Quafu-Qcover:Explore combinatorial optimization problems on cloud-based quantum computers

We introduce Quafu-Qcover,an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends.Quafu-Qcover provides a standardized and comprehensive workflow that utilizes the quantum approximate optimization algorithm(QAOA).It facilitates the automatic conversion of the original problem into a quadratic unconstrained binary optimization(QUBO)model and its corresponding Ising model,which can be subsequently transformed into a weight graph.The core of Qcover relies on a graph decomposition-based classical algorithm,which efficiently derives the optimal parameters for the shallow QAOA circuit.Quafu-Qcover incorporates a dedicated compiler capable of translating QAOA circuits into physical quantum circuits that can be executed on Quafu cloud quantum computers.Compared to a general-purpose compiler,our compiler demonstrates the ability to generate shorter circuit depths,while also exhibiting superior speed performance.Additionally,the Qcover compiler has the capability to dynamically create a library of qubits coupling substructures in real-time,utilizing the most recent calibration data from the superconducting quantum devices.This ensures that computational tasks can be assigned to connected physical qubits with the highest fidelity.The Quafu-Qcover allows us to retrieve quantum computing sampling results using a task ID at any time,enabling asynchronous processing.Moreover,it incorporates modules for results preprocessing and visualization,facilitating an intuitive display of solutions for combinatorial optimization problems.We hope that Quafu-Qcover can serve as an instructive illustration for how to explore application problems on the Quafu cloud quantum computers.

Quafu-RL:The cloud quantum computers based quantum reinforcement learning

With the rapid advancement of quantum computing,hybrid quantum–classical machine learning has shown numerous potential applications at the current stage,with expectations of being achievable in the noisy intermediate-scale quantum(NISQ)era.Quantum reinforcement learning,as an indispensable study,has recently demonstrated its ability to solve standard benchmark environments with formally provable theoretical advantages over classical counterparts.However,despite the progress of quantum processors and the emergence of quantum computing clouds,implementing quantum reinforcement learning algorithms utilizing parameterized quantum circuits(PQCs)on NISQ devices remains infrequent.In this work,we take the first step towards executing benchmark quantum reinforcement problems on real devices equipped with at most 136 qubits on the BAQIS Quafu quantum computing cloud.The experimental results demonstrate that the policy agents can successfully accomplish objectives under modified conditions in both the training and inference phases.Moreover,we design hardware-efficient PQC architectures in the quantum model using a multi-objective evolutionary algorithm and develop a learning algorithm that is adaptable to quantum devices.We hope that the Quafu-RL can be a guiding example to show how to realize machine learning tasks by taking advantage of quantum computers on the quantum cloud platform.

超导量子干涉仪及其在低场核磁共振及成像中的应用

超导量子干涉仪利用约瑟夫森结宏观量子干涉效应,是一种具有超高灵敏度的磁通探测器件。对超导量子干涉仪的基本原理及其在低场核磁共振/成像技术中的应用进行了简要介绍,并报道了在这方面的主要研究成果。搭建了一套低场核磁共振及成像系统并获得具有较高信噪比的水样品1H质子NMR谱及三氟乙醇的纯J-耦合谱,同时还测到了清晰的自旋回波信号。在此基础上,采用直接背投影重建方法,尝试并成功获得了水样品和生物样品的一维及二维核磁共振像。采用8 nm粒径的超顺磁Fe3O4磁性纳米粒子作为对比增强剂,研究了磁性纳米粒子对1H核自旋纵向弛豫时间T1的影响,据此演示了磁性纳米粒子T1加权对比度增强成像实验,所得二维核磁共振像随极化时间的不同显示出显著的对比度变化。

Complete population transfer between next-adjacent energy levels of a transmon qudit

The utilization of qudits in quantum systems has led to significant advantages in quantum computation and information processing.Therefore,qudits have gained increased attention in recent research for their precise and efficient operations.In this work,we demonstrate the complete population transfer between the next-adjacent energy levels of a transmon qudit using the Pythagorean coupling method and energy level mapping.We achieve a|0>to|2>transfer with a process fidelity of 97.76%in the subspace spanned by|0>to|2>.Moreover,the transfer operation is achieved within a remarkably fast timescale,as short as 20 ns.This study may present a promising avenue for enhancing the operation flexibility and efficiency of qudits in future implementations.

