Hanmeng Zhan
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Hanmeng Zhan has a total of 28 co-authors. Here are the top co-authors by number of shared publications:
Ada Chan
Department of Mathematics and Statistics, York University, Toronto, ON, Canada
3 shared publications- Bojan Mohar
Department of Mathematics Simon Fraser University Burnaby British Columbia Canada
2 shared publications - Chris Godsil
Department of Combinatorics & Optimization University of Waterloo Waterloo Ontario Canada
2 shared publications Christino Tamon
2 shared publications- Gabriel Coutinho
Department of Computer Science, Federal University of Minas Gerais, Belo Horizonte, Minas Gerais 31270-901, Brazil
2 shared publications - Hitesh Kumar2 shared publications
Latest Publications
- 27 April 2026
- Published by Springer Nature in Quantum Information Processing
- Vol. 25 (5) , 153
Subspace state transfer in coined quantum walks
- 27 April 2026
- Published by Springer Nature in Quantum Information Processing
- Vol. 25 (5) , 153
Subspace state transfer in coined quantum walks
- Open Access
Convex combination of first and second eigenvalues of trees
For a graph $G$, let $λ_1(G)$ and $λ_2(G)$ denote the largest and the second largest adjacency eigenvalue of $G$. The sum $λ_1(G) + λ_2(G)$ is called the \emph{spectral sum} of $G$. We investigate the spectral sum of trees of order $n$ and determine the extremal trees that achieve maximum/minimum. Moreover, for any $α\in [0,1]$, we determine the extremal trees which maximize the convex combination $αλ_1 + (1-α)λ_2$ in the class of $n$-vertex trees.Open AccessConvex combination of first and second eigenvalues of trees
For a graph $G$, let $λ_1(G)$ and $λ_2(G)$ denote the largest and the second largest adjacency eigenvalue of $G$. The sum $λ_1(G) + λ_2(G)$ is called the \emph{spectral sum} of $G$. We investigate the spectral sum of trees of order $n$ and determine the extremal trees that achieve maximum/minimum. Moreover, for any $α\in [0,1]$, we determine the extremal trees which maximize the convex combination $αλ_1 + (1-α)λ_2$ in the class of $n$-vertex trees. - 9 October 2025
- Published by The Royal Society in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 383 (2306) , 20240418
Simple quantum coins enable pretty good state transfer on every hypercube
We consider pretty good state transfer in coined quantum walks between antipodal vertices on the hypercube Q d . When d is a prime, this was proven to occur in the arc-reversal walk with Grover coins. We extend this result by constructing weighted Grover coins that enable pretty good state transfer on every Q d . Our coins are real and require modification of the weight on only one arc per vertex. We also generalize our approach and establish a sufficient condition for pretty good state transfer to occur on other graphs. This article is part of the theme issue ‘Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms’.
- 9 October 2025
- Published by The Royal Society in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 383 (2306) , 20240418
Simple quantum coins enable pretty good state transfer on every hypercube
We consider pretty good state transfer in coined quantum walks between antipodal vertices on the hypercube Q d . When d is a prime, this was proven to occur in the arc-reversal walk with Grover coins. We extend this result by constructing weighted Grover coins that enable pretty good state transfer on every Q d . Our coins are real and require modification of the weight on only one arc per vertex. We also generalize our approach and establish a sufficient condition for pretty good state transfer to occur on other graphs. This article is part of the theme issue ‘Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms’.
- Open Access
- 9 October 2025
- Published by The Royal Society in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 383 (2306) , 20240426
Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms
Recent progress in quantum computing shows the need to incorporate many branches of mathematics (graph theory, matrix theory, optimization, theory of orthogonal polynomials and more) into physics, computer science and chemistry. At the 2024 SIAM Quantum Intersections Convening, Bert de Jong (Lawrence Berkeley National Laboratory) gave a talk entitled ‘Quantum Science Needs Mathematicians’ (Report of the SIAM Quantum Intersections Convening. Integrating Mathematical Scientists into Quantum Research, 7–9 October 2024, Tysons, Virginia ( doi: 10.11337/25M1741017 )), since despite the growing demand for research in these domains, the mathematical sciences community has remained largely disengaged from quantum research, with only a few isolated areas of active involvement. This issue brings together researchers from different areas of mathematics to show the relation between spectral graph theory, the theory of orthogonal polynomials and numerical analysis. This interconnectedness highlights the versatility and importance of these areas of mathematics in the context of quantum computing. This article is part of the theme issue ‘Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms’.
- 9 October 2025
- Published by The Royal Society in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 383 (2306) , 20240426
Open AccessNumerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms
Recent progress in quantum computing shows the need to incorporate many branches of mathematics (graph theory, matrix theory, optimization, theory of orthogonal polynomials and more) into physics, computer science and chemistry. At the 2024 SIAM Quantum Intersections Convening, Bert de Jong (Lawrence Berkeley National Laboratory) gave a talk entitled ‘Quantum Science Needs Mathematicians’ (Report of the SIAM Quantum Intersections Convening. Integrating Mathematical Scientists into Quantum Research, 7–9 October 2024, Tysons, Virginia ( doi: 10.11337/25M1741017 )), since despite the growing demand for research in these domains, the mathematical sciences community has remained largely disengaged from quantum research, with only a few isolated areas of active involvement. This issue brings together researchers from different areas of mathematics to show the relation between spectral graph theory, the theory of orthogonal polynomials and numerical analysis. This interconnectedness highlights the versatility and importance of these areas of mathematics in the context of quantum computing. This article is part of the theme issue ‘Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms’.
