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.

培养小学生解决数学问题的能力

在新课改背景下,培养学生解决问题的能力已成为小学数学教学的一个核心目标。现阶段,我国小学数学教学的现状并未达到预期效果。学生的思维固化,有的学生虽然数学基础扎实,但在面临实际的数学问题时依然会束手无策。这就需要教师从多种途径加强对学生的思考能力、解决问题能力的锻炼,促使其具备独自解决问题的能力,从而提高学生的数学综合实践能力,为今后的学习及终身发展打下坚实的基础。本文对当前小学生解决数学问题能力不足的影响因素做出了详细的分析,并对培养策略展开了深入探究。

格点量子色动力学组态产生和胶球测量的大规模并行及性能优化

格点量子色动力学(Lattice Quantum Chromo Dynamics,LQCD)是目前已知能系统研究夸克及胶子间低能强相互作用的非微扰计算方法.计算结果的统计和系统误差原则上都是可控的,并能逐步减少.基于格点QCD的基本原理,更大的格子体积意味着可以计算更大空间的物理过程,并且可以对空间进行更加精细的划分,从而得到更加精确的结果.因而大体系的格点计算对QCD理论研究有着重要意义,但对程序计算性能提出了更高要求.本文针对格点QCD组态生成和胶球测量的基本程序,进行了其大规模并行分析和性能优化的研究.基于格点QCD模拟采用的blocking和even-odd算法,我们设计了基于MPI和OpenMP的并行化算法,同时设计优化数据通信模块:针对复矩阵的矩阵乘等数值计算,提出了向量化的计算优化方法:针对组态文件输出瓶颈,提出了并行输出组态文件的实施方法.模拟程序分别在Intel KNL和“天河2号”超级计算机x86_64队列进行了测试分析,证实了相应的优化措施的有效性,并进行了相应的并行计算效率分析,最大测试规模达到了1728个节点(即41472 CPU核).

Color halo scenario of charmonium-like hybrids

The internal structures of J^(PC)=1^(--),(0,1,2)^(-+)charmonium-like hybrids are investigated under lattice QCD in the quenched approximation.We define the Bethe-Salpeter wave function(Φn(r))in the Coulomb gauge as the matrix element of a spatially extended hybrid-like operator(ccg)between the vacuum and n-th state for each J^(PC),with r being the spatial separation between a localized cc component and the chromomagnetic strength tensor.These wave functions exhibit some similarities for states with the aforementioned different quantum numbers,and their r-behaviors(no node for the ground states and one node for the first excited states)imply that r can be a meaningful dynamical variable for these states.Additionally,the mass splittings of the ground states and first excited states of charmonium-like hybrids in these channels are obtained for the first time to be approximately 1.2-1.4 GeV.These results do not support the flux-tube description of heavy-quarkonium-like hybrids in the Born-Oppenheimer approximation.In contrast,a charmonium-like hybrid can be viewed as a"color halo"charmonium for which a relatively localized color octet cc is surrounded by gluonic degrees of freedom,which can readily decay into a charmonium state along with one or more light hadrons.The color halo picture is compatible with the decay properties of Y(4260)and suggests LHCb and BelleⅡto search for(0,1,2)^(-+)charmonium-like hybrids inχ_(c0,1,2η) and J/ψω(φ)final states.

Strangeonium-like hybrids on the lattice

The strangeonium-like ss^-g hybrids are investigated from lattice QCD in the quenched approximation.In the Coulomb gauge,spatially extended operators are constructed for 1^--and(0,1,2)^-+states with the color octet ss^-component being separated from the chromomagnetic field strength by the spatial distance r,whose matrix elements between the vacuum and the corresponding states are interpreted as Bethe-Salpeter(BS)wave functions.In each of the(1,2)^-+channels,the masses and the BS wave functions are reliably derived.The 1^-+ground state mass is approximately 2.1-2.2 GeV,and that of 2^-+is approximately 2.3-2.4 GeV,whereas the mass of the first excited state is approximately 1.4 GeV higher.This mass splitting is much larger compared to that expected based on the phenomenological flux-tube model or constituent gluon model for hybrids,which is usually a few hundred MeV.The BS wave functions with respect to r exhibit clear radial nodal structures of a non-relativistic two-body system,which imply that r is a meaningful dynamical variable for these hybrids and motivate a color halo picture of hybrids,in which the color octet ss^-is surrounded by gluonic degrees of freedom.In the 1^--channel,the properties of the lowest two states are consistent with those ofФ(1020)andФ(1680).We did not obtain convincing information with respect toФ(2170).However,we argue that regardless of whetherФ(2170)is a conventional ss^-meson or a ss^-g hybrid in the color halo scenario,the ratio of partial decay widthsΓ(Фη)andΓ(Фη')observed by BESIII can be understood based on the mechanism of hadronic transition of a strangeonium-like meson in addition toη-η'mixing.

Charmed andϕmeson decay constants from 2+1-flavor lattice QCD

On a lattice with 2+1-flavor dynamical domain-wall fermions at the physical pion mass,we calculate the decay constants of D_s^(*) , D^(*) ,and φ .The lattice size is 48^3×96 ,which corresponds to a spatial extension of -5.5 fm,with a lattice spacing of a\approx a≈0.114 fm.For the valence light,strange,and charm quarks,we use overlap fermions at several mass points close to their physical values.Our results at the physical point are f_(D)=213(5) MeV, f_(D)_(s)=249(7) MeV, f_(D)^(*)=234(6) MeV, f_(D)_(s)^(*)=274(7) MeV,and f_(D)_(s)=241(9) MeV.The couplings of D^(*) and D_s^(*) to the tensor current( f_(V)^(T) )can be derived from ratios f_(D)^(*)^T/f_(D)^(*)=0.91(4) and f_(D)_(s)^(*)^T/f_(D)_(s)^(*)=0.92(4) ,respectively,which are the first lattice quantum chromodynamics(QCD)results.We also obtain ratios f_(D)^(*)/f_(D)=1.10(3) and f_(D)_(s)^(*)/f_(D)_(s)=1.10(4) ,which reflect the size of heavy quark symmetry breaking in charmed mesons.Ratios f_(D)_(s)/f_(D)=1.16(3) and f_(D)_(s)^(*)/f_(D)^(*)=1.17(3) can be taken as a measure of SU(3)flavor symmetry breaking.