In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are dif...In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].展开更多
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science.The mixing property is necessary for Markov chains to approach stationary distribution...Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science.The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated by walks.Quantum walks show promise for faster mixing times than classical methods but lack universal proof,especially in finite group settings.Here,we investigate the continuous-time quantum walks on Cayley graphs of the dihedral group D_(2n)for odd n,generated by the smallest inverse closed symmetric subset.We present a significant finding that,in contrast to the classical mixing time on these Cayley graphs,which typically takes at least orderΩ(n^(2)log(1/2∈)),the continuous-time quantum walk mixing time on D_(2n)is of order O(n(log n)^(5)log(1/∈)),achieving a quadratic improvement over the classical case.Our paper advances the general understanding of quantum walk mixing on Cayley graphs,highlighting the improved mixing time achieved by continuous-time quantum walks on D_(2n).This work has potential applications in algorithms for a class of sampling problems based on non-abelian groups.展开更多
BACKGROUND:Hemiplegia,a prevalent stroke-related condition,is often studied for motor dysfunction;however,spasticity remains under-researched.Abnormal muscle tone significantly hinders hemiplegic patients’walking rec...BACKGROUND:Hemiplegia,a prevalent stroke-related condition,is often studied for motor dysfunction;however,spasticity remains under-researched.Abnormal muscle tone significantly hinders hemiplegic patients’walking recovery.OBJECTIVE:To determine whether early suspension-protected training with a personal assistant machine for stroke patients enhances walking ability and prevents muscle spasms.METHODS:Thirty-two early-stage stroke patients from Shenzhen University General Hospital and the China Rehabilitation Research Center were randomly assigned to the experimental group(n=16)and the control group(n=16).Both groups underwent 4 weeks of gait training under the suspension protection system for 30 minutes daily,5 days a week.The experimental group used the personal assistant machine during training.Three-dimensional gait analysis(using the Cortex motion capture system),Brunnstrom staging,Fugl-Meyer Assessment for lower limb motor function,Fugl-Meyer balance function,and the modified Ashworth Scale were evaluated within 1 week before the intervention and after 4 weeks of intervention.RESULTS AND CONCLUSION:After the 4-week intervention,all outcome measures showed significant changes in each group.The experimental group had a small but significant increase in the modified Ashworth Scale score(P<0.05,d=|0.15|),while the control group had a large significant increase(P<0.05,d=|1.48|).The experimental group demonstrated greater improvements in walking speed(16.5 to 38.44 cm/s,P<0.05,d=|4.01|),step frequency(46.44 to 64.94 steps/min,P<0.05,d=|2.32|),stride length(15.50 to 29.81 cm,P<0.05,d=|3.44|),and peak hip and knee flexion(d=|1.82|to|2.17|).After treatment,the experimental group showed significantly greater improvements than the control group in walking speed(38.44 vs.26.63 cm/s,P<0.05,d=|2.75|),stride length,peak hip and knee flexion(d=|1.31|to|1.45|),step frequency(64.94 vs.59.38 steps/min,P<0.05,d=|0.85|),and a reduced support phase(bilateral:24.31%vs.28.38%,P<0.05,d=|0.88|;non-paretic:66.19%vs.70.13%,P<0.05,d=|0.94|).For early hemiplegia,personal assistant machine-assisted gait training under the suspension protection system helps establish a correct gait pattern,prevents muscle spasms,and improves motor function.展开更多
Quantum algorithms have demonstrated provable speedups over classical counterparts,yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge.In this work,we de...Quantum algorithms have demonstrated provable speedups over classical counterparts,yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge.In this work,we decode the quantum search advantage by investigating the critical role of quantum state properties in random-walk-based algorithms.We propose three distinct variants of quantum random-walk search algorithms and derive exact analytical expressions for their success probabilities.These probabilities are fundamentally determined by specific initial state properties:the coherence fraction governs the first algorithm’s performance,while entanglement and coherence dominate the outcomes of the second and third algorithms,respectively.We show that increased coherence fraction enhances success probability,but greater entanglement and coherence reduce it in the latter two cases.These findings reveal fundamental insights into harnessing quantum properties for advantage and guide algorithm design.Our searches achieve Grover-like speedups and show significant potential for quantum-enhanced machine learning.展开更多
