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:1412.1022 · Physical Review A

Perfect quantum state transfer of hard-core bosons on weighted path graphs

Steven J. Large, Michael S. Underwood, David L. Feder

Published Mar 24, 2015• 4 citations
arXivHTMLPDF

Abstract

The ability to accurately transfer quantum information through networks is an important primitive in distributed quantum systems. While perfect quantum state transfer (PST) can be effected by a single particle undergoing continuous-time quantum walks on a variety of graphs, it is not known if PST persists for many particles in the presence of interactions. We show that if single-particle PST occurs on one-dimensional weighted path graphs, then systems of hard-core bosons undergoing quantum walks on these paths also undergo PST. The analysis extends the Tonks-Girardeau ansatz to weighted graphs using techniques in algebraic graph theory. The results suggest that hard-core bosons do not generically undergo PST, even on graphs which exhibit single-particle PST.

DOI
10.1103/physreva.91.032319

Related papers

State Transfer in Complex Quantum Walks

Antonio Acuaviva, Ada Chan, Eldridge, Summer +5 more

Given a graph with Hermitian adjacency matrix $H$, perfect state transfer occurs from vertex $a$ to vertex $b$ if the $(b,a)$-entry of the unitary matrix $\exp(-iHt)$ has unit magnitude for some time $t$. This phenomenon is relevant for information transmission in quantum spin networks and is known to be monogamous under real symmetric matrices. We prove the following results: 1. For oriented graphs (whose nonzero weights are $\pm i$), the oriented $3$-cycle and the oriented edge are the only graphs where perfect state transfer occurs between every pair of vertices. This settles a conjecture of Cameron et al. On the other hand, we construct an infinite family of oriented graphs with perfect state transfer between any pair of vertices on a subset of size four. 2. There are infinite families of Hermitian graphs with one-way perfect state transfer, where perfect state transfer occurs without periodicity. In contrast, perfect state transfer implies periodicity whenever the adjacency matrix has algebraic entries (as shown by Godsil). 3. There are infinite families with non-monogamous pretty good state transfer in rooted graph products. In particular, we generalize known results on double stars (due to Fan and Godsil) and on paths with loops (due to Kempton, Lippner and Yau). The latter extends the experimental observation of quantum transport (made by Zimborás et al.) and shows non-monogamous pretty good state transfer can occur amongst distant vertices.

arXiv:2301.01473•Jan 4, 2023•0 citations

Perfect State Transfer in Weighted Cubelike Graphs

Jaideep Mulherkar, Rishikant Rajdeepak, V. Sunitha

A continuous-time quantum random walk describes the motion of a quantum mechanical particle on an underlying graph. The graph itself is associated with a Hilbert space of dimension equal to the number of vertices. The dynamics of the walk is governed by the unitary operator $\mathcal{U}(t) = e^{iAt}$, where $A$ is the adjacency matrix of the graph. An important notion in the quantum random walk is the transfer of a quantum state from one vertex to another. If the fidelity of the transfer is unity, we call it a perfect state transfer. Many graph families have been shown to admit PST or periodicity, including cubelike graphs. These graphs are unweighted. In this paper, we generalize the PST or periodicity of cubelike graphs to that of weighted cubelike graphs. We characterize the weights for which they admit PST or show periodicity, both at time $t=\fracπ{2}$.

arXiv:2109.12607•Sep 26, 2021•0 citations

Perfect State Transfer in Quantum Walks on Graphs

Viv M. Kendon, Christino Tamon

We provide a brief survey of perfect state transfer in quantum walks on finite graphs. The ability to transfer a quantum state from one part of a quantum computer to another is a key ingredient of scalable architectures. Transfer through structures that do not require locally varying dynamic control simplifies the design and hence reduces the opportunities for errors to arise. Continuous time walks quantum walks on highly structured graphs exhibit perfect state transfer for the complete graph of size 2, the path of length 3, and the cycle of size 4. From these, larger graphs can be constructed, and the use of edge weights widens this set considerably. Discrete-time quantum walks have more flexibility through exploiting the coin degrees of freedom, but with the disadvantage that local control of the coin is required if the degree of the vertices varies. The closely related property of periodicity (exact return to the starting state) is also mentioned.

