Scattering quantum walk search algorithm on star graph

Liu, Yanmei; Chen, Hanwu; Liu, Zhihao; Xue, Xiling; Zhu, Wanning

doi:10.7498/aps.64.010301

Cited by 8 publications

(3 citation statements)

References 12 publications

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“…[16,18] Quantum walk (QW) is widely applied in physics, quantum computation, quantum information theory, and so on. [19][20][21][22][23][24][25][26][27][28][29][30] QW that we discuss is the discrete-time QW. Using the quantum coin and the "flip operations" instead of flipping the coin as in CW, the walker moves on a line in a discrete manner through the moving operations.…”

Section: Introductionmentioning

confidence: 99%

Quantum walk under coherence non-generating channels*

Chen¹,

Hu²

2021

Chinese Phys. B

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We investigate the probability distribution of the quantum walk under coherence non-generating channels. We define a model called generalized classical walk with memory. Under certain conditions, generalized classical random walk with memory can degrade into classical random walk and classical random walk with memory. Based on its various spreading speed, the model may be a useful tool for building algorithms. Furthermore, the model may be useful for measuring the quantumness of quantum walk. The probability distributions of quantum walks are generalized classical random walks with memory under a class of coherence non-generating channels. Therefore, we can simulate classical random walk and classical random walk with memory by coherence non-generating channels. Also, we find that for another class of coherence non-generating channels, the probability distributions are influenced by the coherence in the initial state of the coin. Nevertheless, the influence degrades as the number of steps increases. Our results could be helpful to explore the relationship between coherence and quantum walk.

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Section: Introductionmentioning

confidence: 99%

Quantum walk under coherence non-generating channels*

Chen¹,

Hu²

2021

Chinese Phys. B

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“…[8,9] Quantum walks have been proven to be a useful framework in designing new quantum algorithms, the most notable of which are search algorithms. [10][11][12][13][14][15][16][17] Recent research have focused on the analysis of quantum search algorithms' performance. It is generally difficult to quantify the dynamics of search algorithms.…”

Section: Introductionmentioning

confidence: 99%

Search algorithm on strongly regular graphs based on scattering quantum walk

Xue¹,

Liu²,

Chen³

2017

Chinese Phys. B

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Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs (SRGs) with parameters (N, k, λ , µ) achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm's performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs. The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as √ N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O( √ N) time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.

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“…An interesting zero failure rate quantum search algorithm based on this condition was subsequently proposed [29], and this algorithm has been applied in different directions, such as quantum pattern recognition [30], sliding mode control of quantum systems [31] and quantum image compression [32]. More ideas of enhancing the quantum search algorithm can be referred to [33][34][35][36][37]. Variants of the quantum search algorithm have also been proposed, such as quantum searching with continuous variables [38][39][40], the fixed point quantum search algorithm [41,42], the Hamiltonian search algorithm [40], etc.…”

Section: Introductionmentioning

confidence: 99%

HUANG XIANGYA, DDS,PHD, Senior Lecturer, Department of Conservative Dentistry & Endodontics, Guanghua School of Stomatology, Hospital of Stomatology, Sun Yat‐Sen University, Guangzhou, China

Huang

2015

Endodontic Topics

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With the development of deep learning techniques, AI-enhanced numerical solvers are expected to become a new paradigm for solving differential equations due to their versatility and effectiveness in alleviating the accuracy-speed trade-off in traditional numerical solvers. However, this paradigm still inevitably requires a large amount of high-quality data, whose acquisition is often very expensive in natural science and engineering problems. Therefore, in this paper, we explore training efficient and robust AI-enhanced numerical solvers with a small data size by mitigating intrinsic noise disturbances. We first analyze the ability of the self-attention mechanism to regulate noise in supervised learning and then propose a simple-yet-effective numerical solver, AttSolver, which introduces an additive self-attention mechanism to the numerical solution of differential equations based on the dynamical system perspective of the residual neural network. Our results on benchmarks, ranging from high-dimensional problems to chaotic systems, demonstrate the effectiveness of AttSolver in generally improving the performance of existing traditional numerical solvers without any elaborated model crafting. Finally, we analyze the convergence, generalization, and robustness of the proposed method experimentally and theoretically.

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Scattering quantum walk search algorithm on star graph

Cited by 8 publications

References 12 publications

Quantum walk under coherence non-generating channels*

Quantum walk under coherence non-generating channels*

Search algorithm on strongly regular graphs based on scattering quantum walk

HUANG XIANGYA, DDS,PHD, Senior Lecturer, Department of Conservative Dentistry & Endodontics, Guanghua School of Stomatology, Hospital of Stomatology, Sun Yat‐Sen University, Guangzhou, China

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