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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., Comment: 22 pages, 5 figures, 1 Table

Fractional quantum Hall (FQH) states, known for their robust topological order and the emergence of non-Abelian anyons, have captured significant interest due to the appealing applications in fault-tolerant quantum computing. Bottom-up approach on an engineered quantum platform will provide opportunities to operate FQH states without external magnetic field and enhance local and coherent manipulation of these exotic states. Here we demonstrate a lattice version of photon FQH state using a programmable on-chip platform based on photon blockade and engineering gauge fields on a novel two-dimensional circuit quantum electrodynamics (QED) system. We first observe the effective photon Lorentz force and butterfly spectrum in the artificial gauge field, a prerequisite for FQH states. After adiabatic assembly of Laughlin FQH wavefunction of 1/2 filling factor from localized photons, we observe strong density correlation and chiral topological flow among the FQH photons. We then verify the unique features of FQH states in response to external fields, including the incompressibility of generating quasiparticles and the smoking-gun signature of fractional quantum Hall conductivity. Our work represents a significant advance in the bottom-up creation and manipulation of novel strongly correlated topological quantum matter composed of photons and opens up possibilities for fault-tolerant quantum information devices., Comment: 8 pages, 6 figures

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 0.986(16), and an overall system efficiency of 0.717(20), simultaneously. This source for the first time reaches the efficiency threshold for scalable photonic quantum computing. With this source, we further demonstrate 1.87(13) dB intensity squeezing, and consecutive 40-photon events with 1.67 mHz count rate.

The construction of a large-scale quantum internet requires quantum repeaters containing multiple entangled photon sources with identical wavelengths. Semiconductor quantum dots can generate entangled photon pairs deterministically with high fidelity. However, realizing wavelength-matched quantum-dot entangled photon sources faces two difficulties: the non-uniformity of emission wavelength and exciton fine-structure splitting induced fidelity reduction. Typically, these two factors are not independently tunable, making it challenging to achieve simultaneous improvement. In this work, we demonstrate wavelength-tunable entangled photon sources based on droplet-etched GaAs quantum dots through the combined use of AC and quantum-confined Stark effects. The emission wavelength can be tuned by ~1 meV while preserving an entanglement fidelity f exceeding 0.955(1) in the entire tuning range. Based on this hybrid tuning scheme, we finally demonstrate multiple wavelength-matched entangled photon sources with f>0.919(3), paving a way towards robust and scalable on-demand entangled photon sources for quantum internet and integrated quantum optical circuits., Comment: Main text: 11 pages, 6 figures, Supplementary information: 7 pages, 6 figures, 2 tables

Quantum non-Gaussianity, a more potent and highly useful form of nonclassicality, excludes all convex mixtures of Gaussian states and Gaussian parametric processes generating them. Here, for the first time, we conclusively test quantum non-Gaussian coincidences of entangled photon pairs with the CHSH-Bell factor $S=2.328\pm0.004$ from a single quantum dot with a depth up to $0.94\pm 0.02$ dB. Such deterministically generated photon pairs fundamentally overcome parametric processes by reducing crucial multiphoton errors. For the quantum non-Gaussian depth of the unheralded (heralded) single-photon state, we achieve the value of $8.08\pm0.05$ dB ($19.06\pm0.29$ dB). Our work experimentally certifies the exclusive quantum non-Gaussianity properties highly relevant for optical sensing, communication and computation.

In the quest to build general-purpose photonic quantum computers, fusion-based quantum computation has risen to prominence as a promising strategy. This model allows a ballistic construction of large cluster states which are universal for quantum computation, in a scalable and loss-tolerant way without feed-forward, by fusing many small n-photon entangled resource states. However, a key obstacle to this architecture lies in efficiently generating the required essential resource states on photonic chips. One such critical seed state that has not yet been achieved is the heralded three-photon Greenberger-Horne-Zeilinger (3-GHZ) state. Here, we address this elementary resource gap, by reporting the first experimental realization of a heralded dual-rail encoded 3-GHZ state. Our implementation employs a low-loss and fully programmable photonic chip that manipulates six indistinguishable single photons of wavelengths in the telecommunication regime. Conditional on the heralding detection, we obtain the desired 3-GHZ state with a fidelity 0.573+-0.024. Our work marks an important step for the future fault-tolerant photonic quantum computing, leading to the acceleration of building a large-scale optical quantum computer., Comment: Submitted. Comments are welcome!

