In-orbit dark count rate performance and radiation damage high-temperature annealing of silicon avalanche photodiode single-photon detectors of the Micius satellite

Silicon avalanche photodiode (APD) single-photon detectors in space are continuously affected by radiation, which gradually degrades their dark count performance. From August 2016 to June 2023, we conducted approximately seven years (2507 days) of in-orbit monitoring of the dark count performance of APD single-photon detectors on the Micius Quantum Science Experimental Satellite. The results showed that due to radiation effects, the dark count growth rate was approximately 6.79 cps/day @ -24 °C and 0.37 cps/day @ -55 °C, with a significant suppression effect on radiation-induced dark counts at lower operating temperature. Based on the proposed radiation damage induced dark count annealing model, simulations were conducted for the in-orbit dark counts of the detector, the simulation results are consistent with in-orbit test data. In May 2022, four of these detectors underwent a cumulative 5.7 hours high-temperature annealing test at 76 °C, dark count rate shows no measurable changes, consistent with annealing model. As of now, these ten APD single-photon detectors on the Micius Quantum Science Experimental Satellite have been in operation for approximately 2507 days and are still functioning properly, providing valuable experience for the future long-term space applications of silicon APD single-photon detectors.

Time transfer over 113 km free space laser communication channel

The space time frequency transfer plays a crucial role in applications such as space optical clock networks, navigation, satellite ranging, and space quantum communication. Here, we propose a high-precision space time frequency transfer and time synchronization scheme based on a simple intensity modulation/direct detection (IM/DD) laser communication system, which occupies a communication bandwidth of approximately 0.2%. Furthermore, utilizing an optical-frequency comb time frequency transfer system as an out-of-loop reference, experimental verification was conducted on a 113 km horizontal atmospheric link, with a long-term stability approximately 8.3 × 10-16 over a duration of 7800 seconds. Over an 11-hour period, the peak-to-peak wander is approximately 100 ps. Our work establishes the foundation of the time frequency transfer, based on the space laser communication channel, for future ground-to-space and inter-satellite links.

Optical transmission of microwave control signal towards large-scale superconducting quantum computing

With the rapid development of superconducting quantum computing and the implementation of surface code, large-scale quantum computing is emerging as an urgent demand. In a superconducting computing system, the qubit is maintained in a cryogenic environment to avoid thermal excitation. Thus, the transmission of control signals, which are generated at room temperature, is needed. Typically, the transmission of these signals to the qubit relies on a coaxial cable wiring approach. However, in a large-scale computing system with hundreds or even thousands of qubits, the coaxial cables will pose great space and heat load to the dilution refrigerator. Here, to tackle this problem, we propose and demonstrate a direct-modulation-based optical transmission line. In our experiment, the average single-qubit XEB error and control error are measured as 0.139% and 0.014% separately, demonstrating the feasibility of the optical wiring approach and paving the way for large-scale superconducting quantum computing.

A 1.25-GHz multi-amplitude modulator driver in 0.18 μm SiGe BiCOMOS technology for high speed quantum key distribution

Quantum key distribution (QKD) research has yielded highly fruitful results and is currently undergoing an industrialization transformation. In QKD systems, electro-optic modulators are typically employed to prepare the required quantum states. While various QKD systems operating at GHz repetition frequency have demonstrated exceptional performance, they predominantly rely on instruments or printed circuit boards to fulfill the driving circuit function of the electro-optic modulator. Consequently, these systems tend to be complex with low integration levels. To address this challenge, we have introduced a modulator driver integrated circuit in 0.18 µm SiGe BiCMOS technology. The circuit can generate multiple-level driving signals with a clock frequency of 1.25 GHz and a rising edge of ∼50 ps. Each voltage amplitude can be independently adjusted, ensuring the precise preparation of quantum states. The measured signal-to-noise ratio was more than 17 dB, resulting in a low quantum bit error rate of 0.24% in our polarization-encoding system. This work will contribute to the advancement of QKD system integration and promote the industrialization process in this field.

