Fusing small resource states into a larger-scale, highly connected graph state is essential for scalable photonic quantum computing. Theoretical analysis reveals that this can only be achieved when the success probability of the fusion gate surpasses a specific percolation threshold of 58.98% by using three-photon Greenberger-Horne-Zeilinger states as resource states. However, such an implementation of a fusion gate has never been experimentally realized before. Here, we successfully demonstrate a boosted fusion gate with a theoretical success probability of 75%, using deterministically generated auxiliary states. The success probability is experimentally measured to be 71.0(7)%. We further demonstrate the effectiveness of the boosted fusion gate by fusing two Bell states with a fidelity of 67(2)%. Our work paves a crucial path toward scalable linear optical quantum computing.

Fault-tolerant quantum computation requires logical operations that manipulate encoded information while preserving quantum error-correction protection. In planar surface-code architectures, code deformation and lattice surgery provide a local, measurement-based route to such operations. Here we experimentally realize key elements of patch-based surface-code logical processing on a 107-qubit superconducting quantum processor. We first implement a reusable primitive layer comprising merge and split, patch expansion and shrinkage, and deformations mediated by domain walls and twist defects. We then compose these primitives to realize logical state routing, the logical controlled-NOT gate, and the single-qubit Hadamard and phase gates, which together form a Clifford-generating set. All operations are implemented on distance-three rotated surface-code patches with multi-round syndrome extraction and neural-network decoding, without post-selection. Our results advance superconducting surface-code experiments from protected logical memory to active, patch-based fault-tolerant logical operations.

Quantum entanglement is a fundamental resource for quantum information processing and serves as a critical benchmark for quantum hardware performance. Cluster states are a special class of entangled states that serve as universal resources for measurement-based quantum computation and possess an intrinsic symmetry-protected topological order, which confers robustness against symmetry-respecting noise. Here we report the scalable preparation and verification of genuine multipartite cluster states on the 105-qubit Zuchongzhi 3.1 superconducting processor. We achieve one-dimensional cluster states of up to 95 qubits and two-dimensional cluster states of up to 72 qubits. The symmetry-protected topological cluster states exhibit input-state-dependent robustness under symmetry-breaking perturbations due to an operational parity structure that enhances the performance of measurement-based quantum computation. Furthermore, we use our two-dimensional cluster states to implement the Deutsch-Jozsa algorithm within the measurement-based quantum computation framework, achieving higher output-state fidelity compared with traditional circuit-based models and a query efficiency advantage over classical approaches. Our work establishes a scalable platform that combines large-scale entanglement generation, symmetry-protected topological order and practical quantum algorithms to enable robust, fault-tolerant measurement-based quantum computation.

Abstract All-solid-state cavity quantum electrodynamics (cQED) has drawn significant research interest because of its potential applications in the development of large-scale integrated quantum photonics. However, the long-lasting issues associated with local spectral tuning of the cavity and emitter, in-plane light confinement for efficient light routing, have hindered its on-chip scalable implementations. Here, we overcome these limitations by proposing and demonstrating a hybrid chip-integrated solid-state cQED device with strong in-plane optical mode confinement. The device consists of semiconducting quantum dots (QDs) integrated onto a thin-film lithium niobate (TFLN) microring resonator. By exploring the TFLN’s piezoelectric strain and electro-optic (EO) properties, we have realized local spectral tuning for waveguide-coupled QDs up to 4.82 nm (7.30 meV), enabling on-chip deterministic single-photon emission with a Purcell factor of 3.52. When further combining the independent EO effect-based cavity tuning, we demonstrate an on-chip wavelength-tunable cQED device with Purcell factors over 1.89 in a 0.30 nm (0.45 meV) tuning range, 230 times more than the reported transform-limited linewidth of the QDs emission. The successful demonstration of scalable cQED with circuits-compatible local strain and EO tuning methods opens the avenue to scale up all-solid-state cQED devices in large-scale quantum photonic circuits.