In this paper, we study the scaling for the mean first-passage time （MFPT） of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from...In this paper, we study the scaling for the mean first-passage time （MFPT） of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from a triangle to a polygon, we obtain the exact scaling for the MFPT. We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order. In addition, we determine the exponents of scaling efficiency characterizing the random walks. Our results are the generalizations of those derived for the Koch network, which shed light on the analysis of random walks over various fractal networks.展开更多
Complex networks display community structures. Nodes within groups are densely connected but among groups are sparsely connected. In this paper, an algorithm is presented for community detection named Markov Random Wa...Complex networks display community structures. Nodes within groups are densely connected but among groups are sparsely connected. In this paper, an algorithm is presented for community detection named Markov Random Walks Ants(MRWA). The algorithm is inspired by Markov random walks model theory, and the probability of ants located in any node within a cluster will be greater than that located outside the cluster.Through the random walks, the network structure is revealed. The algorithm is a stochastic method which uses the information collected during the traverses of the ants in the network. The algorithm is validated on different datasets including computer-generated networks and real-world networks. The outcome shows the algorithm performs moderately quickly when providing an acceptable time complexity and its result appears good in practice.展开更多
We propose an efficient quantum private comparison protocol firstly based on one direction quantum walks.With the help of one direction quantum walk,we develop a novel method that allows the semi-honest third party to...We propose an efficient quantum private comparison protocol firstly based on one direction quantum walks.With the help of one direction quantum walk,we develop a novel method that allows the semi-honest third party to set a flag to judge the comparing result,which improves the qubit efficiency and the maximum quantity of the participants’secret messages.Besides,our protocol can judge the size of the secret messages,not only equality.Furthermore,the quantum walks particle is disentangled in the initial state.It only requires a quantum walks operator to move,making our proposed protocol easy to implement and reducing the quantum resources.Through security analysis,we prove that our protocol can withstand well-known attacks and brute-force attacks.Analyses also reveal that our protocol is correct and practical.展开更多
We consider a broad class of Continuous Time Random Walks(CTRW) with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials,...We consider a broad class of Continuous Time Random Walks(CTRW) with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials,and a L′evy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.展开更多
She Walks in Beauty是英国著名诗人拜伦脍炙人口的一首抒情诗,塑造了温柔、善良、理想的美的女性形象,表达了诗人自己对于美好事物的追求。该文拟选取德国功能翻译派的文本类型理论这一新视角,对该诗的两个汉译本《她身披美丽而行》和...She Walks in Beauty是英国著名诗人拜伦脍炙人口的一首抒情诗,塑造了温柔、善良、理想的美的女性形象,表达了诗人自己对于美好事物的追求。该文拟选取德国功能翻译派的文本类型理论这一新视角,对该诗的两个汉译本《她身披美丽而行》和《伊人倩影》做出对比分析,从而得出赖斯提出的文本类型理论不仅可以指导诗歌翻译的翻译策略和方法,也对诗歌不同译本的评析具有重要的意义。展开更多
We establish a relation between the number of semi-edge walks of a connected graph and the number of walks of two auxiliary graphs. In addition, this relation gives upper bounds on the signless Laplacian spectral radi...We establish a relation between the number of semi-edge walks of a connected graph and the number of walks of two auxiliary graphs. In addition, this relation gives upper bounds on the signless Laplacian spectral radius of connected graphs and planar graphs.展开更多
This article aims to provide a review on quantum walks. Starting form a basic idea of discrete-time quantum walks, we will review the impact of disorder and decoherence on the properties of quantum walks. The evolutio...This article aims to provide a review on quantum walks. Starting form a basic idea of discrete-time quantum walks, we will review the impact of disorder and decoherence on the properties of quantum walks. The evolution of the standard quantum walks is deterministic and disorder introduces randomness to the whole system and change interference pattern leading to the localization effect. Whereas, decoherence plays the role of transmitting quantum walks to classical random walks.展开更多