A co-simulation of superconducting qubit and control electronics for quantum computing

As the number of qubits in quantum computing increases, the scalability of existing qubit circuit structures and control systems may become insufficient for large-scale expansion and high-fidelity control. To address this challenge, we propose a behavioral-level model of a superconducting qubit and its control electronics, followed by a co-simulation to evaluate their performance. In this paper, we present the modeling process, simulation procedure, and resulting design specifications for the qubit control system. Our co-simulation approach utilizes MATLAB and Simulink, enabling us to derive critical circuit design specifications, such as the required Digital-to-Analog Converter (DAC) resolution, which should be 8 bits or higher, to achieve high-fidelity control. By taking into account factors such as DAC sampling rates, integral and differential nonlinearities, and filter characteristics, we optimize the control system for efficient and accurate qubit manipulation. Our model and simulation approach offer a promising solution to the scalability challenges in quantum computing, providing valuable insights for the design of large-scale superconducting quantum computing systems.

Free-Space and Fiber-Integrated Measurement-Device-Independent Quantum Key Distribution under High Background Noise

Measurement-device-independent quantum key distribution (MDI QKD) provides immunity against all attacks targeting measurement devices. It is essential to implement MDI QKD in the future global-scale quantum communication network. Toward this goal, we demonstrate a robust MDI QKD fully covering daytime, overcoming the high background noise that prevents BB84 protocol even when using a perfect single-photon source. Based on this, we establish a hybrid quantum communication network that integrates free-space and fiber channels through Hong-Ou-Mandle (HOM) interference. Additionally, we investigate the feasibility of implementing HOM interference with moving satellites. Our results serve as a significant cornerstone for future integrated space-ground quantum communication networks that incorporate measurement-device-independent security.

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.

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.

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.

Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Qubits

Although near-term quantum computing devices are still limited by the quantity and quality of qubits in the so-called NISQ era, quantum computational advantage has been experimentally demonstrated. Moreover, hybrid architectures of quantum and classical computing have become the main paradigm for exhibiting NISQ applications, where low-depth quantum circuits are repeatedly applied. In order to further scale up the problem size solvable by the NISQ devices, it is also possible to reduce the number of physical qubits by "cutting" the quantum circuit into different pieces. In this work, we experimentally demonstrated a circuit-cutting method for simulating quantum circuits involving many logical qubits, using only a few physical superconducting qubits. By exploiting the symmetry of linear-cluster states, we can estimate the effectiveness of circuit-cutting for simulating up to 33-qubit linear-cluster states, using at most 4 physical qubits for each subcircuit. Specifically, for the 12-qubit linear-cluster state, we found that the experimental fidelity bound can reach as much as 0.734, which is about 19% higher than a direct implementation on the same 12-qubit superconducting processor. Our results indicate that circuit-cutting represents a feasible approach of simulating quantum circuits using much fewer qubits, while achieving a much higher circuit fidelity.

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.

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.

Observation of Thermalization and Information Scrambling in a Superconducting Quantum Processor

Understanding various phenomena in nonequilibrium dynamics of closed quantum many-body systems, such as quantum thermalization, information scrambling, and nonergodic dynamics, is crucial for modern physics. Using a ladder-type superconducting quantum processor, we perform analog quantum simulations of both the XX-ladder model and the one-dimensional XX model. By measuring the dynamics of local observables, entanglement entropy, and tripartite mutual information, we signal quantum thermalization and information scrambling in the XX ladder. In contrast, we show that the XX chain, as free fermions on a one-dimensional lattice, fails to thermalize to the Gibbs ensemble, and local information does not scramble in the integrable channel. Our experiments reveal ergodicity and scrambling in the controllable qubit ladder, and open the door to further investigations on the thermodynamics and chaos in quantum many-body systems.

Experimental demonstration of free-space two-photon interference

Quantum interference plays an essential role in understanding the concepts of quantum physics. Moreover, the interference of photons is indispensable for large-scale quantum information processing. With the development of quantum networks, interference of photons transmitted through long-distance fiber channels has been widely implemented. However, quantum interference of photons using free-space channels is still scarce, mainly due to atmospheric turbulence. Here, we report an experimental demonstration of Hong-Ou-Mandel interference with photons transmitted by free-space channels. Two typical photon sources, i.e., correlated photon pairs generated in spontaneous parametric down conversion (SPDC) process and weak coherent states, are employed. A visibility of 0.744 ± 0.013 is observed by interfering with two photons generated in the SPDC process, exceeding the classical limit of 0.5. Our results demonstrate that the quantum property of photons remains even after transmission through unstable free-space channels, indicating the feasibility and potential application of free-space-based quantum interference in quantum information processing.

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.

