Heralded Three-Photon Entanglement from a Single-Photon Source on a Photonic Chip

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 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 Letter marks an important step for the future fault-tolerant photonic quantum computing, leading to the acceleration of building a large-scale optical quantum computer.

Gaussian Boson Sampling with Pseudo-Photon-Number-Resolving Detectors and Quantum Computational Advantage

We report new Gaussian boson sampling experiments with pseudo-photon-number-resolving detection, which register up to 255 photon-click events. We consider partial photon distinguishability and develop a more complete model for the characterization of the noisy Gaussian boson sampling. In the quantum computational advantage regime, we use Bayesian tests and correlation function analysis to validate the samples against all current classical spoofing mockups. Estimating with the best classical algorithms to date, generating a single ideal sample from the same distribution on the supercomputer Frontier would take ∼600  yr using exact methods, whereas our quantum computer, Jiǔzhāng 3.0, takes only 1.27  μs to produce a sample. Generating the hardest sample from the experiment using an exact algorithm would take Frontier∼3.1×10^{10}  yr.

Berry Curvature and Bulk-Boundary Correspondence from Transport Measurement for Photonic Chern Bands

Berry curvature is a fundamental element to characterize topological quantum physics, while a full measurement of Berry curvature in momentum space was not reported for topological states. Here we achieve two-dimensional Berry curvature reconstruction in a photonic quantum anomalous Hall system via Hall transport measurement of a momentum-resolved wave packet. Integrating measured Berry curvature over the two-dimensional Brillouin zone, we obtain Chern numbers corresponding to -1 and 0. Further, we identify bulk-boundary correspondence by measuring topology-linked chiral edge states at the boundary. The full topological characterization of photonic Chern bands from Berry curvature, Chern number, and edge transport measurements enables our photonic system to serve as a versatile platform for further in-depth study of novel topological physics.

Quantum computer-aided design for advanced superconducting qubit: Plasmonium

Complex quantum electronic circuits can be used to design noise-protected qubits, but their complexity may exceed the capabilities of classical simulation. In such cases, quantum computers are necessary for efficient simulation. In this work, we demonstrate the use of variational quantum computing on a transmon-based quantum processor to simulate a superconducting quantum electronic circuit and design a new type of qubit called "Plasmonium", which operates in the plasmon-transition regime. The fabricated Plasmonium qubits show a high two-qubit gate fidelity of 99.58(3)%, as well as a smaller physical size and larger anharmonicity compared to transmon qubits. These properties make Plasmonium a promising candidate for scaling up multi-qubit devices. Our results demonstrate the potential of using quantum computers to aid in the design of advanced quantum processors.

Schrödinger-Heisenberg Variational Quantum Algorithms

Recent breakthroughs have opened the possibility of intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics. However, the high accuracy needed to surpass classical computers poses a critical demand on the circuit depth, which is severely limited by the non-negligible gate infidelity, currently around 0.1%-1%. The limited circuit depth places restrictions on the performance of variational quantum algorithms (VQA) and prevents VQAs from exploring desired nontrivial quantum states. To resolve this problem, we propose a paradigm of Schrödinger-Heisenberg variational quantum algorithms (SHVQA). Using SHVQA, the expectation values of operators on states that require very deep circuits to prepare can now be efficiently measured by rather shallow circuits. The idea is to incorporate a virtual Heisenberg circuit, which acts effectively on the measurement observables, into a real shallow Schrödinger circuit, which is implemented realistically on the quantum hardware. We choose a Clifford virtual circuit, whose effect on the Hamiltonian can be seen as efficient classical processing. Yet, it greatly enlarges the state's expressivity, realizing much larger unitary t designs. Our method enables accurate quantum simulation and computation that otherwise are only achievable with much deeper circuits or more accurate operations conventionally. This has been verified in our numerical experiments for a better approximation of random states, higher-fidelity solutions to the XXZ model, and the electronic structure Hamiltonians of small molecules. Thus, together with effective quantum error mitigation, our work paves the way for realizing accurate quantum computing algorithms with near-term quantum devices.

[Effect of sugammadex on postoperative nausea and vomiting after surgery for intracranial aneurysm]