Characterizing quantum phases-of-matter at finite-temperature is essential for understanding complex materials and large-scale thermodynamic phenomena. Here, we develop algorithmic protocols for simulating quantum thermodynamics on quantum hardware through quantum kernel function expansion (QKFE), producing the free energy as an analytic function of temperature with uniform convergence. These protocols are demonstrated by simulating transverse field Ising and XY models with superconducting qubits. In both analogue and digital implementations of the QKFE algorithms, we exhibit quantitative agreement of our quantum simulation experiments with the exact results. Our approach provides a general framework for computing thermodynamic potentials on programmable quantum devices, granting access to key thermodynamic properties such as entropy, heat capacity and criticality, with far-reaching implications for material design and drug development.

Quantum light sources, particularly those based on solid-state emitters, are indispensable components for quantum information technology. Single quantum dots, as a prominent candidate, are leading the advancements in performance and applications. The epitaxial growth of III-V quantum dots lays the foundation for their optical and spin properties. In this paper, we outline the efforts to achieve highest quality quantum light sources utilizing the molecular beam epitaxy technique, and explore the applications of quantum dots as single photon sources and entangled photon sources. Our work underscores the importance of optimizing epitaxial growth and delves into the potential of arrays of quantum light sources serving as a cornerstone for integrated quantum photonics.

Similar to superconducting circuit quantum electrodynamics (cQED), the development of a photonic analog--specifically, photonic circuit cQED--has become a major focus in integrated quantum photonics. Current solid-state cQED devices, however, face scalability challenges due to the difficulty in simultaneously spectral tuning of cavity modes and quantum emitters while ensuring in-plane optical modes confinement for efficient on-chip light routing. Here, we overcome these limitations by proposing and demonstrating a hybrid solid-state cQED platform integrated on a chip. Our device integrates semiconducting quantum dots (QDs) with a thin-film lithium niobate (TFLN) microring resonator. Leveraging TFLN's ferroelectric and electro-optic (EO) properties, we implement local spectral tuning of both waveguide-coupled QDs and cavity modes. This approach achieves a broad spectral tuning range of up to 4.82 nm for individual QDs, enabling deterministic on-chip single-photon emission with a Purcell factor of 3.52. When combined with EO cavity tuning, we realize a spectrally tunable hybrid photonic circuit cQED device, sustaining near-constant Purcell factors of 1.89 over a 0.30 nm spectral range. This achievement enables scalable on-chip cavity-enhanced single-photon sources while preserving optical properties and maintaining compatibility with advanced photonic architectures, marking a significant step toward practical implementation of large-scale chip-based quantum networks.

Despite the significant progress in superconducting quantum computation over the past years, quantum state measurement still lags nearly an order of magnitude behind quantum gate operations in speed and fidelity. The main challenge is that the strong coupling and readout signal used to probe the quantum state may also introduce additional channels which may cause qubit state transitions. Here, we design a novel architecture to implement the long-sought longitudinal interaction scheme between qubits and resonators. This architecture not only provides genuine longitudinal interaction by eliminating residual transversal couplings, but also introduces proper nonlinearity to the resonator that can further minimize decay error and measurement-induced excitation error. Combined with the multilevel readout protocol, we achieved a measurement fidelity of 99.8% in 202 ns without requiring any first-stage amplification. This highlights its potential as a highly promising architecture for superconducting qubit measurement.

To fully exploit the potential of quantum technologies, quantum networks are needed to link different systems, enhancing applications in computing, cryptography and metrology. Central to these networks are quantum relays that can facilitate long-distance entanglement distribution and quantum communication. In this work, we present a modular and scalable quantum relay architecture using a high-quality single-photon source. The proposed network incorporates three untrusted intermediate nodes and is capable of a repetition rate of 304.52 MHz. We use a measurement-device-independent protocol to demonstrate secure key establishment over fibres covering up to 300 km. This study highlights the potential of single-photon sources in quantum relays to enhance information transmission, expand network coverage and improve deployment flexibility, with promising applications in future quantum networks.