Experimental exploration of five-qubit quantum error-correcting code with superconducting qubits

Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal quantum error-correcting code, with the subsequent verification of all key features including the identification of an arbitrary physical error, the capability for transversal manipulation of the logical state and state decoding. To address this challenge, we experimentally realise the [5, 1, 3] code, the so-called smallest perfect code that permits corrections of generic single-qubit errors. In the experiment, having optimised the encoding circuit, we employ an array of superconducting qubits to realise the [5, 1, 3] code for several typical logical states including the magic state, an indispensable resource for realising non-Clifford gates. The encoded states are prepared with an average fidelity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$57.1(3)\%$\end{document} while with a high fidelity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$98.6(1)\%$\end{document} in the code space. Then, the arbitrary single-qubit errors introduced manually are identified by measuring the stabilisers. We further implement logical Pauli operations with a fidelity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$97.2(2)\%$\end{document} within the code space. Finally, we realise the decoding circuit and recover the input state with an overall fidelity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$74.5(6)\%$\end{document}, in total with 92 gates. Our work demonstrates each key aspect of the [5, 1, 3] code and verifies the viability of experimental realisation of quantum error-correcting codes with superconducting qubits.

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.

Synchronization using quantum photons for satellite-to-ground quantum key distribution

Time synchronization is crucial for quantum key distribution (QKD) systems. In order to compensate for the time drift caused by the Doppler effect and adapt to the unstable optical link in satellite-to-ground QKD, previous demonstrations generally adopted synchronization methods requiring additional hardware. In this paper, we present a novel synchronization method based on the detected quantum photons, thus simplifying additional hardware and reducing the complexity and cost. This method adopts target frequency scanning to realize fast frequency recovery, utilizes polynomial fitting to compensate for the Doppler effect, and takes use of the vacuum state in the decoy-state BB84 protocol to recover the time offset. This method can avoid the influence of synchronization light jitter, thus improving the synchronization precision and the secure keys as well. Successful satellite-to-ground QKD based on this new synchronization scheme has been conducted to demonstrate its feasibility and performance. The presented scheme provides an effective synchronization solution for quantum communication applications.

Observation of Strong and Weak Thermalization in a Superconducting Quantum Processor

We experimentally study the ergodic dynamics of a 1D array of 12 superconducting qubits with a transverse field, and identify the regimes of strong and weak thermalization with different initial states. We observe convergence of the local observable to its thermal expectation value in the strong-thermalizaion regime. For weak thermalization, the dynamics of local observable exhibits an oscillation around the thermal value, which can only be attained by the time average. We also demonstrate that the entanglement entropy and concurrence can characterize the regimes of strong and weak thermalization. Our work provides an essential step toward a generic understanding of thermalization in quantum systems.

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.

Emulating Quantum Teleportation of a Majorana Zero Mode Qubit

Topological quantum computation based on anyons is a promising approach to achieve fault-tolerant quantum computing. The Majorana zero modes in the Kitaev chain are an example of non-Abelian anyons where braiding operations can be used to perform quantum gates. Here we perform a quantum simulation of topological quantum computing, by teleporting a qubit encoded in the Majorana zero modes of a Kitaev chain. The quantum simulation is performed by mapping the Kitaev chain to its equivalent spin version and realizing the ground states in a superconducting quantum processor. The teleportation transfers the quantum state encoded in the spin-mapped version of the Majorana zero mode states between two Kitaev chains. The teleportation circuit is realized using only braiding operations and can be achieved despite being restricted to Clifford gates for the Ising anyons. The Majorana encoding is a quantum error detecting code for phase-flip errors, which is used to improve the average fidelity of the teleportation for six distinct states from 70.76±0.35% to 84.60±0.11%, well beyond the classical bound in either case.

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.

Single-mode fiber coupling with a M-SPGD algorithm for long-range quantum communications

Satellite-based quantum communication is a promising approach for realizing global-scale quantum networks. For free-space quantum channel, single-mode fiber coupling is particularly important for improving the signal-to-noise ratio of daylight quantum key distribution (QKD) and compatibility with standard fiber-based QKD. However, achieving a highly efficient and stable single-mode coupling efficiency under strong atmospheric turbulence remains experimentally challenging. Here, we develop a single-mode receiver with an adaptive optics (AO) system based on a modal version of the stochastic parallel gradient descent (M-SPGD) algorithm and test its performance over an 8 km urban terrestrial free-space channel. Under strong atmospheric turbulence, the M-SPGD AO system obtains an improvement of about 3.7 dB in the single-mode fiber coupling efficiency and a significant suppression of fluctuation, which can find its applications in free-space long-range quantum communications.