We study the entanglement between the internal(coin)and the external(position)degrees of freedom in the dynamic and the static deterministic aperiodic quantum walks(QWs).For the dynamic(static)aperiodic QWs,the coin d...We study the entanglement between the internal(coin)and the external(position)degrees of freedom in the dynamic and the static deterministic aperiodic quantum walks(QWs).For the dynamic(static)aperiodic QWs,the coin depends on the time(position)and takes two coins C(α)and C(β)arranged in the two classes of generalized Fibonacci(GF)and the Thue–Morse(TM)sequences.We found that for the dynamic QWs,the entanglement of three kinds of the aperiodic QWs are close to the maximal value,which are all much larger than that of the homogeneous QWs.Further,the first class of GF(1st GF)QWs can achieve the maximum entangled state,which is similar to that of the dynamic disordered QWs.And the entanglement of 1st GF QWs is greater than that of the TM QWs,being followed closely by the entanglement of the second class of GF(2nd GF)QWs.For the static QWs,the entanglement of three kinds of the aperiodic QWs are also close to the maximal value and 1st GF QWs can achieve the maximum entangled state.The entanglement of the TM QWs is between1st GF QWs and 2nd GF QWs.However,the entanglement of the static disordered QWs is less than that of three kinds of the aperiodic QWs.This is different from those of the dynamic QWs.From these results,we can conclude that the dynamic and static 1st GF QWs can also be considered as maximal entanglement generators.展开更多
We analyze the process of a discrete-time quantum walk over 4 steps and 5 positions with linear optics elements. The quantum walk is characterized by a ballistic spread of wavepackets along 4 steps. By employing diffe...We analyze the process of a discrete-time quantum walk over 4 steps and 5 positions with linear optics elements. The quantum walk is characterized by a ballistic spread of wavepackets along 4 steps. By employing different initial coin states, we observe non-Gaussian distribution of the walkers＇ finial position, which characterizes a quadratic enhancement of the spread of photon wavepackets compared to a classical random walk. By introducing controllable decoherence, we observe the quantum-to-classical transmission in a quantum walk architecture.展开更多
The properties of the two-dimensional quantum walk with point, line, and circle disorders in phase are reported.Localization is observed in the two-dimensional quantum walk with certain phase disorder and specific ini...The properties of the two-dimensional quantum walk with point, line, and circle disorders in phase are reported.Localization is observed in the two-dimensional quantum walk with certain phase disorder and specific initial coin states.We give an explanation of the localization behavior via the localized stationary states of the unitary operator of the walker＋ coin system and the overlap between the initial state of the whole system and the localized stationary states.展开更多
Quantum walks act in obviously different ways from their classical counterparts, but decoherence will lessen and close this gap between them. To understand this process, it is necessary to investigate the evolution of...Quantum walks act in obviously different ways from their classical counterparts, but decoherence will lessen and close this gap between them. To understand this process, it is necessary to investigate the evolution of quantum walks under different decoherence situations. In this article, we study a non-Markovian decoherent quantum walk on a line. In a short time regime, the behavior of the walk deviates from both ideal quantum walks and classical random walks. The position variance as a measure of the quantum walk collapses and revives for a short time, and tends to have a linear relation with time. That is, the walker’s behavior shows a diffusive spread over a long time limit, which is caused by non-Markovian dephasing affecting the quantum correlations between the quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of the quantum correlations, and observe both collapse and revival in the short time regime, and the tendency to be zero in the long time limit. Therefore, quantum walks with non-Markovian decoherence tend to have diffusive spreading behavior over long time limits, while in the short time regime they oscillate between ballistic and diffusive spreading behavior, and the quantum correlation collapses and revives due to the memory effect.展开更多
We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probabili...We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probability distribution vectors of quantum walks in infinite and finite graphs in the presence of static disorder respectively, and get the distance between these two vectors. We find that when the steps taken are small and the boundary condition is tight, the localization between the infinite and finite cases is greatly different. However, the difference is negligible when the steps taken are large or the boundary condition is loose. It means quantum walks on a one-dimensional finite graph may also suffer from localization in the presence of static disorder. Our approach and results can be generalized to analyze the localization of quantum walks in higher-dimensional cases.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11671145)the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000).
文摘In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].