超导与量子计算

基于量子力学态叠加性和纠缠性的量子计算,以其指数级增长的庞大计算空间和更高级的信息抽象能力,为计算提供了新的范式。这一新技术有可能解决一些经典计算无法解决的计算难题,同时解决经典计算的功耗问题。超导效应作为一种宏观量子效应,为量子态相干操控提供了绝佳的无损耗环境,而约瑟夫森结为构建量子比特提供了必要的能级分立性和非线性。经过二十余年的高速发展,基于超导量子电路的量子计算技术已经在退相干时间、量子态操控和读取、量子比特间可控耦合、中大规模扩展等关键技术上取得大量突破,成为构建通用量子计算机和量子模拟机最有前途的候选技术路线之一。文章就这一技术做一个简要的介绍和梳理,以令读者了解整个技术脉络为目标,尽可能不涉及复杂的符号和公式。最后,还简要讨论了超导量子计算发展的未来,并指出其中部分关键技术难点。

Cavity-induced ATS effect on a superconducting Xmon qubit

We couple a ladder-type three-level superconducting artificial atom to a cavity. Adjusting the artificial atom to make the cavity be resonant with the two upper levels, we then probe the lower two levels of the artificial atom. When driving the cavity to a coherent state, the probe spectrum shows energy level splitting induced by the quantized electromagnetic field in the cavity. This splitting size is related to the coupling strength between the cavity and the artificial atom and, thus, is fixed after the sample is fabricated. This is in contrast to the classical Autler-Townes splitting of a three-level system in which the splitting is proportional to the driving amplitude, which can be continuously changed. Our experiment results show the difference between the classical microwave driving field and the quantum field of the cavity.

Fabrication of superconducting NbN meander nanowires by nano-imprint lithography

Superconducting nanowire single photon detector （SNSPD）, as a new type of superconducting single photon detector （SPD）, has a broad application prospect in quantum communication and other fields. In order to prepare SNSPD with high performance, it is necessary to fabricate a large area of uniform meander nanowires, which is the core of the SNSPD. In this paper, we demonstrate a process of patterning ultra-thin NbN films into meander-type nanowires by using the nano- imprint technology. In this process, a combination of hot embossing nano-imprint lithography （HE-NIL） and ultraviolet nano-imprint lithography （UV-NIL） is used to transfer the meander nanowire structure from the NIL Si hard mold to the NbN film. We have successfully obtained a NbN nanowire device with uniform line width. The critical temperature （Tc） of the superconducting NbN meander nanowires is about 5 K and the critical current （lc） is about 3.5 μA at 2.5 K.

High quality NbTiN films fabrication and rapid thermal annealing investigation

NbTiN thin films are good candidates for applications including single-photon detector, kinetic inductance detector, hot electron bolometer, and superconducting quantum computing circuits because of their favorable characteristics,such as good superconducting properties and easy fabrication.In this work, we systematically investigated the growth of high-quality NbTiN films with different thicknesses on Si substrates by reactive DC-magnetron sputtering method.After optimizing the growth conditions, such as the gas pressure, Ar/N2 mixture ratio, and sputtering power, we obtained films with excellent superconducting properties.A high superconducting transition temperature of 15.5 K with narrow transition width of 0.03 K was obtained in a film of 300 nm thickness with surface roughness of less than 0.2 nm.In an ultra-thin film of 5 nm thick, we still obtained a transition temperature of 7.6 K.In addition, rapid thermal annealing(RTA) in atmosphere of nitrogen or nitrogen and hydrogen mixture was studied to improve the film quality.The results showed that Tc and crystal size of the NbTiN films were remarkably increased by RTA.For ultrathin films, the annealing in N2/H2 mixture had better effect than that in pure N2.The Tc of 10 nm films improved from 9.6 K to 10.3 K after RTA in N2/H2 mixture at 450℃.