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%.

Ergodic-Localized Junctions in a Periodically Driven Spin Chain

We report the analog simulation of an ergodic-localized junction by using an array of 12 coupled superconducting qubits. To perform the simulation, we fabricated a superconducting quantum processor that is divided into two domains: one is a driven domain representing an ergodic system, while the second is localized under the effect of disorder. Because of the overlap between localized and delocalized states, for a small disorder there is a proximity effect and localization is destroyed. To experimentally investigate this, we prepare a microwave excitation in the driven domain and explore how deep it can penetrate the disordered region by probing its dynamics. Furthermore, we perform an ensemble average over 50 realizations of disorder, which clearly shows the proximity effect. Our work opens a new avenue to build quantum simulators of driven-disordered systems with applications in condensed matter physics and material science.

A 5 GHz and 7.5 V multi-amplitude modulator driving circuit for practical high-speed quantum key distribution

Quantum key distribution (QKD) offers the ability of information theoretic security key exchange. The secure key rate is an important indicator for the practical QKD systems, which determines what kinds of applications can be supported. One most effective way to enhance the secure key rate is to increase the system repetition frequency. Here, we report an implementation of a high-speed DC-coupled modulator driving circuit with a repetition rate of up to 5 GHz. The circuit outputs a multi-amplitude return-to-zero pattern pulse with a maximum amplitude of 7.5 V. The design adapts to the various electro-optic modulators widely employed in QKD systems. The minimum pulse width is measured as 75 ps, with the relative noise level less than 1.5% for all the output amplitudes under random modulation.

Polarization design for ground-to-satellite quantum entanglement distribution

High-fidelity transmission of polarization encoded qubits plays a key role in long distance quantum communication. By establishing the channel between ground and satellite, the communication distance can even exceed thousands of kilometers. Aimed to achieve the efficient uplink quantum communication, here we describe a high-fidelity polarization design of a transmitting antenna with an average polarization extinction ratio of 887:1 by a local test. We also implement a feasible polarization-compensation scheme for satellite motions with a fidelity exceeding 0.995 ± 0.001. Based on these works, we demonstrate the ground-to-satellite entanglment distribution with a violation of Bell inequality by 2.312±0.096, which is well above the classic limit 2.

Spaceborne, low-noise, single-photon detection for satellite-based quantum communications

Single-photon detectors (SPDs) play important roles in highly sensitive detection applications, such as fluorescence spectroscopy, remote sensing and ranging, deep space optical communications, elementary particle detection, and quantum communications. However, the adverse conditions in space, such as the increased radiation flux and thermal vacuum, severely limit their noise performances, reliability, and lifetime. Herein, we present the example of spaceborne, low-noise, high reliability SPDs, based on commercial off-the-shelf (COTS) silicon avalanche photodiodes (APD). Based on the high noise-radiation sensitivity of silicon APD, we have developed special shielding structures, multistage cooling technologies, and configurable driver electronics that significantly improved the COTS APD reliability and mitigated the SPD noise-radiation sensitivity. This led to a reduction of the expected in-orbit radiation-induced dark count rate (DCR) increment rate from ∼219 counts per second (cps) per day to ∼0.76 cps/day. During a continuous period of continuous operations in orbit which spanned of 1029 days, the SPD DCR was maintained below 1000 cps, i.e., the actual in-orbit radiation-induced DCR increment rate was ∼0.54 cps/day, i.e., two orders of magnitude lower than those evoked by previous technologies, while its photon detection efficiency was > 45%. Our spaceborne, low-noise SPDs established a feasible satellite-based up-link quantum communication that was validated on the quantum experiment science satellite platform. Moreover, our SPDs open new windows of opportunities for space research and applications in deep-space optical communications, single-photon laser ranging, as well as for testing the fundamental principles of physics in space.

High-speed robust polarization modulation for quantum key distribution

Polarization modulation plays a key role in polarization-encoding quantum key distribution (QKD). Here, we report a new, to the best of our knowledge, polarization modulation scheme based on an inherently stable Sagnac interferometer. The presented scheme is free of polarization mode dispersion and calibration as well as insensitive to environmental influences. Successful experiments at a repetition frequency of 1.25 GHz have been conducted to demonstrate the feasibility and stability of the scheme. The measured average quantum bit-error rate of the four polarization states is as low as 0.27% for 80 consecutive minutes without any adjustment. This high-speed intrinsically stable polarization modulation can be widely applied to many polarization-encoding QKD systems, such as BB84, MDI, etc.

