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A Note on 3-Divisibility of Class Number of Quadratic Field

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Chinese Annals of Mathematics,Series B 2022年第2期43卷 307-318页

作者： Jianfeng XIE Kuok Fai CHAO Wu Wen-Tsun Key Laboratory of Mathematics School of Mathematical SciencesUniversity of Science and Technology of ChinaHefei 230026China Lui Che Woo College University of MacaoMacaoChina

In this paper,the authors show that there exists infinitely many family of pairs of quadratic fields Q(√D)and Q((√D+n)(1/2))with D,n∈Z whose class numbers are both divisible by 3.

关键词： Quadratic field Class number Hilbert class field

On abelian 2-ramification torsion modules of quadratic fields

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Science China Mathematics 2022年第12期65卷 2459-2482页

作者： Jianing Li Yi Ouyang Yue Xu Research Center for Mathematics and Interdisciplinary Sciences Shandong UniversityQingdao 266237China CAS Wu Wen-Tsun Key Laboratory of Mathematics University of Science and Technology of ChinaHefei230026Chin Hefei National Laboratory Hefei 230088China

For a number field F and a prime number p, the Z_(p)-torsion module of the Galois group of the maximal abelian pro-p extension of F unramified outside p over F, denoted by T_(p)(F), is an important subject in the abelian p-ramification theory. In this paper, we study the group T_(2)(F) = T_(2)(m) of the quadratic field F = Q(m_(1/2)). Firstly, assuming m > 0, we prove an explicit 4-rank formula for quadratic fields that rk4(T_(2)(-m))= rk2(T_(2)(-m))-rank(R), where R is a certain explicitly described Rédei matrix over F_(2). Furthermore, using this formula, we obtain the 4-rank density formula of T_(2)-groups of imaginary quadratic fields. Secondly, for l an odd prime, we obtain the results about the 2-power divisibility of orders of T_(2)(±l) and T_(2)(±2l), both of which are cyclic 2-groups. In particular, we find that #T_(2)(l) ≡ 2#T_(2)(2l) ≡ h_(2)(-2l)(mod 16) if l ≡ 7(mod 8),where h_(2)(-2l) is the 2-class number of Q((-2l)_(1/2)). We then obtain the density results for T_(2)(±l) and T_(2)(±2l)when the orders are small. Finally, based on our density results and numerical data, we propose distribution conjectures about T_(p)(F) when F varies over real or imaginary quadratic fields for any prime p, and about T_(2)(±l)and T_(2)(±2l) when l varies, in the spirit of Cohen-Lenstra heuristics. Our conjecture in the T_(2)(l) case is closely connected to Shanks-Sime-Washington’s speculation on the distributions of the zeros of 2-adic L-functions and to the distributions of the fundamental units.

关键词： quadratic fields density theorems abelian 2-ramification

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Observation of photon recoil effects in single-beam absorption spectroscopy with an ultracold strontium gas

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Chinese Physics B 2022年第1期31卷 485-491页

作者： Fachao Hu Canzhu Tan Yuhai Jiang Matthias Weidemüller Bing Zhu Hefei National Laboratory for Physical Sciences at the Microscale University of Science and Technology of ChinaHefei 230026China CAS Center For Excellence in quantum information and quantum Physics University of Science and Technology of ChinaHefei 230026China Shanghai Advanced Research Institute Chinese Academy of Sciences(CAS)Shanghai 201210China Physikalisches Institut Universität HeidelbergIm Neuenheimer Feld 22669120 HeidelbergGermany

We report on observing photon recoil effects in the absorption of a single monochromatic light at 689 nm through an ultracold ^(88)Sr gas,where the recoil frequency is comparable to natural linewidth of the narrow-line transition 5s^(2) ^(1)S_(0)-5s5p ^(3)P_(1) in *** the regime of high-saturation,the absorption profile becomes asymmetric due to the photon-recoil shift,which is of the same order as the natural *** lineshape is described by an extension of the optical Bloch equations including the momentum transfers to atoms during emission and absorption of *** work reveals the photon recoil effects in a simplest single-beam absorption setting,which is of significant relevance to other applications such as saturation spectroscopy,Ramsey interferometry,and absorption imaging.

