Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2203.04108

Comfortable place for quantum walkers on finite path

Yoshihiro Anahara, Norio Konno, Hisashi Morioka, Etsuo Segawa

Published Mar 8, 2022• 0 citations
arXivHTMLPDF

Abstract

We consider the stationary state of a quantum walk on the finite path, where the sink and source are set at the left and right boundaries. The quantum coin is uniformly placed at every vertex of the path graph. At every time step, a new quantum walker penetrates into the internal from the left boundary and also some existing quantum walkers in the internal goes out to the sinks located in the left and right boundaries. The square modulus of the stationary state at each vertex is regarded as the comfortability for a quantum walker to this vertex in this paper. We show the weak convergence theorem for the scaled limit distribution of the comfortability in the limit of the length of the path.

DOI
10.48550/arxiv.2203.04108

Related papers

A comfortable graph structure for Grover walk

Yusuke Higuchi, Mohamed Sabri, Etsuo Segawa

Abstract We consider a Grover walk model on a finite internal graph, which is connected with a finite number of semi-infinite length paths and receives the alternative inflows along these paths at each time step. After the long time scale, we know that the behavior of such a Grover walk should be stable, that is, this model has a stationary state. In this paper our objectives are to give some characterization upon the scattering of the stationary state on the surface of the internal graph and upon the energy of this state in the interior. For the scattering, we concretely give a scattering matrix, whose form is changed depending on whether the internal graph is bipartite or not. On the other hand, we introduce a comfortability function of a graph for the quantum walk, which shows how many quantum walkers can stay in the interior, and we succeed in showing the comfortability of the walker in terms of combinatorial properties of the internal graph.

arXiv:2201.01926•Journal of Physics A Mathematical and Theoretical•May 19, 2023•1 citation

A convergence time of Grover walk on regular graph to stationary state

Ayaka Ishikawa, Sho Kubota, Etsuo Segawa

We consider a quantum walk model on a finite graph which has an interaction with the outside. Here a quantum walker from the outside penetrates the graph and also a quantum walker in the graph goes out to the outside at every time step. This dynamics of the quantum walk converges to a stationary state. In this paper, we estimate the speed of the convergence to the stationary state on the $κ$-regular graph with the uniformly inserting of the inflow to the graph. We show that larger degree of the regular graph makes the convergence speed of this quantum walk model slower.

arXiv:2210.08420•Oct 16, 2022•0 citations

A convergence time of Grover walk on regular graph to stationary state with constant inflow to every vertex

Ayaka Ishikawa, Sho Kubota, Etsuo Segawa

We consider a quantum walk model on a finite graph which has an interaction with the outside. Here a quantum walker from the outside penetrates the graph and also a quantum walker in the graph goes out to the outside at every time step. This dynamics of the quantum walk converges to a stationary state. In this paper, we estimate the speed of the convergence to the stationary state on the κ-regular graph with the uniform insertion of the inflow to the graph. We show that larger degree of the regular graph makes the convergence time of this quantum walk model slower under this set-up.

Linear and Multilinear Algebra•Oct 13, 2023•0 citations

Non-stationary quantum walks on the cycle

Domenico D’Alessandro, Gianfranco Parlangeli, Francesca Albertini

We consider quantum walks on the cycle in the non-stationary case where the 'coin' operation is allowed to change at each time step. We characterize, in algebraic terms, the set of possible state transfers and prove that, as opposed to the stationary case, the associate probability distribution may converge to a uniform distribution among the nodes of the associated graph.

arXiv:0708.0184•Journal of Physics A Mathematical and Theoretical•Nov 14, 2007•13 citations

Conditional limit measure of a one-dimensional quantum walk with an absorbing sink

Mohamed Sabri, Etsuo Segawa, M. Štefaňák

We consider a two-state quantum walk on a line where after the first step an absorbing sink is placed at the origin. The probability of finding the walker at position $j$, conditioned on that it has not returned to the origin, is investigated in the asymptotic limit. We prove a limit theorem for the conditional probability distribution and show that it is given by the Konno's density function modified by a prefactor ensuring that the distribution vanishes at the origin. In addition, we discuss the relation to the problem of recurrence of a quantum walk and determine the P\'olya number. Our approach is based on path counting and the stationary phase approximation.