- 18 June 2025
- Published by Springer Nature in Journal of Algebraic Combinatorics
- Vol. 61 (4) , 1-35
$\epsilon $-Uniform mixing in discrete quantum walks- 18 June 2025
- Published by Springer Nature in Journal of Algebraic Combinatorics
- Vol. 61 (4) , 1-35
$\epsilon $-Uniform mixing in discrete quantum walks- Open Access
- 4 February 2025
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 710, 336-355
Subdivision and graph eigenvalues
- 4 February 2025
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 710, 336-355
Open AccessSubdivision and graph eigenvalues
- Open Access
- 3 October 2024
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 31 (4) , P4.10
Hamiltonians of Bipartite Walks
In this paper, we introduce a discrete quantum walk model called bipartite walks. Bipartite walks include many known discrete quantum walk models, like Grover’s walks, vertex-face walks. For the transition matrix of a quantum walk, there is a Hamiltonian associated with it. We will study the Hamiltonians of the bipartite walks. Let $S$ be a skew-symmetric matrix. We are mainly interested in the Hamiltonians of the form $iS$. We show that the Hamiltonian can be written as $iS$ if and only if the adjacency matrix of the bipartite graph is invertible. We show that Grover’s walks and vertex-face walks are special cases of bipartite walks. Via the Hamiltonians, phenomena of bipartite walks lead to phenomena of continuous walks. We show in detail how we use bipartite walks on paths to construct universal perfect state transfer in continuous walks.- 3 October 2024
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 31 (4) , P4.10
Open AccessHamiltonians of Bipartite Walks
In this paper, we introduce a discrete quantum walk model called bipartite walks. Bipartite walks include many known discrete quantum walk models, like Grover’s walks, vertex-face walks. For the transition matrix of a quantum walk, there is a Hamiltonian associated with it. We will study the Hamiltonians of the bipartite walks. Let $S$ be a skew-symmetric matrix. We are mainly interested in the Hamiltonians of the form $iS$. We show that the Hamiltonian can be written as $iS$ if and only if the adjacency matrix of the bipartite graph is invertible. We show that Grover’s walks and vertex-face walks are special cases of bipartite walks. Via the Hamiltonians, phenomena of bipartite walks lead to phenomena of continuous walks. We show in detail how we use bipartite walks on paths to construct universal perfect state transfer in continuous walks. - Open Access
On the second largest adjacency eigenvalue of trees with given diameter
For a graph $G$, let $λ_2(G)$ denote the second largest eigenvalue of the adjacency matrix of $G$. We determine the extremal trees with maximum/minimum adjacency eigenvalue $λ_2$ in the class $\mathcal{T}(n,d)$ of $n$-vertex trees with diameter $d$. This contributes to the literature on $λ_2$-extremization over different graph families. We also revisit the notion of the spectral center of a tree and the proof of $λ_2$ maximization over trees.Open AccessOn the second largest adjacency eigenvalue of trees with given diameter
For a graph $G$, let $λ_2(G)$ denote the second largest eigenvalue of the adjacency matrix of $G$. We determine the extremal trees with maximum/minimum adjacency eigenvalue $λ_2$ in the class $\mathcal{T}(n,d)$ of $n$-vertex trees with diameter $d$. This contributes to the literature on $λ_2$-extremization over different graph families. We also revisit the notion of the spectral center of a tree and the proof of $λ_2$ maximization over trees. - Open Access
- 31 March 2023
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 56 (16) , 165305
Pretty good state transfer in discrete-time quantum walks
We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that pretty good state transfer is characterized by the spectrum of certain Hermitian adjacency matrix of the graph; more specifically, the vertices involved in pretty good state transfer must be strongly cospectral relative to this matrix, and the arccosines of its eigenvalues must satisfy some number theoretic conditions. Using normalized adjacency matrices, cyclic covers, and the theory on linear relations between geodetic angles, we construct several infinite families of walks that exhibits this phenomenon.
- 31 March 2023
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 56 (16) , 165305
Open AccessPretty good state transfer in discrete-time quantum walks
We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that pretty good state transfer is characterized by the spectrum of certain Hermitian adjacency matrix of the graph; more specifically, the vertices involved in pretty good state transfer must be strongly cospectral relative to this matrix, and the arccosines of its eigenvalues must satisfy some number theoretic conditions. Using normalized adjacency matrices, cyclic covers, and the theory on linear relations between geodetic angles, we construct several infinite families of walks that exhibits this phenomenon.
- Open Access
- 29 September 2022
- Published by Springer Nature in Quantum Information Processing
- Vol. 21 (9) , 1-25
The average search probabilities of discrete-time quantum walks
- 29 September 2022
- Published by Springer Nature in Quantum Information Processing
- Vol. 21 (9) , 1-25
Open AccessThe average search probabilities of discrete-time quantum walks