Objective: To investigate the effect of sugammadex on postoperative nausea and vomiting(PONV) after intracranial aneurysm surgery. Methods: Data from intracranial aneurysms patients who met the inclusion and exclusion criteria and underwent interventional surgery in the Department of Neurosurgery, Peking University International Hospital from January 2020 to March 2021 were prospectively included. According to the random number table method, the patients were divided by 1∶1 into the neostigmine+atropine group (group N) and the sugammadex group (group S). Use an acceleration muscle relaxation monitor for muscle relaxation monitoring, and administer neostigmine+atropine and sugammadex to block residual muscle relaxation drugs after surgery. The incidence rates of PONV and severity, the appearance of anesthesia, and the correlation between PONV and postoperative complications were recorded in both groups during five periods after surgery: 0-0.5 hours (T1),>0.5-2.0 hours(T2),>2.0-6.0 hours (T3),>6.0-12.0 hours (T4) and >12.0-24.0 hours (T5). Group comparisons of quantitative data were performed by the independent sample t-test, and categorical data was performed by the χ2 or rank sum test. Results: A total of 66 patients were included in the study, including 37 males and 29 female, aged (59.3±15.4) years (range: 18 to 77 years). The incidence rates of PONV of 33 patients in group S at different time periods of T1, T2, T3, T4, and T5 after surgery were respectively 27.3%(9/33),30.3%(10/33),12.1%(4/33),3.0%(1/33),0(0/33),and the incidence rates of PONV of 33 patients in the group N at different time periods of T1, T2, T3, T4 and T5 after surgery were respectively 36.4%(12/33),36.4%(12/33),33.3%(11/33),6.1%(2/33) and 0(0/33).The incidence of PONV was lower in the group S only in the T3 period after reversal than in the group N (χ2=4.227, P=0.040).However, there was no statistically significant difference in the incidence of PONV between the two groups of patients in other periods (all P>0.05). The recovery time for spontaneous breathing in patients in group S was (7.7±1.4) minutes, the extubation time was (12.4±5.3) minutes, and the safe exit time for anesthesia recovery was (12.3±3.4) minutes; the N groups were (13.9±2.0) minutes, (18.2±6.0) minutes, and (18.6±5.2) minutes, respectively; three time periods in group S were shorter than those in group N, and the differences were statistically significant (all P<0.05). The results regarding the occurrence of complications in patients with different levels of PONV at different time intervals after surgery in the two groups were as follows: in the T3 time period of group N, a significant difference was observed only in the occurrence of postoperative complications among patients with different levels of PONV (χ2=24.786, P<0.01). However, in the T4 time period, significant differences were found in the occurrence of postoperative complications among both the same level and different level PONV patients (χ2=15.435, 15.435, both P<0.01). Significant differences were also observed in the occurrence of postoperative complications among the same level and different level PONV patients in both the T3 and T4 time periods of group S (all P<0.01). Conclusion: Sugammadex can be used to reverse muscle relaxation in patients undergoing intracranial aneurysm intervention surgery,and it does not have a significant impact on the incidence of PONV, it can also optimize the quality of anesthesia recovery and reduce the incidence of complications after intracranial aneurysm embolization surgery.

Generation of genuine entanglement up to 51 superconducting qubits

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 estimation⁹, 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 eigensolver¹⁰ 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.

Comprehensive measurement of the near-infrared refractive index of GaAs at cryogenic temperatures

The refractive index is a critical parameter in optical and photonic device design. However, due to the lack of available data, precise designs of devices working in low temperatures are still frequently limited. In this work, we have built a homemade spectroscopic ellipsometer (SE) and measured the refractive index of GaAs at a matrix of temperatures (4 K < T < 295 K) and photon wavelengths (700 nm < λ < 1000 nm) with a system error of ∼0.04. We verified the credibility of the SE results by comparing them with afore-reported data at room temperature and with higher precision values measured by vertical GaAs cavity at cryogenic temperatures. This work makes up for the lack of the near-infrared refractive index of GaAs at cryogenic temperatures and provides accurate reference data for semiconductor device design and fabrication.

Introduction to nanoscale quantum technologies

An introduction to the Nanoscale themed collection on emerging quantum technologies at the nanoscale, featuring high-quality research on quantum materials and devices for computing, sensing, imaging and communication.

Experimental Full Network Nonlocality with Independent Sources and Strict Locality Constraints

Nonlocality arising in networks composed of several independent sources gives rise to phenomena radically different from that in standard Bell scenarios. Over the years, the phenomenon of network nonlocality in the entanglement-swapping scenario has been well investigated and demonstrated. However, it is known that violations of the so-called bilocality inequality used in previous experimental demonstrations cannot be used to certify the nonclassicality of their sources. This has put forward a stronger concept for nonlocality in networks, called full network nonlocality. Here, we experimentally observe full network nonlocal correlations in a network where the source-independence, locality, and measurement-independence loopholes are closed. This is ensured by employing two independent sources, rapid setting generation, and spacelike separations of relevant events. Our experiment violates known inequalities characterizing nonfull network nonlocal correlations by over 5 standard deviations, certifying the absence of classical sources in the realization.

Solving Graph Problems Using Gaussian Boson Sampling

Gaussian boson sampling (GBS) is not only a feasible protocol for demonstrating quantum computational advantage, but also mathematically associated with certain graph-related and quantum chemistry problems. In particular, it is proposed that the generated samples from the GBS could be harnessed to enhance the classical stochastic algorithms in searching some graph features. Here, we use Jiǔzhāng, a noisy intermediate-scale quantum computer, to solve graph problems. The samples are generated from a 144-mode fully connected photonic processor, with photon click up to 80 in the quantum computational advantage regime. We investigate the open question of whether the GBS enhancement over the classical stochastic algorithms persists-and how it scales-with an increasing system size on noisy quantum devices in the computationally interesting regime. We experimentally observe the presence of GBS enhancement with a large photon-click number and a robustness of the enhancement under certain noise. Our work is a step toward testing real-world problems using the existing noisy intermediate-scale quantum computers and hopes to stimulate the development of more efficient classical and quantum-inspired algorithms.

Quantum neuronal sensing of quantum many-body states on a 61-qubit programmable superconducting processor

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 and offers better phase resolution than conventional methods, such as measuring the imbalance. 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.