arXiv:1807.02765•Physical Review A•Jul 27, 2018•4 citations

Quantum Walkers and Diffusion

John C Vining, Howard A. Blair

Quantum walks model the behavior of a quantum state traversing a classically defined, generally finite, graph structure. This paper introduces blind quantum diffusion, a technique for evolving quantum walkers through a finite connected network without requiring global knowledge of the graph. We frame the multi-walker problem as a finite quantum cellular automaton where each vertex holds a walker at all times. These walkers will never collide as their vertex position is superpositioned by the network’s evolution and at each time step their positions update by conditioning swaps on quantum coins and partial comparators of the neighboring states. This model generates strong entanglement between vertex states providing a path toward structure independent diffusion driven by highly localized computation. We will examine some mathematical structures underlying state diffusion on arbitrary graphs such as the commutativity of operations and expected time for walkers to reach specified destinations.

International Conference on Quantum Communications, Networking, and Computing (QCNC)•Mar 31, 2025•0 citations
We consider the stationary state of a quantum walk on the finite path, where the sink and source are set at the left and right boundaries. The quantum coin is uniformly placed at every vertex of the path graph. At every time step, a new quantum walker penetrates into the internal from the left boundary and also some existing quantum walkers in the internal goes out to the sinks located in the left and right boundaries. The square modulus of the stationary state at each vertex is regarded as the comfortability for a quantum walker to this vertex in this paper. We show the weak convergence theorem for the scaled limit distribution of the comfortability in the limit of the length of the path.
Abstract We consider a Grover walk model on a finite internal graph, which is connected with a finite number of semi-infinite length paths and receives the alternative inflows along these paths at each time step. After the long time scale, we know that the behavior of such a Grover walk should be stable, that is, this model has a stationary state. In this paper our objectives are to give some characterization upon the scattering of the stationary state on the surface of the internal graph and upon the energy of this state in the interior. For the scattering, we concretely give a scattering matrix, whose form is changed depending on whether the internal graph is bipartite or not. On the other hand, we introduce a comfortability function of a graph for the quantum walk, which shows how many quantum walkers can stay in the interior, and we succeed in showing the comfortability of the walker in terms of combinatorial properties of the internal graph.
We consider a quantum walk model on a finite graph which has an interaction with the outside. Here a quantum walker from the outside penetrates the graph and also a quantum walker in the graph goes out to the outside at every time step. This dynamics of the quantum walk converges to a stationary state. In this paper, we estimate the speed of the convergence to the stationary state on the κκκ-regular graph with the uniformly inserting of the inflow to the graph. We show that larger degree of the regular graph makes the convergence speed of this quantum walk model slower.
We consider a quantum walk model on a finite graph which has an interaction with the outside. Here a quantum walker from the outside penetrates the graph and also a quantum walker in the graph goes out to the outside at every time step. This dynamics of the quantum walk converges to a stationary state. In this paper, we estimate the speed of the convergence to the stationary state on the κ-regular graph with the uniform insertion of the inflow to the graph. We show that larger degree of the regular graph makes the convergence time of this quantum walk model slower under this set-up.
We consider a two-state quantum walk on a line where after the first step an absorbing sink is placed at the origin. The probability of finding the walker at position jjj, conditioned on that it has not returned to the origin, is investigated in the asymptotic limit. We prove a limit theorem for the conditional probability distribution and show that it is given by the Konno's density function modified by a prefactor ensuring that the distribution vanishes at the origin. In addition, we discuss the relation to the problem of recurrence of a quantum walk and determine the P\'olya number. Our approach is based on path counting and the stationary phase approximation.
Quantum walks model the behavior of a quantum state traversing a classically defined, generally finite, graph structure. This paper introduces blind quantum diffusion, a technique for evolving quantum walkers through a finite connected network without requiring global knowledge of the graph. We frame the multi-walker problem as a finite quantum cellular automaton where each vertex holds a walker at all times. These walkers will never collide as their vertex position is superpositioned by the network’s evolution and at each time step their positions update by conditioning swaps on quantum coins and partial comparators of the neighboring states. This model generates strong entanglement between vertex states providing a path toward structure independent diffusion driven by highly localized computation. We will examine some mathematical structures underlying state diffusion on arbitrary graphs such as the commutativity of operations and expected time for walkers to reach specified destinations.