基金supported by the Key-Area Research and Development Program of Guang-Dong Province(Grant No.2018B030326001)the National Natural Science Foundation of China(U1801661)Shenzhen Science and Technology Program(KQTD20200820113010023)。
文摘Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science.The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated by walks.Quantum walks show promise for faster mixing times than classical methods but lack universal proof,especially in finite group settings.Here,we investigate the continuous-time quantum walks on Cayley graphs of the dihedral group D_(2n)for odd n,generated by the smallest inverse closed symmetric subset.We present a significant finding that,in contrast to the classical mixing time on these Cayley graphs,which typically takes at least orderΩ(n^(2)log(1/2∈)),the continuous-time quantum walk mixing time on D_(2n)is of order O(n(log n)^(5)log(1/∈)),achieving a quadratic improvement over the classical case.Our paper advances the general understanding of quantum walk mixing on Cayley graphs,highlighting the improved mixing time achieved by continuous-time quantum walks on D_(2n).This work has potential applications in algorithms for a class of sampling problems based on non-abelian groups.
文摘BACKGROUND:Hemiplegia,a prevalent stroke-related condition,is often studied for motor dysfunction;however,spasticity remains under-researched.Abnormal muscle tone significantly hinders hemiplegic patients’walking recovery.OBJECTIVE:To determine whether early suspension-protected training with a personal assistant machine for stroke patients enhances walking ability and prevents muscle spasms.METHODS:Thirty-two early-stage stroke patients from Shenzhen University General Hospital and the China Rehabilitation Research Center were randomly assigned to the experimental group(n=16)and the control group(n=16).Both groups underwent 4 weeks of gait training under the suspension protection system for 30 minutes daily,5 days a week.The experimental group used the personal assistant machine during training.Three-dimensional gait analysis(using the Cortex motion capture system),Brunnstrom staging,Fugl-Meyer Assessment for lower limb motor function,Fugl-Meyer balance function,and the modified Ashworth Scale were evaluated within 1 week before the intervention and after 4 weeks of intervention.RESULTS AND CONCLUSION:After the 4-week intervention,all outcome measures showed significant changes in each group.The experimental group had a small but significant increase in the modified Ashworth Scale score(P<0.05,d=|0.15|),while the control group had a large significant increase(P<0.05,d=|1.48|).The experimental group demonstrated greater improvements in walking speed(16.5 to 38.44 cm/s,P<0.05,d=|4.01|),step frequency(46.44 to 64.94 steps/min,P<0.05,d=|2.32|),stride length(15.50 to 29.81 cm,P<0.05,d=|3.44|),and peak hip and knee flexion(d=|1.82|to|2.17|).After treatment,the experimental group showed significantly greater improvements than the control group in walking speed(38.44 vs.26.63 cm/s,P<0.05,d=|2.75|),stride length,peak hip and knee flexion(d=|1.31|to|1.45|),step frequency(64.94 vs.59.38 steps/min,P<0.05,d=|0.85|),and a reduced support phase(bilateral:24.31%vs.28.38%,P<0.05,d=|0.88|;non-paretic:66.19%vs.70.13%,P<0.05,d=|0.94|).For early hemiplegia,personal assistant machine-assisted gait training under the suspension protection system helps establish a correct gait pattern,prevents muscle spasms,and improves motor function.
基金supported by the Fundamental Research Funds for the Central Universities,the National Natural Science Foundation of China(Grant Nos.12371132,12075159,12171044,12071179,and 12405006)the specific research fund of the Innovation Platform for Academicians of Hainan Province.
文摘Quantum algorithms have demonstrated provable speedups over classical counterparts,yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge.In this work,we decode the quantum search advantage by investigating the critical role of quantum state properties in random-walk-based algorithms.We propose three distinct variants of quantum random-walk search algorithms and derive exact analytical expressions for their success probabilities.These probabilities are fundamentally determined by specific initial state properties:the coherence fraction governs the first algorithm’s performance,while entanglement and coherence dominate the outcomes of the second and third algorithms,respectively.We show that increased coherence fraction enhances success probability,but greater entanglement and coherence reduce it in the latter two cases.These findings reveal fundamental insights into harnessing quantum properties for advantage and guide algorithm design.Our searches achieve Grover-like speedups and show significant potential for quantum-enhanced machine learning.
