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.

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.

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.

Entering the era of post-quantum supremacy has given one the ability to precisely control noisy intermediatescale quantum (NISQ) processors with multiqubits and extract valuable quantum many-body correlation resources for many distinct quantum applications. We here construct quantum many-body thermalized states on a 62-qubit superconducting quantum processor and use them to demonstrate the principle of Maxwell's demon. We further demonstrate the direct effect caused by Maxwell's demon on the charging process of a quantum battery (QB). We depicted the nonequilibrium transportation in our QB through measuring the dynamics of the Shannon entropy to explore its working conditions. Finally, we evaluate the information-to-work conversion by varying the readout fidelity to verify the validity of the Sagawa-Ueda equality within the NISQ processor environment and evaluate the qubit-environment interaction such as the measurement backaction. Our experiment suggests that the superconducting NISQ processor with appropriate error mitigation methods will be an ideal platform for studying quantum information thermodynamics through quantum many-body simulations.

Quantum computational chemistry has emerged as a potential application of quantum computing. Hybrid quantum-classical computing methods, such as variational quantum eigensolvers, have been designed as promising solutions to quantum chemistry problems. Nonetheless, 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 non-scalable or classically simulable ansatz or limited to a few qubits with large errors. Here, we address the critical challenges associated with solving molecular electronic structures using noisy quantum processors. Our protocol presents 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 overcome theoretical and experimental limitations and successfully scale up the implementation of variational quantum eigensolvers with an optimized 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. Our work demonstrates a feasible path towards a scalable solution to electronic structure calculation. The application of quantum computing to computational chemistry faces various experimental and theoretical challenges. Now, a quantum simulation on a noisy quantum device has achieved chemical accuracy for small H2 and LiH molecules.

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.

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.

Scalable generation of genuine multipartite entanglement with an increasing number of qubits is important for both fundamental interest and practical use in quantum-information technologies 1 , 2 . On the one hand, multipartite entanglement shows a strong contradiction between the prediction of quantum mechanics and local realization and can be used for the study of quantum-to-classical transition 3 , 4 . On the other hand, realizing large-scale entanglement is a benchmark for the quality and controllability of the quantum system and is essential for realizing universal quantum computing 5 – 8 . However, scalable generation of genuine multipartite entanglement on a state-of-the-art quantum device can be challenging, requiring accurate quantum gates and efficient verification protocols. Here we show a scalable approach for preparing and verifying intermediate-scale genuine entanglement on a 66-qubit superconducting quantum processor. We used high-fidelity parallel quantum gates and optimized the fidelitites of parallel single- and two-qubit gates to be 99.91% and 99.05%, respectively. With efficient randomized fidelity estimation 9 , we realized 51-qubit one-dimensional and 30-qubit two-dimensional cluster states and achieved fidelities of 0.637 ± 0.030 and 0.671 ± 0.006, respectively. On the basis of high-fidelity cluster states, we further show a proof-of-principle realization of measurement-based variational quantum eigensolver 10 for perturbed planar codes. Our work provides a feasible approach for preparing and verifying entanglement with a few hundred qubits, enabling medium-scale quantum computing with superconducting quantum systems.

Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum 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-three surface code which consists of 17 qubits, on the 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.

Youwei Zhao,1, 2, 3, ∗ Yangsen Ye,1, 2, 3, ∗ He-Liang Huang,1, 2, 3, ∗ Yiming Zhang,1, 2, 3 Dachao Wu,1, 2, 3 Huijie Guan,1, 2, 3 Qingling Zhu,1, 2, 3 Zuolin Wei,1, 2, 3 Tan He,1, 2, 3 Sirui Cao,1, 2, 3 Fusheng Chen,1, 2, 3 Tung-Hsun Chung,1, 2, 3 Hui Deng,1, 2, 3 Daojin Fan,1, 2, 3 Ming Gong,1, 2, 3 Cheng Guo,1, 2, 3 Shaojun Guo,1, 2, 3 Lianchen Han,1, 2, 3 Na Li,1, 2, 3 Shaowei Li,1, 2, 3 Yuan Li,1, 2, 3 Futian Liang,1, 2, 3 Jin Lin,1, 2, 3 Haoran Qian,1, 2, 3 Hao Rong,1, 2, 3 Hong Su,1, 2, 3 Lihua Sun,1, 2, 3 Shiyu Wang,1, 2, 3 Yulin Wu,1, 2, 3 Yu Xu,1, 2, 3 Chong Ying,1, 2, 3 Jiale Yu,1, 2, 3 Chen Zha,1, 2, 3 Kaili Zhang,1, 2, 3 Yong-Heng Huo,1, 2, 3 Chao-Yang Lu,1, 2, 3 Cheng-Zhi Peng,1, 2, 3 Xiaobo Zhu,1, 2, 3 and Jian-Wei Pan1, 2, 3 Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China Shanghai Research Center for Quantum Sciences, Shanghai 201315, China

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 Zuchongzhi 2.1, which has 66 qubits in a two-dimensional array in a tunable coupler architecture. The readout fidelity of 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, and fidelity of FXEB=(3.66±0.345)×10-4. The achieved sampling task is about 6 orders of magnitude more difficult than that of Sycamore [Nature 574, 505 (2019)] in the classic simulation, and 3 orders of magnitude more difficult than the sampling task on 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 4.8×104 years), while Zuchongzhi 2.1 only takes about 4.2 h, thereby significantly enhancing the quantum computational advantage.

Quantum walks are the quantum mechanical analog 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 8-by-8 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 a milestone in the field, bringing future larger-scale quantum applications closer to realization for noisy intermediate-scale quantum processors.

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, 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 574, 505 (2019)NATUAS0028-083610.1038/s41586-019-1666-5. We estimate that the sampling task finished by Zuchongzhi in about 1.2 h will take the most powerful supercomputer at least 8 yr. 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.