Hanmeng (Harmony) Zhan

Book

• Discrete Quantum Walks on Graphs and Digraphs
C. Godsil, H. Zhan. Cambridge University Press (2023).

Papers

• On the second largest adjacency eigenvalue of trees with given diameter
H. Kumar, B. Mohar, S. Pragada, H. Zhan.
• $\epsilon$-uniform mixing in discrete quantum walks
H. Zhan.
• Subdivision and Graph Eigenvalues
H. Kumar, B. Mohar, S. Pragada, H. Zhan.
• Hamiltonians of bipartite walks
Q. Chen, C. Godsil, M. Sobchuk, H. Zhan. Electronic Journal of Combinatorics (2024) 31(4): P4.10.
• Pretty good state transfer in discrete-time quantum walks
A. Chan, H. Zhan. Journal of Physics A: Mathematical and Theoretical (2023). doi:10.1088/1751-8121/acc4f5
• The average search probabilities of discrete-time quantum walks
H. Zhan. Quantum Information Processing (2022) 21(9): pp. 336. doi:10.1007/s11128-022-03681-9
• Fundamentals of fractional revival in graphs
A. Chan, G. Coutinho, W. Drazen, O. Eisenberg, C. Godsil, M. Kempton, G. Lippner, C. Tamon, H. Zhan. Linear Algebra and its Applications (2022). doi:10.1016/J.LAA.2022.09.010
• Factoring discrete quantum walks on distance regular graphs into continuous quanutm walks
H. Zhan. Linear Algebra and its Applications (2022), 648: pp 88–103. doi:10.1016/J. LAA.2022.04.017
• Laplacian pretty good fractional revival
A. Chan, B. Johnson, M. Liu, M. Schmidt, Z. Yin, H. Zhan. Discrete Mathematics (2022), 345(10), 112971. doi:10.1016/J.DISC. 2022.112971
• Laplacian fractional revival on graphs
A. Chan, B. Johnson, M. Liu, M. Schmidt, Z. Yin, H. Zhan. Electronic Journal of Combinatorics (2021) 28(3): P3.22.
• Fractional Revival and Association Schemes
A. Chan, G. Coutinho, C. Tamon, L. Vinet, H. Zhan. Discrete Mathematics (2020) 343(11), 112018. doi:10.1016/j.disc.2020.112018
• Perfect State Transfer on Weighted Graphs of the Johnson Scheme
L. Vinet, H. Zhan. Letter in Mathematical Physics (2020). doi.org/10.1007/s11005-020-01298-6
• Quantum Walks on Embeddings
H. Zhan. Journal of Algebraic Combinatorics (2020). doi.org/10.1007/s10801-020-00958-z
• An Infinite Family of Circulant Graphs with Perfect State Transfer in Discrete Quantum Walks
H. Zhan. Quantum Information Processing (2019) 18(12): pp. 369.
• Perfect State Transfer in a Spin Chain without Mirror Symmetry
G. Coutinho, L. Vinet, H. Zhan, A. Zhedanov. Journal of Physics A: Mathematical and Theoretical (2019) 52(45), pp. 455302.
• Discrete-Time Quantum Walks and Graph Structures
C. Godsil and H. Zhan. Journal of Combinatorial Theory, Series A (2019), 181–212.
• Quantum Fractional Revival on Graphs
A. Chan, G. Coutinho, C. Tamon, L. Vinet, H. Zhan. Discrete Applied Mathematics (2019) 269, pp. 86-98.
• A New Perspective on the Average Mixing Matrix
G. Coutinho, C. Godsil, K. Guo, H. Zhan. Electronic Journal of Combinatorics (2018) 25(4): P4.14.
• Uniform Mixing on Cayley Graphs
C. Godsil and H. Zhan. Electronic Journal of Combinatorics (2017) 24(3): P3.20.
• Equiangular Lines and Covers of the Complete Graph
G. Coutinho, C. Godsil, M. Shirazi, and H. Zhan. Linear Algebra and its Applications (2016) 488: 264-283.
• Perfect State Transfer in Laplacian Quantum Walk
R. Alvir, S. Dever, B Lovitz, J. Myer, C. Tamon, Y. Xu and H. Zhan. Journal of Algebraic Combinatorics (2016) 43(4): 801-826.