Scalable coherent manipulation of qubit quantum states is crucial for building large-scale superconducting quantum processors towards fault-tolerant quantum computing. Complete coherent manipulation contains quantum gate control and magnetic flux bias for the qubit, especially for quantum processors with frequency-tunable qubits and tunable couplers. In recent years, efforts have been made to propose quantum gate control in a scalable way. However, proposals and experiments for scalable magnetic flux bias for qubits are rarely reported. Here, we propose a scalable scheme to provide magnetic flux for qubits by using an on-chip direct current source (OCDCS). We demonstrate both theoretically and experimentally that only single pulse is needed to deterministically modulate the magnetic flux in the OCDCS, which then provides the qubit with in situ and constant magnetic flux. With the magnetic flux provided by the OCDCS, the experimental results exhibit high-fidelity single-qubit gate and low noise current of the OCDCS, which shows a 15.6 dB reduction compared with that of the RTE scheme. Additionally, we propose a time-division-multiplex (TDM) scheme combining the OCDCS with switch arrays, which could exponentially reduce the number of cables for flux bias from traditional n to log2(n) + 1. Our work thus paves the way for scalable flux bias in large-scale superconducting quantum processors.

Photon loss is the biggest enemy for scalable photonic quantum information processing. This problem can be tackled by using quantum error correction, provided that the overall photon loss is below a threshold of 1/3. However, all reported on-demand and indistinguishable single-photon sources still fall short of this threshold. Here, by using tailor shaped laser pulse excitation on a high-quantum efficiency single quantum dot deterministically coupled to a tunable open microcavity, we demonstrate a high-performance source with a single-photon purity of 0.9795(6), photon indistinguishability of 0.9856(13), and an overall system efficiency of 0.712(18), simultaneously. This source for the first time reaches the efficiency threshold for scalable photonic quantum computing. With this source, we further demonstrate 1.89(14) dB intensity squeezing, and consecutive 40-photon events with 1.67 mHz count rate.

Quantum error correction (QEC) enables practical quantum computing by encoding logical qubits in many physical qubits, which can exponentially suppress the logical error rate with increasing code size provided that the physical error rate is below a critical threshold. However, the leakage of quantum information from the computational subspace presents a critical challenge to the development of scalable QEC, which creates long-lived, correlated errors that spread across space and time. Here, we demonstrate a quantum memory operating below the threshold by implementing an all-microwave leakage suppression architecture on a distance-7 surface code. We achieve a logical error suppression factor of Λ=1.40(6), definitively reversing the above-threshold scaling (Λ<1) caused by unmitigated leakage. This scheme integrates a hardware-efficient leakage reduction unit for data qubits with a fast, unconditional reset for ancilla qubits, suppressing the average leakage population after 40 cycles by a factor of 72 to 6.4(5)×10^{-4}. Our results demonstrate the viability of all-microwave control architectures for suppressing critical errors at scale, paving the way for more advanced quantum error correction implementations.

Single-photon sources are essential for quantum networks, enabling applications ranging from quantum key distribution (QKD) to the burgeoning quantum internet. Despite the remarkable advancements, the current reliance of QKD on attenuated coherent (laser) light sources has imposed a fundamental limit on the secret key rate (SKR). This constraint is primarily attributable to the scarcity of single-photon components within coherent light, confined by an inherent upper bound of 1/e. Here, we report high-rate QKD using a high-efficiency single-photon source, enabling an SKR transcending the fundamental rate limit of coherent light. We developed an on-demand, bright semiconductor quantum-dot single-photon source with an efficiency of 0.71(2), exceeding the inherent bound of coherent light by approximately 2.87 dB. Implementing narrow-bandwidth filtering and random polarization modulation, we conducted a field QKD trial over a 14.6(1.1)-dB-loss free-space urban channel, achieving an SKR of 0.00108 bits per pulse. This surpasses the practical limit of coherent-light-based QKD by 2.53 dB. Our findings conclusively demonstrate the superior performance of nanotechnology-based single-photon sources over coherent light for QKD applications, marking a pivotal stride towards the realization of a global quantum internet.

