基于D-Wave Advantage的量子退火公钥密码攻击算法研究

D-Wave专用量子计算机的原理量子退火凭借独特的量子隧穿效应可跳出传统智能算法极易陷入的局部极值,可视为一类具有全局寻优能力的人工智能算法.本文研究了两类基于量子退火的RSA公钥密码攻击算法(分解大整数N=pq):一是将密码攻击数学方法转为组合优化问题或指数级空间搜索问题,通过Ising模型或QUBO模型求解,提出了乘法表的高位优化模型,建立新的降维公式,使用D-Wave Advantage分解了 200万整数2269753.大幅度超过普渡大学、Lockheed Martin和富士通等实验指标,且Ising模型系数h范围缩小了 84%,系数J范围缩小了 80%,极大地提高了分解成功率,这是一类完全基于D-Wave量子计算机的攻击算法;二是基于量子退火算法融合密码攻击数学方法优化密码部件的攻击,采用量子退火优化CVP问题求解,通过量子隧穿效应获得比Babai算法更近的向量,提高了 CVP问题中光滑对的搜索效率,在D-Wave Advantage上实现首次50比特RSA整数分解.实验表明,在通用量子计算机器件进展缓慢情况下,D-Wave表现出更好的现实攻击能力,且量子退火不存在NISQ量子计算机VQA算法的致命缺陷贫瘠高原问题:算法会无法收敛且无法扩展到大规模攻击.

Anomalous Josephson effect between d-wave superconductors through a two-dimensional electron gas with both Rashba spin-orbit coupling and Zeeman splitting

Based on the Bogoliubov-de Gennes equation and the extended McMillan’s Green’s function formalism,we study theoretically the Josephson effect between two d-wave superconductors bridged by a ballistic two-dimensional electron gas with both Rashba spin-orbit coupling and Zeeman splitting.We show that due to the interplay of Rashba spin-orbit coupling and Zeeman splitting and d-wave pairing,the current-phase relation in such a heterostructure may exhibit a series of novel features and can change significantly as some relevant parameters are tuned.In particular,anomalous Josephson current may occur at zero phase bias under various different situations if both time reversal symmetry and inversion symmetry of the system are simultaneously broken,which can be realized by tuning some relevant parameters of the system,including the relative orientations and the strengths of the Zeeman field and the spin-orbit field in the bridge region,the relative orientations of the a axes in two superconductor leads,or the relative orientations between the Zeeman field in the bridge region and the a axes in the superconductor leads.We show that both the magnitude and the direction of the anomalous Josephson current may depend sensitively on these relevant parameters.

Zeeman effects on Josephson current in d-wave superconductor/d-wave superconductor junctions

This paper solves a self-consistent equation for the d-wave superconducting gap and the effective exchange field in the mean-field approximation, and studies the Zeeman effects on the d-wave superconducting gap and thermodynamic potential. The Josephson currents in the d-wave superconductor（S）/insulating layer（I）/d-wave S junctions are calculated as a function of the temperature, exchange field, and insulating barrier strength under a Zeeman magnetic field on the two d-wave Ss. It is found that the Josephson critical currents in d-wave S/d-wave S junction to a great extent depend on the relative orientation of the effective exchange field of the two S electrodes, and the crystal orientation of the d-wave S. The exchange field under certain conditions can enhance the Josephson critical current in a d-wave S/I/d-wave S junction.

Unconventional chiral d-wave superconducting state in strained graphene

We consider a highly unconventional superconducting state with chiral d-wave symmetry in doped graphene under strain with the Gutzwiller–RVB method in the momentum space. It is shown that flat bands emerge in the normal state for reasonable strain. As a result, the superconducting critical temperature is found to be linearly proportional to the strength of the electron–electron interaction. Furthermore, the chiral d-wave superconducting state is shown with coexistence of the charge density wave and the pair density wave. There are different coexisting states with those orders under different doping levels.

Differential conductance in a normal metal/insulator/metal/d-wave superconductor junction carrying a supercurrent

This paper applies the Bogoliubov-de Gennes equation and the Blonder-Tinkham-Klapwijk approach to study the oscillatory behaviour of differential conductance in a normal metal/insulator/metal/d-wave superconductor junction carrying a supercurrent Is. We find that （i） a three-humped structure appears at a nearly critical supercurrent Is and z ≈ 0.5 for the normal metal/insulator/metal/dx^2＋y^2-wave superconductor junction; （ii） the zero-bias conductance peak splits into two peaks with sufficiently large applied current for the normal metal/insulator/metal/dxy-wave superconductor junction; （iii） the conductance spectrum exhibits oscillating behaviour with the bias voltage and the peaks of the resonances are suppressed by increasing supercurrent Is.