关键词： photon recoil absorption spectroscopy ultracold strontium gas

Measurements of Dipole Moments for the 5s5p^(3)P_(1)–5sns^(3)S_(1)Transitions via Autler–Townes Spectroscopy

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Chinese Physics Letters 2022年第9期39卷 17-22页

作者： Canzhu Tan Fachao Hu Zhijing Niu Yuhai Jiang Matthias Weidemüller Bing Zhu Hefei National Laboratory for Physical Sciences at the Microscale University of Science and Technology of ChinaHefei 230026China CAS Center For Excellence in quantum information and quantum Physics University of Science and Technology of ChinaHefei 230026China Center for Transformative Science and School of Physical Science and Technology ShanghaiTech UniversityShanghai 201210China Physikalisches Institut Universität HeidelbergIm Neuenheimer Feld 22669120 HeidelbergGermany HSBC Lab-China Guangzhou 510620China

We report on experimental measurements of the transition dipole moments(TDMs)between the intermediate state 5s5p^(3)P_(1)and the triplet Rydberg series 5sns^(3)S_(1)in an ultracold strontium *** n is the principal quantum number ranging from 19 to *** transition 5s5p^(3)P_(1)–5sns^(3)S_(1)is coupled via an ultraviolet(UV)beam,inducing Autler–Townes splitting of both *** a splitting of the intermediate state is spectroscopically measured by using absorption imaging on a narrow transition 5s^(21)S_(0)–5s5p^(3)P_(1)in an ultracold gas of strontium *** power and size of the UV beam are carefully determined,with which the TDMs are extracted from the measured Autler–Townes *** experimentally obtained TDMs are compared to the calculations based on a parametric core potential,on a Coulomb potential with quantum defect,and on the open-source library Alkali Ryderg calculator,finding good agreement with the former two models and significant deviation with the latter.

关键词： quantum splitting Transition

quantum Teleportation via Qutrit Entangled State

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Chinese Journal of Electronics 2020年第2期29卷 228-232页

作者： HUANG Yang YANG Wei School of Computer Science and Technology University of South China School of Computer Science and Technology University of Science and Technology of China Suzhou Research Institute University of Science and Technology of China

Qutrit is the natural extension of qubit in quantum information processing and has quite a few advantages that outperform qubit. In this paper, we investigate the feasibility of teleportation of an unknown qubit state, as well as an unknown qutrit state using a two-qutrit entangled pair. We show that by carefully constructing the measurement bases, both the qubit and the qutrit can be faithfully teleported from Alice to Bob with a two-qutrit maximally entangled state.

关键词： Teleportation Qutrit quantum entanglement quantum measurement

A Blockchain-Based Protocol for Malicious Price Discrimination

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Journal of Computer Science & Technology 2022年第1期37卷 266-276页

作者： Li-De Xue Ya-Jun Liu Wei Yang Wei-Lin Chen Liu-Sheng Huang School of Computer Science and Technology University of Science and Technology of ChinaHefei 230000China information Department the First Affiliated Hospital of Soochow UniversitySuzhou 215000China

Serious price discrimination emerges with the development of big data and mobile networks,which harms the interests of *** solve this problem,we propose a blockchain-based price consensus protocol to solve the malicious price discrimination faced by *** give a mathematical definition of price discrimination,which requires the system to satisfy consistency and *** distributed blockchain can make the different pricing of merchants transparent to consumers,thus satisfying the *** aging window mechanism of our protocol ensures that there is no disagreement between any node on the consensus on price or price discrimination within a fixed period,which meets the ***,we evaluate its performance through a prototype implementation and experiments with up to 100 user *** results show that our protocol achieves all the expected goals like price transparency,consistency,and timeliness,and it additionally guarantees the consensus of the optimal price with a high probability.