Fault-tolerant quantum computing based on surface code has emerged as an attractive candidate for practical large-scale quantum computers to achieve robust noise resistance. To achieve universality, magic states preparation is a commonly approach for introducing non-Clifford gates. Here, we present a hardware-efficient and scalable protocol for arbitrary logical state preparation for the rotated surface code, and further experimentally implement it on the \textit{Zuchongzhi} 2.1 superconducting quantum processor. An average of \hhl{$0.8983 \pm 0.0002$} logical fidelity at different logical states with distance-three is achieved, \hhl{taking into account both state preparation and measurement errors.} In particular, \hhl{the magic states $|A^{\pi/4}\rangle_L$, $|H\rangle_L$, and $|T\rangle_L$ are prepared non-destructively with logical fidelities of $0.8771 \pm 0.0009 $, $0.9090 \pm 0.0009 $, and $0.8890 \pm 0.0010$, respectively, which are higher than the state distillation protocol threshold, 0.859 (for H-type magic state) and 0.827 (for T -type magic state).} Our work provides a viable and efficient avenue for generating high-fidelity raw logical magic states, which is essential for realizing non-Clifford logical gates in the surface code., Comment: In this version, we do not employ readout error mitigation strategies (in the previous version, we use readout transition matrix to mitigate the measurement error) to remove measurement errors because we believe it provides a more predictive assessment of the actual fidelity when generating and consuming magic states for a non-Clifford gate, as consuming the state involves measurement

Semiconductor quantum dots, as promising solid-state platform, have exhibited deterministic photon pair generation with high polarization entanglement f\textcompwordmark idelity for quantum information applications. However, due to temporal correlation from inherently cascaded emission, photon indistinguishability is limited, which restricts their potential scalability to multi-photon experiments. Here, by utilizing quantum interferences to decouple polarization entanglement from temporal correlation, we improve multi-photon entanglement f\textcompwordmark idelity from $(58.7\pm 2.2)\%$ to $(75.5\pm 2.0)\%$. Our work paves the way to realize scalable and high-quality multi-photon states from quantum dots.

Quantum computational chemistry has emerged as an important application of quantum computing. Hybrid quantum-classical computing methods, such as variational quantum eigensolvers (VQE), have been designed as promising solutions to quantum chemistry problems, yet challenges due to theoretical complexity and experimental imperfections hinder progress in achieving reliable and accurate results. Experimental works for solving electronic structures are consequently still restricted to nonscalable (hardware efficient) or classically simulable (Hartree-Fock) ansatz, or limited to a few qubits with large errors. The experimental realisation of scalable and high-precision quantum chemistry simulation remains elusive. Here, we address the critical challenges {associated with} solving molecular electronic structures using noisy quantum processors. Our protocol presents significant improvements in the circuit depth and running time, key metrics for chemistry simulation. Through systematic hardware enhancements and the integration of error mitigation techniques, we push forward the limit of experimental quantum computational chemistry and successfully scale up the implementation of VQE with an optimised unitary coupled-cluster ansatz to 12 qubits. We produce high-precision results of the ground-state energy for molecules with error suppression by around two orders of magnitude. We achieve chemical accuracy for H$_2$ at all bond distances and LiH at small bond distances in the experiment, even beyond the two recent concurrent works. Our work demonstrates a feasible path towards a scalable solution to electronic structure calculation, validating the key technological features and identifying future challenges for this goal., Comment: 11 pages, 4 figures in the main text, and 29 pages supplementary materials with 17 figures

Classifying many-body quantum states with distinct properties and phases of matter is one of the most fundamental tasks in quantum many-body physics. However, due to the exponential complexity that emerges from the enormous numbers of interacting particles, classifying large-scale quantum states has been extremely challenging for classical approaches. Here, we propose a new approach called quantum neuronal sensing. Utilizing a 61 qubit superconducting quantum processor, we show that our scheme can efficiently classify two different types of many-body phenomena: namely the ergodic and localized phases of matter. Our quantum neuronal sensing process allows us to extract the necessary information coming from the statistical characteristics of the eigenspectrum to distinguish these phases of matter by measuring only one qubit. Our work demonstrates the feasibility and scalability of quantum neuronal sensing for near-term quantum processors and opens new avenues for exploring quantum many-body phenomena in larger-scale systems., Comment: 7 pages, 3 figures in the main text, and 13 pages, 13 figures, and 1 table in supplementary materials

Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum (NISQ) devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum error correction code for two-dimensional grid architecture. So far, the repeated error correction capability of the surface code has not been realized experimentally. Here, we experimentally implement an error-correcting surface code, the distance-3 surface code which consists of 17 qubits, on the \textit{Zuchongzhi} 2.1 superconducting quantum processor. By executing several consecutive error correction cycles, the logical error can be significantly reduced after applying corrections, achieving the repeated error correction of surface code for the first time. This experiment represents a fully functional instance of an error-correcting surface code, providing a key step on the path towards scalable fault-tolerant quantum computing.