Eliminating temporal correlation in quantum-dot entangled photon source by quantum interference

Semiconductor quantum dots, as promising solid-state platform, have exhibited deterministic photon pair generation with high polarization entanglement fidelity 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 four-photon Greenberger-Horne-Zeilinger (GHZ) state entanglement fidelity from (58.7±2.2)% to (75.5±2.0)%. Our work paves the way to realize scalable and high-quality multi-photon states from quantum dots.

Unconditional and Robust Quantum Metrological Advantage beyond N00N States

Quantum metrology employs quantum resources to enhance the measurement sensitivity beyond that can be achieved classically. While multiphoton entangled N00N states can in principle beat the shot-noise limit and reach the Heisenberg limit, high N00N states are difficult to prepare and fragile to photon loss which hinders them from reaching unconditional quantum metrological advantages. Here, we combine the idea of unconventional nonlinear interferometers and stimulated emission of squeezed light, previously developed for the photonic quantum computer Jiuzhang, to propose and realize a new scheme that achieves a scalable, unconditional, and robust quantum metrological advantage. We observe a 5.8(1)-fold enhancement above the shot-noise limit in the Fisher information extracted per photon, without discounting for photon loss and imperfections, which outperforms ideal 5-N00N states. The Heisenberg-limited scaling, the robustness to external photon loss, and the ease-of-use of our method make it applicable in practical quantum metrology at a low photon flux regime.

[Construction and analysis of functional network of hemi-brain in patients with brain tumors before and after anesthesia based on resting-state functional magnetic resonance imaging]

Objective: To construct and analyze the functional network changes of hemi-brain in patients with brain tumor before and after anesthesia by using resting state functional magnetic resonance imaging (rs-fMRI). Methods: A total of 18 right-handed patients were prospectively included (6 males and 12 females). The patients underwent glioma resection in Peking University International Hospital from December 2018 to December 2021, and age ranged from 20 to 65 (45.1±13.6) years, with American Society of Anesthesiologists (ASA) grade of Ⅰ-Ⅱ. MRI scans were performed while the patient was awake and at the depth of surgical anesthesia. The functional network of healthy lateral brain was constructed and analyzed by means of graph theory, and its global and local topological properties were calculated. Global topology attributes included global efficiency (Eg), local efficiency (Eloc), clustering parameters (Cp), length parameter of shortest path (Lp), and small world (SW). Topology attributes of nodes included node degree (ND), node efficiency (NE) and between centrality (BC). The global and nodal topological properties of the hemi-brain network were compared between patients with different hemispherical space occupying under wakefulness and anesthesia. Results: At the awake state, Eloc and Cp in the global topological attributes of hemi-brain network were 0.259±0.007 and 0.197±0.010, respectively, and decreased to 0.242±0.013 and 0.177±0.021, respectively after anesthesia, with statistically significant differences (all P<0.01). The topological attributes of the nodes in hemi-side brain showed that ND, NE and BC were increased in the default mode network-related brain regions, while NE and BC were decreased in the limbic system and subcortical structures. Eloc and Cp were 0.258±0.008 and 0.198±0.008 respectively in the patients with left hemisphere space occupying, and decreased to 0.241±0.011 and 0.177±0.015 respectively after anesthesia, with statistically significant differences (all P<0.01). However, only Eloc decreased in patients with right hemisphere space occupying after anesthesia, and Eloc was 0.260±0.006 and 0.243±0.016 respectively when awake and after anesthesia, with statistically significant differences (P<0.05). The topological attributes of nodes in patients with space occupying in different cerebral hemispheres showed bidirectional changes after anesthesia, and patients with space occupying in the left cerebral hemisphere were more likely to be widely affected after anesthesia. The effects of anesthetic drugs may show hemispheric laterality. If the tumor was in the dominant hemisphere, the compensatory function of the dominant side was more likely to be damaged. Conclusions: During anesthesia-induced loss of consciousness in patients with brain tumors, both the ability to integrate information and the functional connections between local regions are weakened, and some brain regions have functional connection reorganization. The changes of brain network after anesthesia are bidirectional regulation.

Free-space dissemination of time and frequency with 10-19 instability over 113 km

Networks of optical clocks find applications in precise navigation^1,2, in efforts to redefine the fundamental unit of the 'second'^3-6 and in gravitational tests⁷. As the frequency instability for state-of-the-art optical clocks has reached the 10^-19 level^8,9, the vision of a global-scale optical network that achieves comparable performances requires the dissemination of time and frequency over a long-distance free-space link with a similar instability of 10^-19. However, previous attempts at free-space dissemination of time and frequency at high precision did not extend beyond dozens of kilometres^10,11. Here we report time-frequency dissemination with an offset of 6.3 × 10^-20 ± 3.4 × 10^-19 and an instability of less than 4 × 10^-19 at 10,000 s through a free-space link of 113 km. Key technologies essential to this achievement include the deployment of high-power frequency combs, high-stability and high-efficiency optical transceiver systems and efficient linear optical sampling. We observe that the stability we have reached is retained for channel losses up to 89 dB. The technique we report can not only be directly used in ground-based applications, but could also lay the groundwork for future satellite time-frequency dissemination.

