bayesian networks, and its minimal quantum-inspired extension. We show that this expressivity enhancement is associated with quantum nonlocality and quantum contextuality. Furthermore, we numerically test this separation on standard machine-learning data sets and show that it holds for practical problems. The possibility of quantum-inspired enhancement demonstrated in this work not only sheds light on the design of useful quantum machine-learning protocols but also provides inspiration to draw on ideas from quantum foundations to improve purely classical algorithms.

Simulating generic quantum states and dynamics is practically intractable using classical computers. However, certain special classes—namely, Clifford and matchgate circuits—permit efficient computation. They provide invaluable tools for studying many-body physics, quantum chemistry, and quantum computation. While both play foundational roles across multiple disciplines, the origins of their tractability seem disparate, and their relationship remains unclear. A deeper understanding of such tractable classes could expand their scope and enable a wide range of new applications. In this work, we make progress toward the unified understanding of the Clifford and matchgate—these two classes are, in fact, distinct special cases of a single underlying structure. Specifically, we introduce the 2D quon language, which combines Majorana worldlines with their underlying spacetime topology to diagrammatically represent quantum processes and tensor networks. In full generality, the 2D quon language is universal—capable of representing arbitrary quantum states, dynamics, or tensor networks—yet they become especially powerful in describing Clifford and matchgate classes. Each class can be efficiently characterized in a visually recognizable manner using the quon framework. This capability naturally gives rise to several families of efficiently computable tensor networks introduced in this work: punctured matchgates, hybrid Clifford-matchgate MPS, and ansatze generated from factories of tractable networks. All of these exhibit high non-Cliffordness, high nonmatchgateness, and large bipartite entanglement entropy. We discuss a range of applications of our approach, from recovering well-known results such as the Kramers-Wannier duality and the star-triangle relation of the Ising model, to enabling variational optimization with novel ansatz states.

Superconducting qubits provide a promising path toward building large-scale quantum computers. The simple and robust transmon qubit has been the leading platform, achieving multiple milestones. However, fault-tolerant quantum computing calls for qubit operations at error rates significantly lower than those exhibited in the state of the art. Consequently, alternative superconducting qubits with better error protection have attracted increasing interest. Among them, fluxonium is a particularly promising candidate, featuring large anharmonicity and long coherence times. Here, we engineer a fluxonium-based quantum processor that integrates high qubit coherence, fast frequency tunability, and individual-qubit addressability for reset, readout, and gates. With simple and fast gate schemes, we achieve an average single-qubit gate fidelity of 99.97% and a two-qubit gate fidelity of up to 99.72%. This performance is comparable to the highest values reported in the literature of superconducting circuits. Thus our work, within the realm of superconducting qubits, reveals an alternative qubit platform that is competitive with the transmon system.

Quantum computing promises to speed up machine-learning algorithms. However, noisy intermediate-scale quantum (NISQ) devices pose engineering challenges to realizing quantum machine-learning (QML) advantages. Recently, a series of QML computational models inspired by the noise-tolerant dynamics of the brain has emerged as a means to circumvent the hardware limitations of NISQ devices. In this paper, we introduce a quantum version of a recurrent neural network (RNN), a well-known model for neural circuits in the brain. Our quantum RNN (qRNN) makes use of the natural Hamiltonian dynamics of an ensemble of interacting spin-1/2 particles as a means for computation. In the limit where the Hamiltonian is diagonal, the qRNN recovers the dynamics of the classical version. Beyond this limit, we observe that the quantum dynamics of the qRNN provide it with quantum computational features that can aid it in computation. To this end, we study a fixed-geometry qRNN, i.e., a quantum reservoir computer, based on arrays of Rydberg atoms and show that the Rydberg reservoir is indeed capable of replicating the learning of several cognitive tasks such as multitasking, decision making, and long-term memory by taking advantage of several key features of this platform such as interatomic species interactions and quantum many-body scars.