Journal of Computational and Theoretical Nanoscience•Mar 1, 2011•109 citations

Peak state transfer in continuous quantum walks

Gabriel Coutinho, Krystal Guo, Vincent Schmeits

We introduce and study peak state transfer, a notion of high state transfer in qubit networks modeled by continuous-time quantum walks. Unlike perfect or pretty good state transfer, peak state transfer does not require fidelity arbitrarily close to 1, but crucially allows for an explicit determination of the time at which transfer occurs. We provide a spectral characterization of peak state transfer, which allows us to find many examples of peak state transfer, and we also establish tight lower bounds on fidelity and success probability. As a central example, we construct a family of weighted path graphs that admit peak state transfer over arbitrarily long distances with transfer probability approaching $π/4 \approx 0.78$. These graphs offer exponentially improved sensitivity over known perfect state transfer examples such as the weighted paths related to hypercubes, making them practical candidates for efficient quantum wires.

arXiv:2505.11986•May 17, 2025•0 citations

Quantum Walks on Graphs: Group State Transfer

Luke C. Brown

Graphs that exhibit perfect state transfer (PST), by which a quantum walk beginning at one vertex is guaranteed to end at another after a nonzero displacement in time, are of great interest to researchers in the field of quantum computing. The conditions imposed by PST are strong, and many of the graphs that are known to exhibit PST are highly symmetric, which provides motivation to relax the restrictions imposed by perfect state transfer. This project introduces the property of group state transfer (GST), by which quantum walks are guaranteed to transfer states between nontrivial vertex sets. We define GST, examine its implications for finite simple graphs, and provide examples of graphs that exhibit GST.

•Apr 24, 2019•0 citations

Symmetric perfect state transfer on bipartite graphs

Xi Li, Xiao Chen, Shouwei Hu +1 more

Abstract Continuous-time quantum walks (CTQW) becoming more significant for quantum information and quantum computation. The perfect state transfer (PST) on graphs is a specific phenomena of CTQW which is widely used in quantum communication of small system, and be found critical for quantum algorithm design recently, such as quantum approximate optimization algorithms and quantum search. If a network $G$ contains $2N$ vertices, and PST occurs between $N$ pairs of vertices at the same time $T$, then we say $G$ admits symmetric PST (SPST). In this work, we will study the SPST on bipartite graphs via spectra. And then, we will present how to set couplings of special bipartite graphs such as cycles, grids and chains to admit SPST is given. For cycles with 6, 8, 10, 12 vertices, we give the analytical method to obtain the couplings to admit SPST. Analogously, the couplings for chains and grids to admit SPST are analytical obtained. We also present a typical approach by using the graph tensor product to construct new quantum networks that admit SPST, in which the new quantum networks are derived from special kinds of integral graphs, such as complete graphs, strongly regular graphs and distance regular graphs.