11-watt single-frequency 1342-nm laser based on multi-segmented Nd:YVO4 crystal

High power continuous-wave (CW) single-frequency 1342 nm lasers are of interest for fundamental research, particularly, for laser cooling of lithium atoms. Using the popular Nd:YVO₄ laser crystal requires careful heat management, because strong thermal effects in the gain medium are the most severe limitations of output power. Here, we present a multi-segmented Nd:YVO₄ crystal design that consists of three segments with successive doping concentrations, optimized using a theoretical model. In order to quantify the optimization, we measured the thermal lens power of conventional crystal designs and compare them to our multi-segmented design. The optimized design displays a two times lower thermal lens dioptric power for the same amount of absorbed pump power in the non-lasing case. Using the optimized design, we demonstrate a high power all-solid-state laser emitting 10.0 W single-frequency radiation at 1342 nm when operating the laser crystal at room temperature. Further integration of the laser allows us to operate the laser crystal below room temperature for improving output power up to 11.4 W at 8°C. This is explained by the reduction of energy-transfer upconversion and excited-state absorption effects. Stable free-running operation at the low temperature of 8 °C is achieved with the power stability of ± 0.42 % by peak-to-peak fluctuation and frequency peak-to-peak fluctuation of ± 72 MHz in three hours.

[Preliminary application value of ultrasound contrast agent with enteral nutritional suspension as mixed medium in locating indwelling nasointestinal tube in critically ill patients]

Objective: To evaluate the value of ultrasound contrast agent with enteral nutrition suspension as mixed medium in locating indwelling nasointestinal tube in critically ill patients. Methods: Total of 45 critically ill patients had nasointestinal tube indwelled were collected from June 1,2018 to April 1,2019 in the Intensive Care Unit of Zhejiang Provincial People's Hospital, including 30 males and 15 females, with an average age of (63±17) years.Enteral nutritional suspension Peptisorb Liquid was used as research medium,with the ultrasonic imaging performance of it confirmed by in vitro and in vivo experiments.The optimal mixing ratio of microbubble ultrasound contrast agent and Peptisorb Liquid was confirmed by in vitro experiment, then the mixture was quietly placed and its stability was dynamically observed. The nasointestinal tube was confirmed in the digestive tract by conventional ultrasound and then the ultrasound contrast mode turned on. Ultrasound contrast agent with Peptisorb Liquid as mixed medium was injected into the nasointestinal tube and the tube direction and end position were observed and recorded in real time. Abdominal X-ray examination or CT was used as the gold standard for verifying the location of the nasointestinal tube and the same result represented successful positioning. Results: The in vitro and in vivo experiments showed that Peptisorb Liquid had good ultrasound imaging uniformity and penetrating power, which could clearly show the range and boundary of the filling intestine cavity; the in vitro experiment showed that the ultrasound contrast agent prepared with the microbubble ultrasound contrast agent and Peptisorb Liquid by the ratio of 1∶1 000 and 1∶500 which had the best imaging effect and the best distribution uniformity, with the best stability within 10 minutes after quietly placed. Nasointestinal tubes were successfully located by using ultrasound contrast agent with enteral nutritional suspension as mixed medium in 95.6%(43/45) of the patients collected in this study,including success at one attempt in 39 cases, the operating time was (1.6±0.5) minutes and 4 cases were successfully located after multiple operations with (5.1±0.5) minutes, the tube bent in the stomach in one case and flexed back into the stomach from the descending duodenum in another. The operation failed in 2 cases (4.4%). No significant complications occurred during the examination. Conclusion: The ultrasound contrast agent with enteral nutritional suspension as mixed medium has the advantages of both, which can conveniently, safely and effectively locate the direction and end position of nasointestinal tube in critically ill patients.

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.