Tunneling Conductance in Quantum-Wire/Ferromagnetic-Insulator/d-Wave Superconductor Junction

We have studied the quasiparticle transport in quantum-wire /ferromagnetic-insulator/d wave super- conductor Junction （q/FI/d） in the framework of the Blonder-Tinkham-Klapwijk model. We calculate the tunneling conductance in q/FI/d as a function of the bias voltage at zero temperature and finite temperature based on Bogoliubov- de Gennes equations. Different from the case in normal-metal/insulator/d wave superconductor Junctions, the zero-bias conductance peaks vanish for the single-mode case. The tunneling conductance spectra depend on the magnitude of the exchange interaction at the ferromagnetic-insulator.

Superfluid phases and excitations in a cold gas of d-wave interacting bosonic atoms and molecules

Motivated by recent advances in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model with d-wave symmetric interactions and background s-wave interactions is adopted to characterize the gas. The ground state is found to have three interesting superfluid phases: atomic, molecular, and atomic–molecular. In great contrast to what was previously known about the p-wave case, the atomic superfluid is found to be momentum-independent for the d-wave case discussed here. The Bogoliubov spectra above each superfluid phase are obtained both analytically and numerically.

Josephson Current in Superconductor-Ferromagnet／Insulator／d-Wave Superconductor Junctions

Solving the Bogoliubov-de Gennes equation, the energy levels of bound statesare obtained in the ferromagnetic superconductor. The Josephson currents in a ferromagneticsuperconductor/Insulator/d-wave superconductor junction are calculated as a function of the exchangefield, temperature, and insulating barrier strength. It is found that the Josephson criticalcurrent is always suppressed by the presence of exchange Geld h and depends on crystalline axisorientation of d-wave superconductor.

A New Approach to the Ground State of Superfluid Fermi Gas near the Feshbach Resonance of d-Wave

The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the author’s name: Alireza Heidari. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.2, 151-154, 2012, has been removed from this site.

Deciphering a Million-Plus RSA Integer with Ultralow Local Field Coefficient h and Coupling Coefficient J of the Ising Model by D-Wave 2000Q

This work is the first to determine that a real quantum computer(including generalized and specialized)can decipher million-scale RSA relying solely on quantum algorithms,showing the real attack potential of D-Wave machines.The influence of different column widths on RSA factorization results is studied on the basis of a multiplication table,and the optimal column method is determined by traversal experiments.The traversal experiment of integer factorization within 10000 shows that the local field and coupling coefficients are 75%–93%lower than the research of Shanghai University in 2020 and more than 85%lower than that of Purdue University in 2018.Extremely low Ising model parameters are crucial to reducing the hardware requirements,prompting factoring 1245407 on the D-Wave 2000Q real machine.D-Wave advantage already has more than 5000 qubits and will be expanded to 7000 qubits during 2023–2024,with remarkable improvements in decoherence and topology.This machine is expected to promote the solution of large-scale combinatorial optimization problems.One of the contributions of this paper is the discussion of the long-term impact of D-Wave on the development of post-quantum cryptography standards.

Quest towards “factoring larger integers with commercial D-Wave quantum annealing machines”

Integer factorization (IFP), also called prime factorization, is an important problem in number theory, cryptography, and quantum computation. Factoring large integers to attack the RSA cryptosystem is intractable for powerful supercomputers, let alone classical computers. In 1994, Shor [1]presented an algorithm that potentially enabled a quantum computer to find prime factors in polynomial time.

FINITE ELEMENT METHODS FOR A BI-WAVE EQUATION MODELING D-WAVE SUPERCONDUCTORS

In this paper we develop two conforming finite element methods for a fourth order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in absence of applied magnetic field. Unlike the biharmonic operator A2, the bi-wave operator □^2 is not an elliptic operator, so the energy space for the bi-wave equation is much larger than the energy space for the biharmonic equation. This then makes it possible to construct low order conforming finite elements for the bi-wave equation. However, the existence and construction of such finite elements strongly depends on the mesh. In the paper, we first characterize mesh conditions which allow and not allow construction of low order conforming finite elements for approximating the bi-wave equation. We then construct a cubic and a quartic conforming finite element. It is proved that both elements have the desired approximation properties, and give optimal order error estimates in the energy norm, suboptimal （and optimal in some cases） order error estimates in the H1 and L^2 norm. Finally, numerical experiments are presented to guage the efficiency of the proposed finite element methods and to validate the theoretical error bounds.