Fabrication and properties of the meander nanowires based on ultra-thin Nb films

We report the fabrication and the study of superconducting properties of ultra-thin Nb superconducting meander nanowires, which can be used as superconducting nanowire single-photon detectors （SNSPDs）. The ultra-thin （about 7- nm thick） Nb films are patterned into micro-bridges, and 100-nm wide meander nanowires by using e-beam lithography （EBL）. The average transition temperature （Tc） of the nanowires is about 4.8 K and the critical current density jc is about 2.8 × 10^6 A/cm2. Superconducting characteristics of the specimens at different applied magnetic fields up to 8 T （parallel or perpendicular to the specimen） are systematically investigated. The normalized temperature t （= T/Tc） dependences of the parallel critical field （HcⅡ） for both the micro-bridge and the meander nanowire are almost the same, following the Ginzburg and Landau （GL） formalism for ultra-thin films. However, in perpendicular field and in the vicinity of Tc （〉 0.95Tc）, the critical field Hc⊥ of the nanowire exhibits a down-turn curvature nonlinear temperature dependence while the micro-bridge displays a linear temperature dependence. The nonlinear behavior of Hc⊥ in the nanowire is believed to be due to the fact that in the vicinity of Tc the coherence length becomes larger than the line width. Additionally, the localization of carriers in the nanowire could also contribute to the nonlinear behavior. The resistive transitions could be described by the phase-slip model for quasi-one-dimensional system. Moreover, the hysteresis in I-V curve of the meander nanowires can be illustrated by a simple model of localized normal hotspot maintained by Joule heating.

Spectroscopy and coherent manipulation of single and coupled flux qubits

Measurements of three-junction flux qubits, both single flux qubits and coupled flux qubits, using a coupled direct current superconducting quantum interference device （dc-SQUID） for readout are reported. The measurement procedure is described in detail. We performed spectroscopy measurements and coherent manipulations of the qubit states on a single flux qubit, demonstrating quantum energy levels and Rabi oscillations, with Rabi oscillation decay time TRabi =- 78 ns and energy relaxation time T~ = 315 ns. We found that the value of TRabi depends strongly on the mutual inductance between the qubit and the magnetic coil. We also performed spectroscopy measurements on inductively coupled flux qubits.

Hardware for multi-superconducting qubit control and readout

We have developed an electronic hardware system for the control and readout of multi-superconducting qubit devices.The hardware system is based on the design ideas of good scalability,high synchronization and low latency.The system,housed inside a VPX-6U chassis,includes multiple arbitrary-waveform generator(AWG)channels,analog-digital-converter(ADC)channels as well as direct current source channels.The system can be used for the control and readout of up to twelve superconducting transmon qubits in one chassis,and control and readout of more and more qubit can be carried out by interconnecting the chassis.By using field programmable gate array(FPGA)processors,the system incorporates three features that are specifically useful for superconducting qubit research.Firstly,qubit signals can be processed using the on-board FPGA after being acquired by ADCs,significantly reducing data processing time and data amount for storage and transmission.Secondly,different output modes,such as direct output and sequential output modes,of AWG can be implemented with pre-encoded FPGA.Thirdly,with data acquisition ADCs and control AWGs jointly controlled by the same FPGA,the feedback latency can be reduced,and in our test a 178.4 ns latency time is realized.This is very useful for future quantum feedback experiments.Finally,we demonstrate the functionality of the system by applying the system to the control and readout of a 10 qubit superconducting quantum processor.