Experimental Refutation of Real-Valued Quantum Mechanics under Strict Locality Conditions

Quantum mechanics is commonly formulated in a complex, rather than real, Hilbert space. However, whether quantum theory really needs the participation of complex numbers has been debated ever since its birth. Recently, a Bell-like test in an entanglement-swapping scenario has been proposed to distinguish standard quantum mechanics from its real-valued analog. Previous experiments have conceptually demonstrated, yet not satisfied, the central requirement of independent state preparation and measurements and leave several loopholes. Here, we implement such a Bell-like test with two separated independent sources delivering entangled photons to three separated parties under strict locality conditions that are enforced by spacelike separation of the relevant events, rapid random setting generation, and fast measurement. With the fair-sampling assumption and closed loopholes of independent source, locality, and measurement independence simultaneously, we violate the constraints of real-valued quantum mechanics by 5.30 standard deviations. Our results disprove the real-valued quantum theory to describe nature and ensure the indispensable role of complex numbers in quantum mechanics.

Experimental Demonstration of Genuine Tripartite Nonlocality under Strict Locality Conditions

Nonlocality captures one of the counterintuitive features of nature that defies classical intuition. Recent investigations reveal that our physical world's nonlocality is at least tripartite; i.e., genuinely tripartite nonlocal correlations in nature cannot be reproduced by any causal theory involving bipartite nonclassical resources and unlimited shared randomness. Here, by allowing the fair sampling assumption and postselection, we experimentally demonstrate such genuine tripartite nonlocality in a network under strict locality constraints that are ensured by spacelike separating all relevant events and employing fast quantum random number generators and high-speed polarization measurements. In particular, for a photonic quantum triangular network we observe a locality-loophole-free violation of the Bell-type inequality by 7.57 standard deviations for a postselected tripartite Greenberger-Horne-Zeilinger state of fidelity (93.13±0.24)%, which convincingly disproves the possibility of simulating genuine tripartite nonlocality by bipartite nonlocal resources with globally shared randomness.

Topological Spin Texture of Chiral Edge States in Photonic Two-Dimensional Quantum Walks

Topological insulators host topology-linked boundary states, whose spin and charge degrees of freedom could be exploited to design topological devices with enhanced functionality. We experimentally observe that dissipationless chiral edge states in a spin-orbit coupled anomalous Floquet topological phase exhibit topological spin texture on boundaries, realized via a two-dimensional quantum walk. Our experiment shows that, for a walker traveling around a closed loop along the boundary in real space, its spin evolves and winds through a great circle on the Bloch sphere, which implies that edge-spin texture has nontrivial winding. This topological spin winding is protected by a chiral-like symmetry emerging for the low-energy Hamiltonian. Our experiment confirms that two-dimensional anomalous Floquet topological systems exhibit topological spin texture on the boundary, which could inspire novel topology-based spintronic phenomena and devices.

Realization of an Error-Correcting Surface Code with Superconducting Qubits

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.

Closing the Locality and Detection Loopholes in Multiparticle Entanglement Self-Testing

First proposed by Mayers and Yao, self-testing provides a certification method to infer the underlying physics of quantum experiments in a black-box scenario. Numerous demonstrations have been reported to self-test various types of entangled states. However, all the multiparticle self-testing experiments reported so far suffer from both detection and locality loopholes. Here, we report the first experimental realization of multiparticle entanglement self-testing closing the locality loophole in a photonic system, and the detection loophole in a superconducting system, respectively. We certify three-party and four-party GHZ states with at least 0.84(1) and 0.86(3) fidelities in a device-independent way. These results can be viewed as a meaningful advance in multiparticle loophole-free self-testing, and also significant progress on the foundations of quantum entanglement certification.

Quantum State Transfer over 1200 km Assisted by Prior Distributed Entanglement

Long-distance quantum state transfer (QST), which can be achieved with the help of quantum teleportation, is a core element of important quantum protocols. A typical situation for QST based on teleportation is one in which two remote communication partners (Alice and Bob) are far from the entanglement source (Charlie). Because of the atmospheric turbulence, it is challenging to implement the Bell-state measurement after photons propagate in atmospheric channels. In previous long-distance free-space experiments, Alice and Charlie always perform local Bell-state measurement before the entanglement distribution process is completed. Here, by developing a highly stable interferometer to project the photon into a hybrid path-polarization dimension and utilizing the satellite-borne entangled photon source, we demonstrate proof-of-principle QST at the distance of over 1200 km assisted by prior quantum entanglement shared between two distant ground stations with the satellite Micius. The average fidelity of transferred six distinct quantum states is 0.82±0.01, exceeding the classical limit of 2/3 on a single copy of a qubit.

Ruling Out Real-Valued Standard Formalism of Quantum Theory

Standard quantum theory was formulated with complex-valued Schrödinger equations, wave functions, operators, and Hilbert spaces. Previous work attempted to simulate quantum systems using only real numbers by exploiting an enlarged Hilbert space. A fundamental question arises: are the complex numbers really necessary in the standard formalism of quantum theory? To answer this question, a quantum game has been developed to distinguish standard quantum theory from its real-number analog, by revealing a contradiction between a high-fidelity multiqubit quantum experiment and players using only real-number quantum theory. Here, using superconducting qubits, we faithfully realize the quantum game based on deterministic entanglement swapping with a state-of-the-art fidelity of 0.952. Our experimental results violate the real-number bound of 7.66 by 43 standard deviations. Our results disprove the real-number formulation and establish the indispensable role of complex numbers in the standard quantum theory.