D-Wave量子计算机,到底能不能进行量子计算

最近Google宣布在量子计算领域取得了突破性进展,他们用D-Wave量子计算机（图1）在解决某些问题上比传统计算机过程快了1亿倍。果真这样,它将带来人工智能技术的巨大进步。不过,有专家对此表示质疑,认为这些说法夸大其词了。那么Google所谓的D-Wave量子计算机,到底能不能做量子计算,这1亿倍的加速又是怎么回事？

三维TTI介质qP波透射立体层析方法研究

致力于研究三维TTI介质下的qP波立体层析反演算法.将射线扰动理论应用于三维具有倾斜对称轴的横向各向同性(TTI)介质拟声波程函方程,导出立体层析所需的三维TTI介质qP波数据空间与三维TTI介质模型空间之间的所有Frechét导数.在通过灵敏度测试验证了相应Frechét导数对于三个各向异性THOMSEN参数的正确性之后,使用两步法反演策略——即先使用坐标分量和射线参数水平分量(不包括走时)实施初始反演而后再使用所有数据空间分量进行反演,在三维qP波TTI介质情形下针对三个各向异性THOMSEN参数可以获得理想的反演结果,为三维qP波TTI介质下透射立体层析的应用做好了理论准备.用一个典型的理论数据算例证实了上述观点.

Zeeman effects on d-wave superconductor and tunneling spectrum in normal-metal/d-wave superconductor tunnel junction

We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal state, exhibiting a first-order phase transition; (2) the Zeeman magnetic field may make the zero-bias conductance peak split into two peaks, and the energy difference between the two splitting peaks in the conductance spectrum is equal to 2h0 (h0 is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear out the peaks, however, neither of them can influence the Zeeman effect.

空间效应下超长型钢混凝土结构地震响应研究

超长结构空间效应下的地震响应分析是当前抗震研究的热点之一,空间效应对尺寸较小的建筑影响不大,但对平面投影尺度很大的结构地震响应的影响不可忽略。在传统三角级数法合成人工一维地震的基础上采用了三维相干函数矩阵,通过选取合适的模型及相应参数合成考虑空间效应的人工三向地震动。采用了4条自然波及2条人工波对超长型钢混凝土结构进行抗震计算。结果表明:超长结构不适宜仅采用振型分解反应谱法进行地震计算,还需采用地震时程分析法补充计算;与一致激励相比,行波效应会促使构件内力响应两极分化,既能减小整体内力响应,又能增大部分峰值内力,其效果不仅与视波速有关还与激励方向有关,低视波速和长边激励时行波效应加强;与单向激励相比,双向激励下的行波效应影响更复杂,既能改变构件内力响应和主、次动力响应的变化趋势,也能改变不利构件的分布位置;相干效应与行波效应叠加时,会进一步改变构件动力和内力响应。高视波速下相干效应为主导,底层构件内力响应增大。低视波速下行波效应为主导,地震响应呈现两极分化;不利构件的分布不仅与建筑的开洞、设缝及楼层刚度变化等因素有关,还与地震激励方向有关,不利构件沿激励方向有规律地延伸分布。

Effects of dopamine D_(1) receptor blockade on the ERG b- and d-waves during blockade of ionotropic GABA receptors

Background:Some data indicate that the dopaminergic and GABAergic systems interact in the vertebrate retina,but the type of interactions is not well understood.Methods:In this study we investigated the effect of dopamine D_(1) receptor blockade by 75μM SCH 23390 on the electroretinographic ON(b-wave)and OFF(d-wave)responses in intact frog eyecup preparations and in eyecups where the ionotropic GABA receptors were blocked by 50μM picrotoxin.Student’s t-test,One-way repeated measures ANOVA with Bonferroni post-hoc test and Two-way ANOVA were used for statistical evaluation of the data.Results:We found that SCH 23390 alone significantly enhanced the amplitude of the b-and d-waves without altering their latency.The effect developed rapidly and was fully expressed within 8-11 min after the blocker application.Picrotoxin alone also markedly enhanced the amplitude of the ERG ON and OFF responses and increased their latency significantly.The effect was fully expressed within 25-27 min after picrotoxin application and remained very stable in the next 20 min.The effects of SCH 23390 and picrotoxin are similar to that reported in our previous studies.When SCH 23390 was applied on the background of the fully developed picrotoxin effect,it diminished the amplitude of the b-and d-waves in comparison to the corresponding values obtained during application of picrotoxin alone.Conclusion:Our results demonstrate that the enhancing effect of D_(1) receptor blockade on the amplitude of the ERG b-and d-waves is not evident during the ionotropic GABA receptor blockade,indicating an interaction between these neurotransmitter systems in the frog retina.We propose that the inhibitory effect of endogenous dopamine mediated by D_(1) receptors on the ERG ON and OFF responses in the frog retina may be due to the dopamine-evoked GABA release.