基金Project supported by the Research Foundation of Hangzhou Dianzi University,China (Grant Nos. KYF075610032 andzx100204004-7)the Hong Kong Research Grants Council,China (Grant No. CityU 1114/11E)
文摘In this paper, we study the scaling for the mean first-passage time （MFPT） of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from a triangle to a polygon, we obtain the exact scaling for the MFPT. We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order. In addition, we determine the exponents of scaling efficiency characterizing the random walks. Our results are the generalizations of those derived for the Koch network, which shed light on the analysis of random walks over various fractal networks.
基金the National High Technology Research and Development(863)Program of China(No.2015AA043701)
文摘Complex networks display community structures. Nodes within groups are densely connected but among groups are sparsely connected. In this paper, an algorithm is presented for community detection named Markov Random Walks Ants(MRWA). The algorithm is inspired by Markov random walks model theory, and the probability of ants located in any node within a cluster will be greater than that located outside the cluster.Through the random walks, the network structure is revealed. The algorithm is a stochastic method which uses the information collected during the traverses of the ants in the network. The algorithm is validated on different datasets including computer-generated networks and real-world networks. The outcome shows the algorithm performs moderately quickly when providing an acceptable time complexity and its result appears good in practice.
基金Project supported by the National Key R&D Program of China(Grant No.2020YFB1805405)the 111 Project(Grant No.B21049)+1 种基金the Foundation of Guizhou Provincial Key Laboratory of Public Big Data(Grant No.2019BDKFJJ014)the Fundamental Research Funds for the Central Universities,China(Grant No.2020RC38)。
文摘We propose an efficient quantum private comparison protocol firstly based on one direction quantum walks.With the help of one direction quantum walk,we develop a novel method that allows the semi-honest third party to set a flag to judge the comparing result,which improves the qubit efficiency and the maximum quantity of the participants’secret messages.Besides,our protocol can judge the size of the secret messages,not only equality.Furthermore,the quantum walks particle is disentangled in the initial state.It only requires a quantum walks operator to move,making our proposed protocol easy to implement and reducing the quantum resources.Through security analysis,we prove that our protocol can withstand well-known attacks and brute-force attacks.Analyses also reveal that our protocol is correct and practical.
基金supported by the Granular Chaos projectfunded by the Italian MIUR under Grant No.RIBD08Z9JE
文摘We consider a broad class of Continuous Time Random Walks(CTRW) with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials,and a L′evy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.
文摘She Walks in Beauty是英国著名诗人拜伦脍炙人口的一首抒情诗,塑造了温柔、善良、理想的美的女性形象,表达了诗人自己对于美好事物的追求。该文拟选取德国功能翻译派的文本类型理论这一新视角,对该诗的两个汉译本《她身披美丽而行》和《伊人倩影》做出对比分析,从而得出赖斯提出的文本类型理论不仅可以指导诗歌翻译的翻译策略和方法,也对诗歌不同译本的评析具有重要的意义。
基金Supported by GRF of Hong Kong(Grant No.HKBU202413)FRG of Hong Kong Baptist University(Grant No.FRG2/14-15/012)
文摘We establish a relation between the number of semi-edge walks of a connected graph and the number of walks of two auxiliary graphs. In addition, this relation gives upper bounds on the signless Laplacian spectral radius of connected graphs and planar graphs.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11004029 and 11174052)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2010422)+3 种基金the Ph.D.Program of the Ministry of Education of Chinathe Excellent Young Teachers Program of Southeast University of Chinathe National Basic Research Program of China(Grant No.2011CB921203)the Open Fund from the State Key Laboratory of Precision Spectroscopy of East China Normal University
文摘This article aims to provide a review on quantum walks. Starting form a basic idea of discrete-time quantum walks, we will review the impact of disorder and decoherence on the properties of quantum walks. The evolution of the standard quantum walks is deterministic and disorder introduces randomness to the whole system and change interference pattern leading to the localization effect. Whereas, decoherence plays the role of transmitting quantum walks to classical random walks.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575087 and 11175087)
文摘We study the entanglement between the internal(coin)and the external(position)degrees of freedom in the dynamic and the static deterministic aperiodic quantum walks(QWs).For the dynamic(static)aperiodic QWs,the coin depends on the time(position)and takes two coins C(α)and C(β)arranged in the two classes of generalized Fibonacci(GF)and the Thue–Morse(TM)sequences.We found that for the dynamic QWs,the entanglement of three kinds of the aperiodic QWs are close to the maximal value,which are all much larger than that of the homogeneous QWs.Further,the first class of GF(1st GF)QWs can achieve the maximum entangled state,which is similar to that of the dynamic disordered QWs.And the entanglement of 1st GF QWs is greater than that of the TM QWs,being followed closely by the entanglement of the second class of GF(2nd GF)QWs.For the static QWs,the entanglement of three kinds of the aperiodic QWs are also close to the maximal value and 1st GF QWs can achieve the maximum entangled state.The entanglement of the TM QWs is between1st GF QWs and 2nd GF QWs.However,the entanglement of the static disordered QWs is less than that of three kinds of the aperiodic QWs.This is different from those of the dynamic QWs.From these results,we can conclude that the dynamic and static 1st GF QWs can also be considered as maximal entanglement generators.