Robust Self-Testing of Multiparticle Entanglement

Quantum self-testing is a device-independent way to certify quantum states and measurements using only the input-output statistics, with minimal assumptions about the quantum devices. Because of the high demand on tolerable noise, however, experimental self-testing was limited to two-photon systems. Here, we demonstrate the first robust self-testing for multiphoton genuinely entangled quantum states. We prepare two examples of four-photon graph states, the Greenberger-Horne-Zeilinger states with a fidelity of 0.957(2) and the linear cluster states with a fidelity of 0.945(2). Based on the observed input-output statistics, we certify the genuine four-photon entanglement and further estimate their qualities with respect to realistic noise in a device-independent manner.

Strong Quantum Computational Advantage Using a Superconducting Quantum Processor

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.

Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light

We report phase-programmable Gaussian boson sampling (GBS) which produces up to 113 photon detection events out of a 144-mode photonic circuit. A new high-brightness and scalable quantum light source is developed, exploring the idea of stimulated emission of squeezed photons, which has simultaneously near-unity purity and efficiency. This GBS is programmable by tuning the phase of the input squeezed states. The obtained samples are efficiently validated by inferring from computationally friendly subsystems, which rules out hypotheses including distinguishable photons and thermal states. We show that our GBS experiment passes a nonclassicality test based on inequality constraints, and we reveal nontrivial genuine high-order correlations in the GBS samples, which are evidence of robustness against possible classical simulation schemes. This photonic quantum computer, Jiuzhang 2.0, yields a Hilbert space dimension up to ∼10^{43}, and a sampling rate ∼10^{24} faster than using brute-force simulation on classical supercomputers.

[Effectiveness and safety of ultrasound-guided microwave ablation for the treatment of primary hyperparathyroidism in 12 patients with parathyroid adenoma]

To investigate the effectiveness and safety of ultrasound-guided microwave ablation (MWA) in treatment of primary hyperparathyroidism (PHPT). A total of 12 PHPT patients with parathyroid adenoma were treated with MWA in Nanjing University of Chinese Medicine Affiliated Hospital of Integrated Traditional Chinese and Western Medicine from May 2019 to February 2021. The patients were followed up once every 3 months for 3-12 months. Levels of serum parathyroid hormone (PTH), calcium and phosphorus were detected before and 20 min, 4h and 1day after ablation, and during follow-up period. The volume and volume reduction rate of parathyroid lesion were compared before the treatment and at the end of follow-up. The technical and clinical success of MWA were assessed as well. At the end of follow-up, median serum PTH [66.60 (42.21,80.03) ng/L vs.169.90 (89.01,396.50) ng/L] and calcium [2.39 (2.32,2.49) mmol/L vs. 2.75 (2.57,2.96) mmol/L] levels in 12 patients decreased significantly (all P<0.05). A complete response in terms of PTH and calcium levels was achieved in 6 of the 12 patients, while 4 of the patients had slightly elevated PTH levels just above the upper limit of normal reference range, and 2 of the patients remained abnormal PTH and calcium levels. The clinical cure rate was 50%. The volumes of all lesion after ablation were significantly decreased (P<0.05), with the technical success rate reaching 92.3%. No serious complications were observed. Ultrasound-guided MWA, thus, is safe and effective in the treatment of PHPT.

Quantum teleportation of physical qubits into logical code spaces

Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that nontransverse operations, which are essential for universal quantum computation, lead to the spread of errors. Quantum gate teleportation has been proposed as an elegant solution for this. Here, one replaces these fragile, nontransverse inline gates with the generation of specific, highly entangled offline resource states that can be teleported into the circuit to implement the nontransverse gate. As the first important step, we create a maximally entangled state between a physical and an error-correctable logical qubit and use it as a teleportation resource. We then demonstrate the teleportation of quantum information encoded on the physical qubit into the error-corrected logical qubit with fidelities up to 0.786. Our scheme can be designed to be fully fault tolerant so that it can be used in future large-scale quantum technologies.

Directly Measuring a Multiparticle Quantum Wave Function via Quantum Teleportation

We propose a new method to directly measure a general multiparticle quantum wave function, a single matrix element in a multi-particle density matrix, by quantum teleportation. The density matrix element is embedded in a virtual logical qubit and is nondestructively teleported to a single physical qubit for readout. We experimentally implement this method to directly measure the wave function of a photonic mixed quantum state beyond a single photon using a single observable for the first time. Our method also provides an exponential advantage over the standard quantum state tomography in measurement complexity to fully characterize a sparse multiparticle quantum state.

