A5008696931- Quantum Computing Algorithms and Architecture
- Quantum Information and Cryptography
- Quantum-Dot Cellular Automata
- Algebraic structures and combinatorial models
- Quantum and electron transport phenomena
- Finite Group Theory Research
- Advanced Topics in Algebra
- Graph theory and applications
- Advanced Memory and Neural Computing
- Geometric and Algebraic Topology
- Advanced Graph Theory Research
- Advanced Operator Algebra Research
- Advanced Combinatorial Mathematics
- graph theory and CDMA systems
- Coding theory and cryptography
- Graphene research and applications
- Advanced Biosensing Techniques and Applications
- Neural Networks and Reservoir Computing
- Optimization and Search Problems
- Interconnection Networks and Systems
- Advanced Algebra and Geometry
- Mitochondrial Function and Pathology
- Stochastic Gradient Optimization Techniques
- Quantum many-body systems
- Cellular Automata and Applications
York University
2016-2025
Children's Hospital of Philadelphia
2022
University of Wisconsin–Madison
2021
California Institute of Technology
2003-2004
University of Waterloo
1990-2004
Northeastern University
2002
Abstract We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that is characterized by spectrum certain Hermitian adjacency matrix graph; more specifically, vertices involved must be strongly cospectral relative to this matrix, and arccosines its eigenvalues satisfy some number theoretic conditions. Using normalized matrices, cyclic covers, on linear relations between geodetic angles, construct several infinite families walks...
We study Nordhaus-Gaddum problems for Kemeny's constant $\mathcal{K}(G)$ of a connected graph $G$. prove bounds on $\min\{\mathcal{K}(G),\mathcal{K}(\overline{G})\}$ and the product $\mathcal{K}(G)\mathcal{K}(\overline{G})$ various families graphs. In particular, we show that if maximum degree $G$ $n$ vertices is $n-O(1)$ or $n-\Omega(n)$, then at most $O(n)$.
We study the continuous-time quantum walks on graphs in adjacency algebra of $n$-cube and its related distance regular graphs. For $k\geq 2$, we find $(2^{k+2}-8)$-cube that admit instantaneous uniform mixing at time $\pi/2^k$ have perfect state transfer $\pi/2^k$. characterize folded $n$-cubes, halved $n$-cubes whose contains a complex Hadamard matrix. obtain same conditions for characterization these admitting mixing.
We study state transfer in quantum walks on graphs relative to the adjacency matrix. Our motivation is understand how addition of pendant subgraphs affect transfer. For two $G$ and $H$, Frucht-Harary corona product $G \circ H$ obtained by taking $|G|$ copies cone $K_{1} + identifying conical vertices according $G$. work explores conditions under which exhibits also describe new families with based product. Some these constructions provide a generalization related known results.
We study the continuous-time quantum walks on graphs in adjacency algebra of n-cube and its related distance regular graphs.
Over forty years ago, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph $X$ contains Hadamard matrix then is either Latin square type or negative type. We extend their result to complex matrices find only three additional families parameters for which graphs have in algebras. Moreover we show there are distance covers complete give matrices.
We introduce and discuss Jones pairs. These provide a generalization new approach to the four-weight spin models of Bannai Bannai. show that each model determines “dual” pair association schemes.
We develop the theory of fractional revival in quantum walk on a graph using its Laplacian matrix as Hamiltonian. first give spectral characterization revival, which leads to polynomial time algorithm check this phenomenon and find earliest when it occurs. then apply theorem special families graphs. In particular, we show that no tree admits except for paths two three vertices, only graphs prime number vertices admit are double cones. Finally, construct, through Cartesian products joins,...
To investigate the correlations between occupational risk factors and reproductive health to provide targeted healthcare services female civil aviation employees based on surveys about menstrual status.Subjects were selected from flight attendants working for China Southern Airlines, Air China, other airlines; of Aviation Oil Limited, TravelSky, Supplies Holding Company; airport ground service crews. Data collected using anonymous questionnaires. A total 1175 valid questionnaires recovered....
We develop a general spectral framework to analyze quantum fractional revival in spin networks. In particular, we introduce generalizations of the notions cospectral and strongly vertices arbitrary subsets vertices, give various examples. This work resolves two open questions Chan et.~al. ["Quantum Fractional Revival on graphs". Discrete Applied Math, 269:86-98, 2019.]
Spatial search occurs in a connected graph if continuous-time quantum walk on the adjacency matrix of graph, suitably scaled, plus rank-one perturbation induced by any vertex will unitarily map principal eigenvector to characteristic vector vertex. This phenomenon is natural analogue Grover search. The spatial said be optimal it with constant fidelity and time inversely proportional shadow target eigenvector. Extending result Chakraborty \etal ({\em Physical Review A}, {\bf 102}:032214,...
We develop the theory of pretty good fractional revival in quantum walks on graphs using their Laplacian matrices as Hamiltonian. classify paths and double stars that have revival.
In the study of quantum state transfer, one is interested in being able to transmit a with high fidelity within spin network. most literature, interest taken be associated standard basis vector; however, more general states have recently been considered. Here, we consider linear combination two vertex states, which encompasses definitions pair and plus connected weighted graphs. A two-state graph $X$ form $\mathbf{e}_u+s\mathbf{e}_v$, where $u$ $v$ are vertices $s$ non-zero real number. If...