关键词： blockchain digital economy distributed application price discrimination price transparency

Variational quantum Algorithms for the Steady States of Open quantum Systems

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Chinese Physics Letters 2021年第8期38卷 11-16页

作者： Huan-Yu Liu Tai-Ping Sun Yu-Chun Wu Guo-Ping Guo Key Laboratory of quantum information Chinese Academy of SciencesSchool of PhysicsUniversity of Science and Technology of ChinaHefei 230026China CAS Center For Excellence in quantum information and quantum Physics University of Science and Technology of ChinaHefei 230026China Institute of Artificial Intelligence Hefei Comprehensive National Science CenterHefei 230088China Origin quantum Computing Hefei Hefei 230026China

The solutions of the problems related to open quantum systems have attracted considerable *** propose a variational quantum algorithm to find the steady state of open quantum *** this algorithm,we employ parameterized quantum circuits to prepare the purification of the steady state and define the cost function based on the Lindblad master equation,which can be efficiently evaluated with quantum *** then optimize the parameters of the quantum circuit to find the steady *** simulations are performed on the one-dimensional transverse field Ising model with dissipative *** result shows that the fidelity between the optimal mixed state and the true steady state is over 99%.This algorithm is derived from the natural idea of expressing mixed states with purification and it provides a reference for the study of open quantum systems.

关键词： state quantum mixed

Harmonics-assisted optical phase amplifier

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Light(Science & Applications) 2022年第11期11卷 2748-2754页

作者： Wu-Zhen Li Chen Yang Zhi-Yuan Zhou Yan Li Yin-Hai Li Su-jian Niu Zheng Ge Li Chen Guang-Can Guo Bao-Sen Shi CAS Key Laboratory of quantum information University of Science and Technology of ChinaHefeiAnhui 230026China CAS Center for Excellence in quantum information and quantum Physics University of Science and Technology of ChinaHefei 230026China Hefei National Laboratory University of Science and Technology of ChinaHefei 230088China

The change in the relative phase between two light fields serves as a basic principle for the measurement of the physical quantity that guides this *** would therefore be highly advantageous if the relative phase could be amplified to enhance the measurement *** well-known method for phase amplification involves the use of the multi-photon number and path-entangled state known as the NOON state;however,a high-number NOON state is very diffcult to prepare and is highly sensitive to optical *** we propose and experimentally demonstrate in principle a phase amplifer scheme with the assistance of a harmonic generation *** relative phase difference between two polarization modes in a polarized interferometer is amplified coherently four times with cascaded second-harmonic generation *** demonstrate that these amplification processes can be recycled and therefore have the potential to realize much higher numbers of multiple amplification *** phase amplification method presented here shows considerable advantages over the method based on NOON states and willbe highly promising for use in precision optical measurements.

关键词： process phase harmonic

Codegree Threshold for Tiling k-graphs with Two Edges Sharing Exactly l Vertices

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Acta Mathematica Sinica,English Series 2020年第1期36卷 13-20页

作者： Lei YU Xin Min HOU Key Laboratory of Wu Wen-Tsun Mathematics School of Mathematical Sciences University of Science and Technology of China

Given integer k and a k-graph F,let t(k-1)(n,F)be the minimum integer t such that every k-graph H on n vertices with codegree at least t contains an *** integers k>3 and 0≤l≤k-1,let y(k,l)be a k-graph with two edges that shares exactly l *** and Zhao(*** Ser.A,(2015))asked the following question:For all k≥3,0≤l≤k-1 and sufficiently large n divisible by 2 k-l,determine the exact value of t_(k-1)(n,y(k,l)).In this paper,we show that t(k-1)(n,y(k,l))=n/(2 k-l)for k>3 and 1≤l≤k-2,combining with two previously known results of R?dl,Rucinski and Szemeredi(*** Ser.A,(2009))and Gao,Han and Zhao(Combinatorics,Probability and Computing,(2019)),the question of Han and Zhao is solved completely.

关键词： Hypergraph codegree factor