To ensure a long-term quantum computational advantage, the quantum hardware should be upgraded to withstand the competition of continuously improved classical algorithms and hardwares. Here, we demonstrate a superconducting quantum computing systems \textit{Zuchongzhi} 2.1, which has 66 qubits in a two-dimensional array in a tunable coupler architecture. The readout fidelity of \textit{Zuchongzhi} 2.1 is considerably improved to an average of 97.74\%. The more powerful quantum processor enables us to achieve larger-scale random quantum circuit sampling, with a system scale of up to 60 qubits and 24 cycles. The achieved sampling task is about 6 orders of magnitude more difficult than that of Sycamore [Nature \textbf{574}, 505 (2019)] in the classic simulation, and 3 orders of magnitude more difficult than the sampling task on \textit{Zuchongzhi} 2.0 [arXiv:2106.14734 (2021)]. The time consumption of classically simulating random circuit sampling experiment using state-of-the-art classical algorithm and supercomputer is extended to tens of thousands of years (about $4.8\times 10^4$ years), while \textit{Zuchongzhi} 2.1 only takes about 4.2 hours, thereby significantly enhancing the quantum computational advantage.

In the quest to realize a scalable quantum network, semiconductor quantum dots (QDs) offer distinct advantages including high single-photon efficiency and indistinguishability, high repetition rate (tens of GHz with Purcell enhancement), interconnectivity with spin qubits, and a scalable on-chip platform. However, in the past two decades, the visibility of quantum interference between independent QDs rarely went beyond the classical limit of 50$\%$ and the distances were limited from a few meters to kilometers. Here, we report quantum interference between two single photons from independent QDs separated by 302 km optical fiber. The single photons are generated from resonantly driven single QDs deterministically coupled to microcavities. Quantum frequency conversions are used to eliminate the QD inhomogeneity and shift the emission wavelength to the telecommunication band. The observed interference visibility is 0.67$\pm$0.02 (0.93$\pm$0.04) without (with) temporal filtering. Feasible improvements can further extend the distance to 600 km. Our work represents a key step to long-distance solid-state quantum networks., Comment: 14 pages, 5 figures

Scaling up to a large number of qubits with high-precision control is essential in the demonstrations of quantum computational advantage to exponentially outpace the classical hardware and algorithmic improvements. Here, we develop a two-dimensional programmable superconducting quantum processor, \textit{Zuchongzhi}, which is composed of 66 functional qubits in a tunable coupling architecture. To characterize the performance of the whole system, we perform random quantum circuits sampling for benchmarking, up to a system size of 56 qubits and 20 cycles. The computational cost of the classical simulation of this task is estimated to be 2-3 orders of magnitude higher than the previous work on 53-qubit Sycamore processor [Nature \textbf{574}, 505 (2019)]. We estimate that the sampling task finished by \textit{Zuchongzhi} in about 1.2 hours will take the most powerful supercomputer at least 8 years. Our work establishes an unambiguous quantum computational advantage that is infeasible for classical computation in a reasonable amount of time. The high-precision and programmable quantum computing platform opens a new door to explore novel many-body phenomena and implement complex quantum algorithms.

Quantum walks are the quantum mechanical analogue of classical random walks and an extremely powerful tool in quantum simulations, quantum search algorithms, and even for universal quantum computing. In our work, we have designed and fabricated an 8x8 two-dimensional square superconducting qubit array composed of 62 functional qubits. We used this device to demonstrate high fidelity single and two particle quantum walks. Furthermore, with the high programmability of the quantum processor, we implemented a Mach-Zehnder interferometer where the quantum walker coherently traverses in two paths before interfering and exiting. By tuning the disorders on the evolution paths, we observed interference fringes with single and double walkers. Our work is an essential milestone in the field, brings future larger scale quantum applications closer to realization on these noisy intermediate-scale quantum processors., Comment: 13 pages, 4 figures, and supplementary materials with 21 pages, 13 figures and 1 table

Heralded entangling quantum gates are an essential element for the implementation of large-scale optical quantum computation. Yet, the experimental demonstration of genuine heralded entangling gates with free-flying output photons in linear optical system, was hindered by the intrinsically probabilistic source and double-pair emission in parametric down-conversion. Here, by using an on-demand single-photon source based on a semiconductor quantum dot embedded in a micro-pillar cavity, we demonstrate a heralded controlled-NOT (CNOT) operation between two single photons for the first time. To characterize the performance of the CNOT gate, we estimate its average quantum gate fidelity of ($87.8\pm1.2$)%. As an application, we generated event-ready Bell states with a fidelity of ($83.4\pm2.4$)%. Our results are an important step towards the development of photon-photon quantum logic gates., Comment: main text: 5 pages, 3 figures; supplement: 18 pages, 2 figure, 2 tables; comments are welcome!