Presentations

• Average mixing in discrete quantum walks with marked vertices. In: AMS Fall Meeting, Albany, MA, USA, October 19 - 20, 2024.
• Laplacian fractional revival on graphs. In: Math Colloquium, University of Hartford, Hartford, CT, United States, October 4, 2024.
• Epsilon-uniform mixing on strongly regular graphs via coined quantum walks. In: 05C50 Online, University of Manitoba, Winnipeg, MB, Canada, September 13, 2024.
• Generating quantum uniform mixing in association schemes. In: CMS Summer Meeting, University of Saskatchewan, Saskatoon, SK, Canada, May 31 - June 3, 2024.
• Discrete quantum walks in schemes. In: AMS Sectional Meeting, University of Wisconsin-Milwaukee, Milwaukee, WI, United States, April 20 - 21, 2024.
• Quantum walks: from continuous to discrete. In: Godsil75, University of Waterloo, Waterloo, ON, Canada, March 15 - 17, 2024.
• Strongly cospectral vertices and their phantom mates. In: Joint Mathematics Meetings, Moscone Center, San Francisco, CA, United States, January 3 - 6, 2024.
• Quantum search: an averaging perspective. In: Joint Mathematics Meetings, Moscone Center, San Francisco, CA, United States, January 3 - 6, 2024.
• $\epsilon$-uniform mixing in discrete quantum walks. In: CMS Winter Meeting, DoubleTree by Hilton Montreal, Montreal, QC, Canada, December 1 - 4, 2023.
• Spectra of line digraphs and their applications. In: CMS Winter Meeting, DoubleTree by Hilton Montreal, Montreal, QC, Canada, December 1 - 4, 2023.
• How graph spectra determine the behavior of discrete quantum walks. In: 10th International Workshop of Quantum Simulation and Quantum Walks, Tsukuba International Congress Center, Tsukuba, Japan, November 10 - 12, 2023.
• On the second largest eigenvalue of a tree. In: On-line Combinatorics Seminar, University of Wisconsin-Madison, Madison, WI, October 23, 2023.
• Some recent results in quantum walks. In: Algebraic structures and special functions in theoretical physics, Ghent University, Ghent, Belgium, June 26 - 30, 2023.
• Discrete quantum walks in association schemes. In: 10th Slovenian Conference on Graph Theory, Kranjska Gora, Slovenia, June 18 - 24, 2023.
• Some open problems in discrete quantum walks. In: Canadian Discrete and Algorithmic Mathematics Conference, University of Manitoba and University of Winnipeg, Winnipeg, MB, Canada, June 5 - 8, 2023.
• Discrete quantum walks on distance regular graphs. In: Canadian Discrete and Algorithmic Mathematics Conference, University of Manitoba and University of Winnipeg, Winnipeg, MB, Canada, June 5 - 8, 2023.
• Discrete quantum walk search on graphs. In: Coast Combinatorics Conference 2023, SFU Harbour Centre, Vancouver, BC, Canada, March 4 - 5, 2023.
• The second largest eigenvalue of a tree. In: CMS Winter Meeting, Chelsea Hotel, Toronto, ON, Canada, December 2 - 5, 2022.
• Mini-course: Introduction to discrete quantum walks. In: CMS Winter Meeting, Chelsea Hotel, Toronto, ON, Canada, December 2 - 5, 2022.
• The effect of marking vertices in discrete quantum walks. In: Graph Theory, Algebraic Combinatorics and Mathematical Physics, Centre de Recherches Mathématiques, July 25 - August 19, 2022.
• The average search probability in a quantum walk with an oracle. In: Algebraic Graph Theory Seminar, University of Waterloo, Waterloo, ON, Canada, August 2, 2021.
• Arc-reversal quantum walks. In: Discrete Math Seminar, Simon Fraser University, Vancouver, BC, Canada, February 24, 2021.
• DRACKNs and their applications in quantum information. In: Codes and Expansions, United States, September 8, 2020.
• Factoring discrete quantum walks into continuous quantum walks. In: Algebraic Graph Theory Seminar, University of Waterloo, Waterloo, ON, Canada, August 3, 2020.