[A dose-response meta-analysis on the relationship between daily tea intake and cardiovascular mortality based on the GRADE system]

Objective: To explore the relationship between daily tea intake and cardiovascular disease (CVD) mortality. Methods: PubMed, EMbase, The Cochrane, Chinese Biomedical Literature Database, CNKI, and Wanfang Database were searched to collect research on tea intake and CVD mortality. The search period was from the establishment of the database to June 2020. Two researchers independently screened and extracted literature. The risk of bias was evaluated in the included studies, a dose-response meta-analysis was conducted, sensitivity analysis and publication bias analysis of the research results, and quality evaluation of the included literature and GRADE classification of the evidence body were performed. Results: A total of 21 cohort or case-control studies were included, including 1 304 978 subjects. Among them, 38 222 deaths from CVD were reported. The quality scores of the included studies were all ≥ 6 points. The dose-response meta-analysis showed that for every additional cup of tea intake per day, the mortality rate of CVD decreased by about 3% (95%CI 0.95-0.98, P<0.05), and there was a non-linear dose-response relationship (P<0.05). Compared with people who do not drink tea, people who drink 1 to 8 cups of tea a day have 8% lower CVD mortality (RR=0.92, 95%CI 0.89-0.95), 13% (RR=0.87, 95 %CI 0.84-0.91), 15% (RR=0.85, 95%CI 0.82-0.89), 15% (RR=0.85, 95%CI 0.81-0.89), 16% (RR=0.84, 95%CI 0.80-0.89), 16% (RR=0.84, 95%CI 0.81-0.88), 16% (RR=0.84, 95%CI 0.81-0.87), 16% (RR=0.84, 95%CI 0.80-0.88), respectively. The results of traditional meta-analysis showed that compared with people who do not drink tea, people who drink more than 1 cup of tea a day are associated with 14% lower CVD mortality rate (RR=0.86, 95%CI 0.81-0.91, I²=73.2%, P<0.05). The results of subgroup analysis showed that compared with the corresponding people who did not drink tea, men who drank more than 1 cup of tea a day reduced the CVD mortality rate by 24%, women by 14%, European and American populations by 12%, and Asian populations by 15%. The population who consumed green tea decreased CVD mortality by 15%, and the population of non-smokers decreased CVD mortality by 20% (all P<0.05). The population who consumed black tea decreased CVD mortality by 8%, and the smoking population who consumed black tea decreased CVD mortality by 3%, and the difference was not statistically significant (all P>0.05). The results of the bias analysis showed that Begg=0.42 and Egger=0.62, indicating that the distribution on both sides of the funnel chart is symmetrical, suggesting that there is no publication bias. The results of sensitivity analysis showed that the effect size of the outcome index did not change significantly after excluding any article, indicating that the results are robust and credible. The GRADE evaluation showed that the evidence grades of the outcome indicators were all low grade. Conclusions: Daily tea consumption is related to reduced CVD mortality. It is therefore recommended to drink an appropriate amount of tea daily.

Quantum walks on a programmable two-dimensional 62-qubit superconducting processor

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.

Heralded Nondestructive Quantum Entangling Gate with Single-Photon Sources

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 micropillar 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±1.2)%. As an application, we generated event-ready Bell states with a fidelity of (83.4±2.4)%. Our results are an important step towards the development of photon-photon quantum logic gates.

Long-Distance Free-Space Measurement-Device-Independent Quantum Key Distribution

Measurement-device-independent quantum key distribution (MDI-QKD), based on two-photon interference, is immune to all attacks against the detection system and allows a QKD network with untrusted relays. Since the MDI-QKD protocol was proposed, fiber-based implementations aimed at longer distance, higher key rates, and network verification have been rapidly developed. However, owing to the effect of atmospheric turbulence, MDI-QKD over a free-space channel remains experimentally challenging. Herein, by developing a robust adaptive optics system, high-precision time synchronization and frequency locking between independent photon sources located far apart, we realized the first free-space MDI-QKD over a 19.2-km urban atmospheric channel, which well exceeds the effective atmospheric thickness. Our experiment takes the first step toward satellite-based MDI-QKD. Moreover, the technology developed herein opens the way to quantum experiments in free space involving long-distance interference of independent single photons.

Quantum computational advantage using photons

Quantum computers promise to perform certain tasks that are believed to be intractable to classical computers. Boson sampling is such a task and is considered a strong candidate to demonstrate the quantum computational advantage. We performed Gaussian boson sampling by sending 50 indistinguishable single-mode squeezed states into a 100-mode ultralow-loss interferometer with full connectivity and random matrix-the whole optical setup is phase-locked-and sampling the output using 100 high-efficiency single-photon detectors. The obtained samples were validated against plausible hypotheses exploiting thermal states, distinguishable photons, and uniform distribution. The photonic quantum computer, Jiuzhang, generates up to 76 output photon clicks, which yields an output state-space dimension of 10³⁰ and a sampling rate that is faster than using the state-of-the-art simulation strategy and supercomputers by a factor of ~10¹⁴.

Cloning of Quantum Entanglement

Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement-a highly nonclassical correlation-remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two-photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement.

Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum Coprocessor

Adiabatic quantum computing enables the preparation of many-body ground states. Realization poses major experimental challenges: Direct analog implementation requires complex Hamiltonian engineering, while the digitized version needs deep quantum gate circuits. To bypass these obstacles, we suggest an adiabatic variational hybrid algorithm, which employs short quantum circuits and provides a systematic quantum adiabatic optimization of the circuit parameters. The quantum adiabatic theorem promises not only the ground state but also that the excited eigenstates can be found. We report the first experimental demonstration that many-body eigenstates can be efficiently prepared by an adiabatic variational algorithm assisted with a multiqubit superconducting coprocessor. We track the real-time evolution of the ground and excited states of transverse-field Ising spins with a fidelity that can reach about 99%.