Hybrid integrated quantum photonics offers a scalable route to chip-based quantum networks by combining solid-state quantum dots (QDs) with low-loss and reconfigurable photonic circuits. However, limited integration scalability, spectral inhomogeneity of QD emissions and the challenge of achieving quantum interference between independent sources have impeded progress towards this goal. Here we demonstrate a hybrid lithium niobate photonic platform integrating arrays of QD-containing waveguides with 20 deterministic single-photon sources. Leveraging the piezoelectric properties of thin-film lithium niobate, we develop a circuit-compatible local strain-tuning technique that enables on-chip spectral tuning of individual QDs by up to 7.7 meV. This capability allows quantum interference with a visibility of 0.73 between two spatially separated waveguide-coupled QD single-photon sources, thereby establishing a functional on-chip quantum network. The large-scale integration of tunable and interconnected QD-based single-photon sources within low-loss lithium niobate circuits paves the way for realizing compact and scalable quantum networks on a photonic chip.

The degradation caused by surface states restricts the performance of near-surface semiconductor quantum dots (QDs). Here, we demonstrate optimized passivation techniques to improve the resonance fluorescence (RF) with dot-to-dot comparisons. These optimized techniques, for the first time, reduce the linewidth and noise level of existing pulsed-RF signals, as well as revive pulsed-RF signals which originally are vanishing. The improvements are confirmed to originate from reduced surface state density and electric field after passivation, through optical and surface science characterizations. Our study promotes applications of the passivation techniques in thin-film quantum devices, paving the way for the further development of optimal QD-based quantum light sources.

Symmetry-protected topological (SPT) phases are fundamental features of cluster states, serving as key resources for measurement-based quantum computation (MBQC). Generating large-scale cluster states and verifying their SPT phases are essential steps toward practical MBQC, which however still presents significant experimental challenges. In this work, we address these challenges by utilizing advanced superconducting hardware with optimized gate operations, enhanced readout fidelity, and error mitigation techniques. We successfully generate and verify 95-qubit one-dimensional and 72-qubit two-dimensional genuine entangled cluster states, achieving fidelities of 0.5603 ± 0.0084 and 0.5519 ± 0.0054, respectively. Leveraging these high-fidelity cluster states, we investigate SPT phases through quantum teleportation across all 95 qubits and demonstrate input-state-dependent robustness against symmetry-breaking perturbations, highlighting the practicality and intrinsic robustness of MBQC enabled by the SPT order. Our results represent a significant advancement in large-scale entanglement generation and topological phase simulation, laying the foundation for scalable and practical MBQC using superconducting quantum systems.

Topological phases of matter are of both fundamental and practical interest. In this study, we implemented both equilibrium and nonequilibrium higher-order topological phases using a two-dimensional programmable superconducting quantum processor. Quantum programming of nonequilibrium higher-order topological phases was achieved by constructing quantum circuits comprising >50 cycles of Floquet operators on a six-by-six qubit array. Additionally, we introduce a universal approach based on measuring the dynamics of chiral density to identify distinct nonequilibrium higher-order topological features, including Floquet corner topological invariants and π-energy topological corner modes. Our work may enable the use of programmable quantum processors to explore exotic higher-order nonequilibrium topological phases of matter.

In the relentless pursuit of quantum computational advantage, we present a significant advancement with the development of Zuchongzhi 3.0. This superconducting quantum computer prototype, comprising 105 qubits, achieves high operational fidelities, with single-qubit gates, two-qubit gates, and readout fidelity at 99.90%, 99.62%, and 99.13%, respectively. Our experiments with an 83-qubit, 32-cycle random circuit sampling on the Zuchongzhi 3.0 highlight its superior performance, achieving 1×10^{6} samples in just a few hundred seconds. This task is estimated to be infeasible on the most powerful classical supercomputers, Frontier, which would require approximately 5.9×10^{9}  yr to replicate the task. This leap in processing power places the classical simulation cost 6 orders of magnitude beyond Google's SYC-67 and SYC-70 experiments [Morvan et al., Nature 634, 328 (2024)10.1038/s41586-024-07998-6], firmly establishing a new benchmark in quantum computational advantage. Our work not only advances the frontiers of quantum computing but also lays the groundwork for a new era where quantum processors play an essential role in tackling sophisticated real-world challenges.