• Quantum fractional revival. In: Discrete Math Seminar, University of Delaware, Newark, DE, United States, April 23, 2020.
• How far does the quantum walker go. In: 9th International Conference on Quantum Simulation and Quantum Walks, Centre International de Rencontres Mathématiques, Marseille, Bouches-du-Rhone, France, January 20 - 24, 2020.
• New advances in quantum walks. In: AMS Joint Mathematics Meetings, Colorado Convention Center, Denver, CO, United States, January 15 - 18, 2020.
• Discrete quantum walks on Cayley graphs. In: CMS Winter Meeting, Chelsea Hotel, Toronto, ON, Canada, December 6 - 9, 2019.
• State Transfer via Orthogonal Polynomials. In: AMS Sectional Meeting, University of Wisconsin-Madison, Madison, WI, United States, September 14 - 15, 2019.
• The Vertex Face Walk. In: Finite Geometry and Extremal Combinatorics, University of Delaware, Newark, DE, United States, August 21 - 24, 2019.
• Quantum State Transfer in the Algebra of the Johnson Scheme. In : CMS Summer Meeting, University of Regina, Regina, SK, Canada, Jun 7 - 10, 2019.
• Some Elegant Results in Algebraic Graph Theory. In: Canadian Discrete and Algorithmic Mathematics Conference, Simon Frase University, Vancouver, BC, Canada, May 28 - 31, 2019.
• Quantum Walks, Orthogonal Polynomials, and Spectral Graph Theory. In: Quantum Walks and Information Tasks, Banff International Research Station for Mathematical Innovation and Discovery, Banff, AB, Canada, April 21 - 26, 2019.
• Generating Entanglement Using Quantum Walks. In: David A. Walsh Seminar Series, Clarkson University, Potsdam, NY, United States, February 8, 2019.
• Combinatorial Aspects of Quantum walks. In: Prairie Discrete Math Workshop, Brandon University, Brandon, MB, Canada, June 12 – 15, 2018.
• Some Open Problems in Discrete Quantum Walks. In: Algebraic Graph Theory and Quantum Walks, University of Waterloo, Waterloo, ON, Canada, April 23 - 27, 2018.
• Recent Progress in Discrete Quantum Walks. In AMS Sectional Meeting, Northeastern University, Boston, MA, United States, April 21 - 22, 2018, 2018.
• Graph covers and equiangular frames. In AMS Sectional Meeting, Ohio State University, Columbus, OH, United States, March 16 - 18, 2018.
• Discrete-Time Quantum Walks and Graph Embeddings. In: CMS Winter Meeting, University of Waterloo, Waterloo, ON, Canada, December 8 - 11, 2017.
• Quantum Walks and Mixing. In: Algebraic and Extremal Graph Theory, University of Delaware, Newark, DE, United States, August 7 - 10, 2017.
• Discrete-Time Quantum Walks and Graph Structures. In: Canadian Discrete and Algorithmic Mathematics Conference, Ryerson University, Toronto, ON, Canada, June 12 - 15, 2017.
• From Covers to Tight Frames. In: AMS Sectional Meeting, College of Charleston, Charleston, SC, United States, March 10 - 12, 2017.
• Spectra of Discrete Quantum Walks. In: CMS Summer Meeting, University of Alberta, Edmonton, AB, Canada, June 24 - 27, 2016.
• Lines and Covers of Complete Graphs 2. In: Systems of Lines: Applications of Algebraic Combinatorics, Worcester Polytechnic Institute, Worcester, MA, United States, August 10 - 14, 2015.
• Uniform Mixing in Continuous-Time Quantum Walks. In: Summer Combo, Saint Michael's College, Burlington, VT, United States, July 21, 2015.
• Some Open Problems in Uniform Mixing. In: Summer Research Program, Clarkson University, Potsdam, NY, United States, July 20, 2015.
• Uniform Mixing in Quantum Walks. In: 22nd Ontario Combinatorics Workshop, York University, Toronto, ON, Canada, May 16 - 17, 2014.

Theses

• Discrete Quantum Walks on Graphs and Digraphs
Ph.D. thesis.
• Uniform Mixing on Cayley Graphs over $\mathbb{Z}_3^d$
Master's thesis.