Observation of Intensity Squeezing in Resonance Fluorescence from a Solid-State Device

Intensity squeezing-i.e., photon number fluctuations below the shot-noise limit-is a fundamental aspect of quantum optics and has wide applications in quantum metrology. It was predicted in 1979 that intensity squeezing could be observed in resonance fluorescence from a two-level quantum system. However, its experimental observation in solid states was hindered by inefficiencies in generating, collecting, and detecting resonance fluorescence. Here, we report the intensity squeezing in a single-mode fiber-coupled resonance fluorescence single-photon source based on a quantum dot-micropillar system. We detect pulsed single-photon streams with 22.6% system efficiency, which show sub-shot-noise intensity fluctuation with an intensity squeezing of 0.59 dB. We estimate a corrected squeezing of 3.29 dB at the first lens. The observed intensity squeezing provides the last piece of the fundamental picture of resonance fluorescence, which can be used as a new standard for optical radiation and in scalable quantum metrology with indistinguishable single photons.

Proof-of-principle demonstration of compiled Shor's algorithm using a quantum dot single-photon source

We report a proof-of-principle demonstration of Shor's algorithm with photons generated by an on-demand semiconductor quantum dot single-photon source for the first time. A fully compiled version of Shor's algorithm for factoring 15 has been accomplished with a significantly reduced resource requirement that employs the four-photon cluster state. Genuine multiparticle entanglement properties are confirmed to reveal the quantum character of the algorithm and circuit. The implementation realizes the Shor's algorithm with deterministic photonic qubits, which opens new applications for cluster state beyond one-way quantum computing.

[Epidemiological characteristics of novel coronavirus pneumonia in Henan]

Objective: To study the epidemiological characteristics of COVID-19 in Henan Province. Methods: An epidemiological study was conducted based on the latest epidemic information of 1 265 confirmed cases (including regional distribution, severe illness, and deaths) announced by Health Commission of Henan Province, as well as the details of 1 079 COVID-19 officially released by Health Commission of municipalities in Henan Province collected as of 24: 00 on February 19, 2020. Results: Among 1 079 patients diagnosed with COVID-19, there were 573 male (53.2%) and 505 female (46.8%), with the ratio of male to female of 1.14∶1; The majority of patients were 36-59 years old (553 cases, 51.3%), and the mean age was 46 (interquartile range is 24) years old; 515 cases (47.7%) had a history of living, traveling, doing business in Wuhan or a brief stopover at Wuhan train stop, and 382 (35.4%) had a history of close contact with confirmed patients; There were 72 severe cases (5.7%) in 1 265 patients, and the fatality rate was 1.5%. A high number of cases were reported in Xinyang (269 cases, 21.26%), Zhengzhou (156 cases, 12.33%), Nanyang (155 cases, 12.25%), Zhumadian (139 cases, 10.99%), followed by Shangqiu (91 cases, 7.19%), Zhoukou (76 cases, 6.01%). Among 605 patients, the symptoms were fever (553 cases, 91.4%), debilitation (44 cases, 7.3%), cough (110 cases, 18.2%), expectoration (19 cases, 3.1%), chills (6 cases, 1.0%), shiver (7 cases, 1.2%), running nose (21 cases, 3.5%), stuffy noses (8 cases, 1.3%), throat dryness and sore (24 cases, 4.0%), headache (21 cases, 3.5%), chest pain (6 cases, 1.0%), anhelation (18 cases, 3.0%), and gastrointestinal symptom (21 cases, 3.5%). The age of deaths ranged from 33 to 86 years old, with an average age of 72 (interquartile range of 17) years old; there be 7 males (63.6%) and 4 females (36.4%). Conclusion: The cases in Henan Province were mainly imported cases and had certain geographical location relevance; meanwhile, there was a family-focused incidence. The overall trend of new cases was wave-like decline, and the number of deaths was high among elderly men with underlying diseases.

[Prediction of short-term prognosis of hepatocellular carcinoma after TACE surgery based on MRI texture analysis technology]

Objective: To explore the feasibility of short-term efficacy prognosis prediction model for HCC patients undergoing transcatheter arterial chemoembolization (TACE) based on MRI-based radiomics technique. Methods: A total of 123 patients with liver cancer who received TACE treatment in Lishui Central Hospital from June 2016 to July 2018 were retrospectively collected, including 90 males and 33 females, with an average age of 24-83 (58±10) years. All the patients were pathologically confirmed as hepatocellular carcinoma and underwent MRI scan before surgery.All patients were followed up 3-4 months after TACE, and further divided into training group (n=85, 42 of which were effective and 43 cases were ineffective) and the validation group (n=38, 19 of which were effective and 19 were ineffective) according to the modified response evaluation criteria in solid tumors (mRECIST). There was no statistical difference in the general information between the two groups of patients, which was comparable. Then, preoperative T(2)WI images were used for radiomics analysis, texture parameters were screened based on R language, and short-term efficacy prediction model of TACE for training group and verification group was constructed. Results: T(2)WI image analysis of each patient received 396 different texture parameters, and further used Lasso dimensionality reduction and 10 times cross-validation screening to obtain 5 characteristic texture parameters, specifically stdDeviation, ClusterProminence_angle135_offset4, Correlation_angle135_offset4, Inertia_angle135_offset4, InverseDifferenceMoment_angle45_offset4. According to the above five texture parameters and their corresponding coefficient values, the corresponding radiomics scores (Radscore) were calculated, and the prediction models of the training group and the verification group were further constructed.It was found that the area under the ROC curve of the training group was 0.812 (95%CI: 0.722-0.901), the sensitivity and specificity were 83.7% and 69.0%, respectively. The area under the ROC curve of the validation group was 0.801 (95%CI:0.654-0.947), and the sensitivity and specificity were 89.5% and 63.2%, respectively. Conclusion: The constructed TACE prediction model in the present study has high prediction accuracy, sensitivity and specificity.The short-term efficacy prognosis prediction model for HCC based on MRI is constructed, stable and reliable.