Propagation and Localization of Collective Excitations on a 24-Qubit Superconducting Processor

Superconducting circuits have emerged as a powerful platform of quantum simulation, especially for emulating the dynamics of quantum many-body systems, because of their tunable interaction, long coherence time, and high-precision control. Here in experiments, we construct a Bose-Hubbard ladder with a ladder array of 20 qubits on a 24-qubit superconducting processor. We investigate theoretically and demonstrate experimentally the dynamics of single- and double-excitation states with distinct behaviors, indicating the uniqueness of the Bose-Hubbard ladder. We observe the linear propagation of photons in the single-excitation case, satisfying the Lieb-Robinson bounds. The double-excitation state, initially placed at the edge, localizes; while placed in the bulk, it splits into two single-excitation modes spreading linearly toward two boundaries, respectively. Remarkably, these phenomena, studied both theoretically and numerically as unique properties of the Bose-Hubbard ladder, are represented coherently by pairs of controllable qubits in experiments. Our results show that collective excitations, as a single mode, are not free. This work paves the way to simulation of exotic logic particles by subtly encoding physical qubits and exploration of rich physics by superconducting circuits.

Strongly correlated quantum walks with a 12-qubit superconducting processor

Quantum walks are the quantum analogs of classical random walks, which allow for the simulation of large-scale quantum many-body systems and the realization of universal quantum computation without time-dependent control. We experimentally demonstrate quantum walks of one and two strongly correlated microwave photons in a one-dimensional array of 12 superconducting qubits with short-range interactions. First, in one-photon quantum walks, we observed the propagation of the density and correlation of the quasiparticle excitation of the superconducting qubit and quantum entanglement between qubit pairs. Second, when implementing two-photon quantum walks by exciting two superconducting qubits, we observed the fermionization of strongly interacting photons from the measured time-dependent long-range anticorrelations, representing the antibunching of photons with attractive interactions. The demonstration of quantum walks on a quantum processor, using superconducting qubits as artificial atoms and tomographic readout, paves the way to quantum simulation of many-body phenomena and universal quantum computation.

Optically injected intensity-stable pulse source for secure quantum key distribution

The security of decoy-state quantum key distribution (QKD) highly depends on the accurate control of multiple intensity states. Although several theoretical studies on the QKD with loosely controlled source intensities have been proposed, there is still a large gap between the experimental realization and the theoretical analysis. In this paper, we adopt the gain-switching method to generate short optical pulses, and the corresponding intensity stabilities are quantitatively measured. The method via optical injection is proposed to make effective reductions of the intensity fluctuations from 6.47%∼1.59% to 1.95%∼1.15% at different optical powers. QKD performance adopting the experimental results is also analyzed and discussed. For a typical 40 dB high-attenuation QKD system, the relative increase on the secure key rates reaches 51.89% for the corresponding intensity fluctuations of 1.15% with optical injection and 1.59% without optical injection. The presented intensity-stable optical pulse source can find wide applications in different QKD protocols, such as BB84, DPS, COW, etc.

Time-tagged coincidence counting unit for large-scale photonic quantum computing

Real-time analysis of single-photon coincidence is critical in photonic quantum computing. The large channel number and high counting rate foreseen in such experiments pose a big challenge for the conventional time tagged method and coincidence instruments. Here we propose a real-time time-tagged coincidence method and a data filtering solution, demonstrated by a 32-channel coincidence counting unit that has been implemented successfully on a field-programmable gate array system. The unit provides high counting rates, a tunable coincidence window, and a timing resolution of 390 ps. Beyond that, it is feasible to be scaled up to 104 channels and is thus ideally suited for channel consuming applications such as boson sampling. Based on the versatility and scalability the unit has shown, we believe that it is the turn-key solution for many single-photon coincidence counting applications in photonic quantum computing.

Large scale quantum key distribution: challenges and solutions [Invited]

Quantum key distribution (QKD) together with one time pad encoding can provide information-theoretical security for communication. Currently, though QKD has been widely deployed in many metropolitan fiber networks, its implementation in a large scale remains experimentally challenging. This letter provides a brief review on the experimental efforts towards the goal of global QKD, including the security of practical QKD with imperfect devices, QKD metropolitan and backbone networks over optical fiber and satellite-based QKD over free space.