基金supported by the National Natural Science Foundation of China(Grant Nos.11174052 and 11474049)the National Basic Research Development Program of China(Grant No.2011CB921203)the Open Fund from the State Key Laboratory of Precision Spectroscopy of East China Normal University,China
文摘We analyze the process of a discrete-time quantum walk over 4 steps and 5 positions with linear optics elements. The quantum walk is characterized by a ballistic spread of wavepackets along 4 steps. By employing different initial coin states, we observe non-Gaussian distribution of the walkers＇ finial position, which characterizes a quadratic enhancement of the spread of photon wavepackets compared to a classical random walk. By introducing controllable decoherence, we observe the quantum-to-classical transmission in a quantum walk architecture.
基金Project supported by the National Natural Science Foundation of China(Grant No.11174052)the National Basic Research Program of China(Grant No.2011CB921203)the Open Fund from the State Key Laboratory of Precision Spectroscopy of East China Normal University
文摘The properties of the two-dimensional quantum walk with point, line, and circle disorders in phase are reported.Localization is observed in the two-dimensional quantum walk with certain phase disorder and specific initial coin states.We give an explanation of the localization behavior via the localized stationary states of the unitary operator of the walker＋ coin system and the overlap between the initial state of the whole system and the localized stationary states.
基金the National Natural Science Foundation of China(Grant Nos.10974192,11004029,and 11174052)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2010422)+2 种基金the Ph.D.Program of the Ministry of Education of Chinathe Excellent Young Teachers Program of Southeast University,Chinathe National Basic Research Program of China(Grant No.2011CB921203)
文摘Quantum walks act in obviously different ways from their classical counterparts, but decoherence will lessen and close this gap between them. To understand this process, it is necessary to investigate the evolution of quantum walks under different decoherence situations. In this article, we study a non-Markovian decoherent quantum walk on a line. In a short time regime, the behavior of the walk deviates from both ideal quantum walks and classical random walks. The position variance as a measure of the quantum walk collapses and revives for a short time, and tends to have a linear relation with time. That is, the walker’s behavior shows a diffusive spread over a long time limit, which is caused by non-Markovian dephasing affecting the quantum correlations between the quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of the quantum correlations, and observe both collapse and revival in the short time regime, and the tendency to be zero in the long time limit. Therefore, quantum walks with non-Markovian decoherence tend to have diffusive spreading behavior over long time limits, while in the short time regime they oscillate between ballistic and diffusive spreading behavior, and the quantum correlation collapses and revives due to the memory effect.
基金Project supported by the National Natural Science Foundation of China(Grant No.11174370)
文摘We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probability distribution vectors of quantum walks in infinite and finite graphs in the presence of static disorder respectively, and get the distance between these two vectors. We find that when the steps taken are small and the boundary condition is tight, the localization between the infinite and finite cases is greatly different. However, the difference is negligible when the steps taken are large or the boundary condition is loose. It means quantum walks on a one-dimensional finite graph may also suffer from localization in the presence of static disorder. Our approach and results can be generalized to analyze the localization of quantum walks in higher-dimensional cases.