Quantum-Teleportation-Inspired Algorithm for Sampling Large Random Quantum Circuits

Quantum teleportation transfers and processes quantum information through quantum entanglement channels. It is one of the most versatile protocols in quantum information science and leads to many remarkable applications, particularly the one-way quantum computing. Here, we show, for the first time, that the concept of teleportation can also be used to facilitate an important classical computing task, sampling random quantum circuits, which is highly relevant to prove the near-term demonstration of quantum computational supremacy. In our method, the classical computation in the physical-qubit state space is converted to simulate teleportation in logical-qubit state space, resulting in a much smaller number of qubits involved in classical computing. We tested this new method on 1D and 2D lattices up to 1000 qubits. This Letter presents a new quantum-inspired classical computing technology and is helpful to design and optimize classically hard quantum sampling experiments.

Quantum Beat between Sunlight and Single Photons

We demonstrate fourth-order quantum beat between sunlight and single photons from a quantum dot. With a fast time-resolved detection system, we observed high-visibility quantum beat between the independent photons of different frequencies from the two astronomically separated light sources. The temporal dynamics of the beat oscillation indicate the coherent behavior of the interfering photons, and the raw visibility of two-photon interference shows violation of the classical limit with a frequency mismatch of three-times the line width.

Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a 10^{14}-Dimensional Hilbert Space

Quantum computing experiments are moving into a new realm of increasing size and complexity, with the short-term goal of demonstrating an advantage over classical computers. Boson sampling is a promising platform for such a goal; however, the number of detected single photons is up to five so far, limiting these small-scale implementations to a proof-of-principle stage. Here, we develop solid-state sources of highly efficient, pure, and indistinguishable single photons and 3D integration of ultralow-loss optical circuits. We perform experiments with 20 pure single photons fed into a 60-mode interferometer. In the output, we detect up to 14 photons and sample over Hilbert spaces with a size up to 3.7×10^{14}, over 10 orders of magnitude larger than all previous experiments, which for the first time enters into a genuine sampling regime where it becomes impossible to exhaust all possible output combinations. The results are validated against distinguishable samplers and uniform samplers with a confidence level of 99.9%.

Satellite testing of a gravitationally induced quantum decoherence model

Quantum mechanics and the general theory of relativity are two pillars of modern physics. However, a coherent unified framework of the two theories remains an open problem. Attempts to quantize general relativity have led to many rival models of quantum gravity, which, however, generally lack experimental foundations. We report a quantum optical experimental test of event formalism of quantum fields, a theory that attempts to present a coherent description of quantum fields in exotic spacetimes containing closed timelike curves and ordinary spacetime. We experimentally test a prediction of the theory with the quantum satellite Micius that a pair of time-energy-entangled particles probabilistically decorrelate passing through different regions of the gravitational potential of Earth. Our measurement results are consistent with the standard quantum theory and hence do not support the prediction of event formalism.

Quantum Interference between Light Sources Separated by 150 Million Kilometers

We report an experiment to test quantum interference, entanglement, and nonlocality using two dissimilar photon sources, the Sun and a semiconductor quantum dot on the Earth, which are separated by ∼150  million kilometers. By making the otherwise vastly distinct photons indistinguishable in all degrees of freedom, we observe time-resolved two-photon quantum interference with a raw visibility of 0.796(17), well above the 0.5 classical limit, providing unambiguous evidence of the quantum nature of thermal light. Further, using the photons with no common history, we demonstrate postselected two-photon entanglement with a state fidelity of 0.826(24) and a violation of Bell inequality by 2.20(6). The experiment can be further extended to a larger scale using photons from distant stars and open a new route to quantum optics experiments at an astronomical scale.

Quantum Teleportation in High Dimensions

Quantum teleportation allows a "disembodied" transmission of unknown quantum states between distant quantum systems. Yet, all teleportation experiments to date were limited to a two-dimensional subspace of quantized multiple levels of the quantum systems. Here, we propose a scheme for teleportation of arbitrarily high-dimensional photonic quantum states and demonstrate an example of teleporting a qutrit. Measurements over a complete set of 12 qutrit states in mutually unbiased bases yield a teleportation fidelity of 0.75(1), which is well above both the optimal single-copy qutrit state-estimation limit of 1/2 and maximal qubit-qutrit overlap of 2/3, thus confirming a genuine and nonclassical three-dimensional teleportation. Our work will enable advanced quantum technologies in high dimensions, since teleportation plays a central role in quantum repeaters and quantum networks.