Test of Local Realism into the Past without Detection and Locality Loopholes

Inspired by the recent remarkable progress in the experimental test of local realism, we report here such a test that achieves an efficiency greater than (78%)^{2} for entangled photon pairs separated by 183 m. Further utilizing the randomness in cosmic photons from pairs of stars on the opposite sides of the sky for the measurement setting choices, we not only close the locality and detection loopholes simultaneously, but also test the null hypothesis against local hidden variable mechanisms for events that took place 11 years ago (13 orders of magnitude longer than previous experiments). After considering the bias in measurement setting choices, we obtain an upper bound on the p value of 7.87×10^{-4}, which clearly indicates the rejection with high confidence of potential local hidden variable models. One may further push the time constraint on local hidden variable mechanisms deep into the cosmic history by taking advantage of the randomness in photon emissions from quasars with large aperture telescopes.

Free-space quantum key distribution in urban daylight with the SPGD algorithm control of a deformable mirror

Free-space quantum key distribution (QKD) is important to realize a global-scale quantum communication network. However, performing QKD in daylight against the strong background light noise is a major challenge. Here, we develop the stochastic parallel gradient descent (SPGD) algorithm with a deformable mirror to improve the signal-to-noise ratio (SNR). We then experimentally demonstrate free-space QKD in the presence of urban daylight. The final secure key rate of the QKD is 98∼419 bps throughout the majority of the daylight hours.

Point-ahead demonstration of a transmitting antenna for satellite quantum communication

A low-divergence beam is an essential prerequisite for a high-efficiency long-distance optical link, particularly for satellite-based quantum communication. A point-ahead angle, caused by satellite motion, is always several times larger than the divergence angle of the signal beam. We design a novel transmitting antenna with a point-ahead function, and provide an easy-to-perform calibration method with an accuracy better than 0.2 μrad. Subsequently, our antenna establishes an uplink to the quantum satellite, Micius, with a link loss of 41-52 dB over a distance of 500-1,400 km. The results clearly confirm the validity of our model, and provide the ability to conduct quantum communications. Our approach can be adopted in various free space optical communication systems between moving platforms.

High-power 671 nm laser by second-harmonic generation with 93% efficiency in an external ring cavity

Second-harmonic generation (SHG) is useful for obtaining single-frequency continuous-wave laser sources at various wavelengths for applications ranging from biology to fundamental physics. Using an external power-enhancement cavity is an effective approach to improve the frequency conversion efficiency. However, thermal effects limit the efficiency, particularly, in high-power operation. Therefore, reducing thermal effects is important when designing a cavity. This Letter reports the use of an external ring cavity for SHG, yielding a 5.2 W, 671 nm laser light with a conversion efficiency of 93.8±0.8% which, to the best of our knowledge, is a new record of conversion efficiency for an external ring cavity. It is achieved using a 10 mm length periodically poled potassium titanyl phosphate crystal and a 65 μm radius beam waist in the cavity so as to minimize thermal dephasing and thermal lensing. Furthermore, a method is developed to determine a conversion efficiency more accurately based on measuring the pump depletion using a photodiode detector and a maximum pump depletion up to 97% is recorded. In this method, the uncertainty is much less than that achieved in a common method by direct measuring with a power meter.

Bell Test over Extremely High-Loss Channels: Towards Distributing Entangled Photon Pairs between Earth and the Moon

Quantum entanglement was termed "spooky action at a distance" in the well-known paper by Einstein, Podolsky, and Rosen. Entanglement is expected to be distributed over longer and longer distances in both practical applications and fundamental research into the principles of nature. Here, we present a proposal for distributing entangled photon pairs between Earth and the Moon using a Lagrangian point at a distance of 1.28 light seconds. One of the most fascinating features in this long-distance distribution of entanglement is as follows. One can perform the Bell test with human supplying the random measurement settings and recording the results while still maintaining spacelike intervals. To realize a proof-of-principle experiment, we develop an entangled photon source with 1 GHz generation rate, about 2 orders of magnitude higher than previous results. Violation of Bell's inequality was observed under a total simulated loss of 103 dB with measurement settings chosen by two experimenters. This demonstrates the feasibility of such long-distance Bell test over extremely high-loss channels, paving the way for one of the ultimate tests of the foundations of quantum mechanics.