Disorder driven superconductor-insulator transition in inhomogenous d-wave superconductor

We study the effect of disorder on the superconductor-insulator transition in an inhomogeneous d-wave superconductor using the kernel polynomial method. As the Bogoliubov-de Gennes equations of the two-dimensional square lattice are solved self-consistently for the cases with more than 100000 unit cells, it is possible to observe the spatial fluctuations of the superconducting order parameters at the nanoscale. We find that strong spatial fluctuation of the superconducting order parameters can be introduced by disorder, and some superconducting specific order parameters are even enhanced. Moreover, we find that some isolated superconducting "islands" can survive the strong disorder, giving a boson insulator with some localized Cooper pairs. Our numerical calculations predict the existence of two sequential transitions with the increasing disorder strength: a d-wave to s-wave superconductor transition, and then an s-wave superconductor to insulator transition. The possibility of the appearance of a metallic phase between the superconducting and insulating phases is excluded by performing the lattice-size scaling of the generalized inverse participation ratio. In addition, we also discuss the effect of disorder on the optical conductivity of the d-wave superconductors.

不同中医证型H型高血压25羟维生素D与脉搏波速度相关性研究

目的研究不同中医证型H型高血压患者25羟维生素D与脉搏波速度的相关性。方法选取新余市人民医院2021年12月至2022年9月H型高血压患者100例,将患者根据不同证型分为痰湿内盛、阴阳两虚、肝火亢盛、阴虚阳亢4组,收集患者一般资料(包括年龄、性别、既往史等),测量并比较各证型患者血糖、血脂、血清同型半胱氨酸(Hcy)、25羟基维生素D与脉搏波速度,分析各证型脉搏波速度与25羟维生素D的相关性。结果各证型之间总体收缩压为(155.61±10.61)mmHg,总体舒张压为(87.91±11.15)mmHg,各证型组间血压比较差异无统计学意义(P>0.05)。各证型之间血清Hcy比较差异有统计学意义(P<0.05),痰湿内盛证、阴阳两虚证Hcy水平显著高于肝火亢盛证、阴虚阳亢证(P<0.05),其余各组间两两比较差异无统计学意义(P>0.05)。各证型之间脉搏波速度和25羟维生素D水平比较差异无统计学意义(P>0.05)。各证型间空腹血糖、血脂比较差异无统计学意义(P>0.05)。痰湿内盛证、阴阳两虚证脉搏波速度与25羟维生素D水平呈负相关(P<0.05),肝火亢盛证、阴虚阳亢证脉搏波速度与25羟维生素D呈负相关但相关性无统计学意义(P>0.05)。结论H型高血压若证属痰湿内盛或阴阳两虚,同时患有维生素D缺乏,应及时纠正,降低脉搏波速度,改善血管弹性,延缓动脉粥样硬化的发展,从而降低卒中的发生。

基于单频走时敏感度核函数的三维波动方程初至层析

地震波走时层析是主要的近地表速度建模技术.对于变速模型,尤其是复杂近地表模型,波动方程能够更加精确地描述地震波的一阶绕射效应,理论上反演精度高于射线(束)类层析.然而,波动方程的数值求解的计算量较射线理论增加了几个数量级,严重制约了波动方程走时层析技术的三维实用化.为解决波动方程走时层析中遇到的计算和存储问题,本文通过引入随机边界条件以及离散Fourier积分,提出了基于单频梯度反演策略的实用化三维波动方程初至层析方法.本文方法的优势在于:在计算和存储方面,相比于基于波场重构算法(需要三次波传播)的梯度计算策略,本文提出的单频梯度计算方法对内存需求极低(相对于波动方程正演,仅需要增加两个单频波场以及一个成像体),且计算量至少减少1/3(仅需要两次波传播且无需处理数值吸收边界).此外,随机边界的引入使得正演算法大幅简化因而更适用于GPU(Graphics Processing Unit,图形处理器)加速.在理论层面,由于影响地震波一阶散射效应的主要区域集中在连接炮检的中心射线邻域的第一菲涅尔带内,随机边界条件的引入降低了随机边界内产生的散射波的空间相关性,使得第一菲涅尔带内的单频梯度相干加强;同时,地震观测系统的多次覆盖特性有助于第一菲涅尔带外的高波数振荡相互干涉.数值实验表明,光滑处理后的单频梯度仍然保留了非常可观的低波数成分,有助于实现背景速度反演.此外,三维复杂模型反演结果验证了本文方法能够较为准确地反演近地表速度结构.相对于传统的波动方程走时层析实现方案,本文方法在显著降低内存需求的同时进一步提高了计算效率,有望将波动方程初至层析技术推向三维实用化.