Investigation of dimensionality in superconducting NbN thin film samples with different thicknesses and NbTiN meander nanowire samples by measuring the upper critical field

We study superconducting properties of NbN thin film samples with different thicknesses and an ultra-thin NbTiN meander nanowire sample.For the ultra-thin samples,we found that the temperature dependence of upper critical field(Hc2)in parallel to surface orientation shows bending curvature close to critical temperature Tc,suggesting a two-dimensional(2D)nature of the samples.The 2D behavior is further supported by the angular dependence measurements of Hc2 for the thinnest samples.The temperature dependence of parallel upper critical field for the thick films could be described by a model based on the anisotropic Ginzburg-Landau theory.Interestingly,the results measured in the field perpendicular to the film surface orientation show a similar bending curvature but in a much narrow temperature region close to Tc for the ultra-thin samples.We suggest that this feature could be due to suppression of pair-breaking caused by local in-homogeneity.We further propose the temperature dependence of perpendicular Hc2 as a measure of uniformity of superconducting ultra-thin films.For the thick samples,we find that Hc2 shows maxima for both parallel and perpendicular orientations.The Hc2 peak for the perpendicular orientation is believed to be due to the columnar structure formed during the growth of the thick films.The presence of columnar structure is confirmed by transmission electron microscopy(TEM).In addition,we have measured the angular dependence of magneto-resistance,and the results are consistent with the Hc2 data.

Study on signal intensity of low field nuclear magnetic resonance via an indirect coupling measurement

We carry out an ultra-low-field nuclear magnetic resonance （NMR） experiment based on high-T c superconducting quantum interference devices （SQUIDs）. The measurement field is in a micro-tesla range （～10 μT-100 μT） and the experiment is conducted in a home-made magnetically-shielded-room （MSR）. The measurements are performed by the indirect coupling method in which the signal of nuclei precession is indirectly coupled to the SQUID through a tuned copper coil transformer. In such an arrangement, the interferences of applied measurement and polarization field to the SQUID sensor are avoided and the performance of the SQUID is not destroyed. In order to compare the detection sensitivity obtained by using the SQUID with that achieved using a conventional low-noise-amplifier, we perform the measurements using a commercial room temperature amplifier. The results show that in a wide frequency range （～1 kHz-10 kHz） the measurements with the SQUID sensor exhibit a higher signal-to-noise ratio. Further, we discuss the dependence of NMR peak magnitude on measurement frequency. We attribute the reduction of the peak magnitude at high frequency to the increased field inhomogeneity as the measurement field increases. This is verified by compensating the field gradient using three sets of gradient coils.

Fabrication of Josephson parameter amplifier and its application in squeezing vacuum fluctuations

Josephson parameter amplifier(JPA)is a microwave signal amplifier device with near-quantum-limit-noise performance.It has important applications in scientific research fields such as quantum computing and dark matter detection.This work reports the fabrication and characterization of broadband JPA devices and their applications in multi-qubit readout and squeezing of vacuum state.We use a process in which transmission lines and electrodes are made of niobium thin film and aluminum Josephson junctions are made by Dolan bridge technique.We believe this process is more convenient than the process we used previously.The whole production process adopts electron beam lithography technology to ensure high structural resolution.The test result shows that the gain value of the manufactured JPA can exceed 15 dB,and the amplification bandwidth is about 400 MHz.The noise temperature is about 400 mK at the working frequency of 6.2 GHz.The devices have been successfully used in experiments involving superconducting multi-qubit quantum processors.Furthermore,the device is applied to squeeze vacuum fluctuations and a squeezing level of 1.635 dB is achieved.

Realization of adiabatic and diabatic CZ gates in superconducting qubits coupled with a tunable coupler

High fidelity two-qubit gates are fundamental for scaling up the superconducting qubit number.We use two qubits coupled via a frequency-tunable coupler which can adjust the coupling strength,and demonstrate the CZ gate using two different schemes,adiabatic and diabatic methods.The Clifford based randomized benchmarking(RB) method is used to assess and optimize the CZ gate fidelity.The fidelities of adiabatic and diabatic CZ gates are 99.53(8)% and 98.72(2)%,respectively.We also analyze the errors induced by the decoherence.Comparing to 30 ns duration time of adiabatic CZ gate,the duration time of diabatic CZ gate is 19 ns,revealing lower incoherence error rate r’_(incoherent),int=0.0197(5) compared to r_(incoherent,int)=0.0223(3).