•Apr 15, 2024•0 citations
The ability to accurately transfer quantum information through networks is an important primitive in distributed quantum systems. While perfect quantum state transfer (PST) can be effected by a single particle undergoing continuous-time quantum walks on a variety of graphs, it is not known if PST persists for many particles in the presence of interactions. We show that if single-particle PST occurs on one-dimensional weighted path graphs, then systems of hard-core bosons undergoing quantum walks on these paths also undergo PST. The analysis extends the Tonks-Girardeau ansatz to weighted graphs using techniques in algebraic graph theory. The results suggest that hard-core bosons do not generically undergo PST, even on graphs which exhibit single-particle PST.
Given a graph with Hermitian adjacency matrix HHH, perfect state transfer occurs from vertex aaa to vertex bbb if the (b,a)(b,a)(b,a)-entry of the unitary matrix exp⁡(−iHt)\exp(-iHt)exp(−iHt) has unit magnitude for some time ttt. This phenomenon is relevant for information transmission in quantum spin networks and is known to be monogamous under real symmetric matrices. We prove the following results: 1. For oriented graphs (whose nonzero weights are ±i\pm i±i), the oriented 333-cycle and the oriented edge are the only graphs where perfect state transfer occurs between every pair of vertices. This settles a conjecture of Cameron et al. On the other hand, we construct an infinite family of oriented graphs with perfect state transfer between any pair of vertices on a subset of size four. 2. There are infinite families of Hermitian graphs with one-way perfect state transfer, where perfect state transfer occurs without periodicity. In contrast, perfect state transfer implies periodicity whenever the adjacency matrix has algebraic entries (as shown by Godsil). 3. There are infinite families with non-monogamous pretty good state transfer in rooted graph products. In particular, we generalize known results on double stars (due to Fan and Godsil) and on paths with loops (due to Kempton, Lippner and Yau). The latter extends the experimental observation of quantum transport (made by Zimborás et al.) and shows non-monogamous pretty good state transfer can occur amongst distant vertices.
A continuous-time quantum random walk describes the motion of a quantum mechanical particle on an underlying graph. The graph itself is associated with a Hilbert space of dimension equal to the number of vertices. The dynamics of the walk is governed by the unitary operator U(t)=eiAt\mathcal{U}(t) = e^{iAt}U(t)=eiAt, where AAA is the adjacency matrix of the graph. An important notion in the quantum random walk is the transfer of a quantum state from one vertex to another. If the fidelity of the transfer is unity, we call it a perfect state transfer. Many graph families have been shown to admit PST or periodicity, including cubelike graphs. These graphs are unweighted. In this paper, we generalize the PST or periodicity of cubelike graphs to that of weighted cubelike graphs. We characterize the weights for which they admit PST or show periodicity, both at time t=π2t=\fracπ{2}t=2π​.
We provide a brief survey of perfect state transfer in quantum walks on finite graphs. The ability to transfer a quantum state from one part of a quantum computer to another is a key ingredient of scalable architectures. Transfer through structures that do not require locally varying dynamic control simplifies the design and hence reduces the opportunities for errors to arise. Continuous time walks quantum walks on highly structured graphs exhibit perfect state transfer for the complete graph of size 2, the path of length 3, and the cycle of size 4. From these, larger graphs can be constructed, and the use of edge weights widens this set considerably. Discrete-time quantum walks have more flexibility through exploiting the coin degrees of freedom, but with the disadvantage that local control of the coin is required if the degree of the vertices varies. The closely related property of periodicity (exact return to the starting state) is also mentioned.
We introduce and study peak state transfer, a notion of high state transfer in qubit networks modeled by continuous-time quantum walks. Unlike perfect or pretty good state transfer, peak state transfer does not require fidelity arbitrarily close to 1, but crucially allows for an explicit determination of the time at which transfer occurs. We provide a spectral characterization of peak state transfer, which allows us to find many examples of peak state transfer, and we also establish tight lower bounds on fidelity and success probability. As a central example, we construct a family of weighted path graphs that admit peak state transfer over arbitrarily long distances with transfer probability approaching π/4≈0.78π/4 \approx 0.78π/4≈0.78. These graphs offer exponentially improved sensitivity over known perfect state transfer examples such as the weighted paths related to hypercubes, making them practical candidates for efficient quantum wires.
Graphs that exhibit perfect state transfer (PST), by which a quantum walk beginning at one vertex is guaranteed to end at another after a nonzero displacement in time, are of great interest to researchers in the field of quantum computing. The conditions imposed by PST are strong, and many of the graphs that are known to exhibit PST are highly symmetric, which provides motivation to relax the restrictions imposed by perfect state transfer. This project introduces the property of group state transfer (GST), by which quantum walks are guaranteed to transfer states between nontrivial vertex sets. We define GST, examine its implications for finite simple graphs, and provide examples of graphs that exhibit GST.
Abstract Continuous-time quantum walks (CTQW) becoming more significant for quantum information and quantum computation. The perfect state transfer (PST) on graphs is a specific phenomena of CTQW which is widely used in quantum communication of small system, and be found critical for quantum algorithm design recently, such as quantum approximate optimization algorithms and quantum search. If a network GGG contains 2N2N2N vertices, and PST occurs between NNN pairs of vertices at the same time TTT, then we say GGG admits symmetric PST (SPST). In this work, we will study the SPST on bipartite graphs via spectra. And then, we will present how to set couplings of special bipartite graphs such as cycles, grids and chains to admit SPST is given. For cycles with 6, 8, 10, 12 vertices, we give the analytical method to obtain the couplings to admit SPST. Analogously, the couplings for chains and grids to admit SPST are analytical obtained. We also present a typical approach by using the graph tensor product to construct new quantum networks that admit SPST, in which the new quantum networks are derived from special kinds of integral graphs, such as complete graphs, strongly regular graphs and distance regular graphs.