[Multi-variated analysis of differential diagnosis in ultrasonography of idiopathic granulomatous mastitis and invasive ductal carcinoma]

Objective: To evaluate the differential diagnosis of idiopathic granulomatous mastitis (IGM) and invasive ductal carcinoma. Methods: The ultrasonographic data of 37 IGM patients and 50 cases of IDC were analyzed retrospectively. The shape, growth direction, margin, internal echo, posterior echo, calcification, Adler blood flow classification, PSV(peak sestolic velocity), RI (resistance index)and elasticity scores were analyzed by χ(2) test and independent sample t test. The optimal cutoff values of age, PSV and RI were calculated by receiver operating characteristic (ROC) curve. Logistic regression analysis was used to calculate the odds ratio (OR) of ultrasonic variates in the diagnosis of both diseases. Results: There were no significant differences in the shape, margin, internal echo and blood flow grading between the two groups. The age, lesion growth direction, posterior echo, calcification, PSV, RI and elasticity were statistically different. The cut-of value of Age, PSV and RI were 38.5 years old, 13.20 cm/s, and 0.655. Logistic regression multi-variated analysis revealed that elastic score (OR=9.806) had the best value of the differential diagnosis, as well as calcification (OR=6.937), posterior echo decay (OR=4.613), RI (OR=3.257), lesion growth orientation (OR=3.198), and PSV (OR=1.202). Lesion shape, margin, internal echo, and Adler blood flow classification did not help in differential diagnosis. Conclusion: Ultrasound multi-parameter analysis has high value in IGM and IDC differential diagnosis.

Satellite-based entanglement distribution over 1200 kilometers

Long-distance entanglement distribution is essential for both foundational tests of quantum physics and scalable quantum networks. Owing to channel loss, however, the previously achieved distance was limited to ~100 kilometers. Here we demonstrate satellite-based distribution of entangled photon pairs to two locations separated by 1203 kilometers on Earth, through two satellite-to-ground downlinks with a summed length varying from 1600 to 2400 kilometers. We observed a survival of two-photon entanglement and a violation of Bell inequality by 2.37 ± 0.09 under strict Einstein locality conditions. The obtained effective link efficiency is orders of magnitude higher than that of the direct bidirectional transmission of the two photons through telecommunication fibers.

Satellite-Relayed Intercontinental Quantum Network

We perform decoy-state quantum key distribution between a low-Earth-orbit satellite and multiple ground stations located in Xinglong, Nanshan, and Graz, which establish satellite-to-ground secure keys with ∼kHz rate per passage of the satellite Micius over a ground station. The satellite thus establishes a secure key between itself and, say, Xinglong, and another key between itself and, say, Graz. Then, upon request from the ground command, Micius acts as a trusted relay. It performs bitwise exclusive or operations between the two keys and relays the result to one of the ground stations. That way, a secret key is created between China and Europe at locations separated by 7600 km on Earth. These keys are then used for intercontinental quantum-secured communication. This was, on the one hand, the transmission of images in a one-time pad configuration from China to Austria as well as from Austria to China. Also, a video conference was performed between the Austrian Academy of Sciences and the Chinese Academy of Sciences, which also included a 280 km optical ground connection between Xinglong and Beijing. Our work clearly confirms the Micius satellite as a robust platform for quantum key distribution with different ground stations on Earth, and points towards an efficient solution for an ultralong-distance global quantum network.

High-Speed Device-Independent Quantum Random Number Generation without a Detection Loophole

Quantum mechanics provides the means of generating genuine randomness that is impossible with deterministic classical processes. Remarkably, the unpredictability of randomness can be certified in a manner that is independent of implementation devices. Here, we present an experimental study of device-independent quantum random number generation based on a detection-loophole-free Bell test with entangled photons. In the randomness analysis, without the independent identical distribution assumption, we consider the worst case scenario that the adversary launches the most powerful attacks against the quantum adversary. After considering statistical fluctuations and applying an 80  Gb×45.6  Mb Toeplitz matrix hashing, we achieve a final random bit rate of 114  bits/s, with a failure probability less than 10^{-5}. This marks a critical step towards realistic applications in cryptography and fundamental physics tests.

Satellite-to-Ground Entanglement-Based Quantum Key Distribution

We report on entanglement-based quantum key distribution between a low-Earth-orbit satellite equipped with a space borne entangled-photon source and a ground observatory. One of the entangled photons is measured locally at the satellite, and the other one is sent via a down link to the receiver in the Delingha ground station. The link attenuation is measured to vary from 29 dB at 530 km to 36 dB at 1000 km. We observe that the two-photon entanglement survives after being distributed between the satellite and the ground, with a measured state fidelity of ≥0.86. We then perform the entanglement-based quantum key distribution protocol and obtain an average final key rate of 3.5  bits/s at the distance range of 530-1000 km.