Modulation of energy spectrum and control of coherent microwave transmission at single-photon level by longitudinal field in a superconducting quantum circuit

We study the effect of longitudinally applied field modulation on a two-level system using superconducting quantum circuits. The presence of the modulation results in additional transitions and changes the magnitude of the resonance peak in the energy spectrum of the qubit. In particular, when the amplitude ,λz and the frequency COl of the modulation field meet certain conditions, the resonance peak of the qubit disappears. Using this effect, we further demonstrate that the longitudinal field modulation of the Xmon qubit coupled to a one-dimensional transmission line could be used to dynamically control the transmission of single-photon level coherent resonance microwave.

Fabrication and characterization of ultra-low noise narrow and wide band Josephson parametric amplifiers

We have fabricated two types of lumped-element Josephson parameter amplifiers（JPAs） by using a multilayer microfabrication process involving wet etching of Al films. The first type is a narrow band JPA which shows typical gain above14 dB in a bandwidth around 35 MHz. The second type is a wideband JPA which is coupled to an input 50Ω transmission line via an impedance transformer that changes the impedance from about 15 Ω on the non-linear resonator side to 50 Ωon the input transmission line side. The wideband JPA could operate in a 200 MHz range with a gain higher than 14 d B.The amplifiers were used for superconducting qubit readout. The results showed that the signal to noise ratio and hence the readout fidelity were improved significantly.

Degradation Mechanism of the Superconducting Transition Temperature in Nb Thin Films

Systemic measurements show that there is no 3D to 2D crossover in the reduction of the superconducting transition temperature Tc in Nb thin films. This result is consistent with all previous measurements while it is contrary to the prevailing understanding based on the interplay between proximity, localization, and lifetime broadening. Our study indicates that the decrease of Tc can be interpreted by the combined effects of electron-phonon coupling parameter λ and the defect scattering rate pw, being uniquely determined by their ratio λ/ρw. Other factors such as film thickness and irradiation do not produce additional effects beyond these two parameters.

Calibration of the cryogenic measurement system of a resonant haloscope cavity

Possible light bosonic dark matter interactions with the Standard Model photon have been searched using microwave resonant cavities.In this paper,we describe the cryogenic readout system calibration of a 7.138 GHz copper cavity with a loaded quality factorQ1=10^(4)whose operation at a temperature of 22 mK is based on a dilution refrigerator.Our readout system consists of High Electron Mobility Transistors working as cryogenic amplifiers at 4 K,plus room-temperature amplifiers and a spectrum analyzer for signal power detection.We tested the system with a superconducting two-level system based on a single-photon source in the microwave frequency regime.We obtained an overall 95.6 dB system gain and–71.4 dB attenuation in the cavity's input channel.The effective noise temperature of the measurement system is 7.5 K.

超导量子计算：长退相干量子比特发展之路

超导量子计算是基于约瑟夫森结电路的固态量子计算技术方案.由于其易于扩展、耦合与操控等特点,已成为最有可能实现实用量子计算机/模拟机的候选方案之一.由于固态器件复杂的电磁环境,超导量子比特一直受到退相干时间不足的制约.本文简要介绍了超导量子比特的基本结构并重点论述了近期发展出的几种新型长退相干时间超导量子比特,包括Transmon/Xmon,Fluxonium和C-shunt Flux qubit等,整理了这几个不同设计方案在抑制电荷、磁通和准粒子等几种主要噪声来源方面做出的探索和贡献.最后,对几种主要的设计思想做了简要的归纳总结,以期对未来进一步发展提供参考和依据.