arXiv subjects

Rishikant Rajdeepak

Publications and source records attributed to Rishikant Rajdeepak.

6 recordsLinked to original sources

arXiv2024

Quantum Correlations in One Parameter Mixed Quantum States

Munero et. al. developed one parameter family of mixed states $ρ^{l}$, which are more entangled than bipartite Werner state. The similar family of mixed states $ρ^{n}$ are developed by L. Derkacz et. al. with differed approach. Further the author extend $ρ^{n}$ to two parameter family of quantum states $ρ^{m}$ and characterized these states in terms of Bell inequality violation against their mixedness. In the present article, we investigate the comparative dynamics of all mixed states $(ρ^{l},ρ^{n},ρ^{m})$ under the bipartite Ising Hamiltonian exposed by the external magnetic field and investigate the dynamics of quantum correlations against the mixedness quantified by linear entropy

quant-ph↗

arXiv2024

Quantum Information Scrambling and Entanglement: An Elegant Mathematical Connection

Studying the behavior of quantum information scrambling in various quantum systems is an active area of research. Recently, Sharma et al. [K.K. Sharma, V.P Gerdt, Quantum Inf. Process 20, 195 (2021)] have shown the mathematical connection between quantum information scrambling (QIS) and bipartite entanglement in non-thermal states. In the present work, we elegantly generalize this mathematical connection and study such connections in X-states, non-maximally entangled Bell states, and Werner states

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arXiv2021

Quantum simulation of perfect state transfer on weighted cubelike graphs

A continuous-time quantum walk on a graph evolves according to the unitary operator $e^{-iAt}$, where $A$ is the adjacency matrix of the graph. Perfect state transfer (PST) in a quantum walk is the transfer of a quantum state from one node of a graph to another node with $100\%$ fidelity. It can be shown that the adjacency matrix of a cubelike graph is a finite sum of tensor products of Pauli $X$ operators. We use this fact to construct an efficient quantum circuit for the quantum walk on cubelike graphs. In \cite{Cao2021, rishi2021(2)}, a characterization of integer weighted cubelike graphs is given that exhibit periodicity or PST at time $t=π/2$. We use our circuits to demonstrate PST or periodicity in these graphs on IBM's quantum computing platform~\cite{Qiskit, IBM2021}.

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arXiv2021

Embedding perfectly balanced 2-caterpillar into its optimal hypercube

A long-standing conjecture on spanning trees of a hypercube states that a balanced tree on $2^n$ vertices with maximum degree at most $3$ spans the hypercube of dimension $n$ \cite{havel1986}. In this paper, we settle the conjecture for a special family of binary trees. A $0$-caterpillar is a path. For $k\geq 1$, a $k$-caterpillar is a binary tree consisting of a path with $j$-caterpillars $(0\leq j\leq k-1)$ emanating from some of the vertices on the path. A $k$-caterpillar that contains a perfect matching is said to be perfectly balanced. In this paper, we show that a perfectly balanced $2$-caterpillar on $2^n$ vertices spans the hypercube of dimension $n$.

math.CO↗

arXiv2021

Perfect State Transfer in Weighted Cubelike Graphs

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 $t=\fracπ{2}$.

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arXiv2021

Implementation of hitting times of discrete time quantum random walks on Cubelike graphs

We demonstrate an implementation of the hitting time of a discrete time quantum random walk on cubelike graphs using IBM's Qiskit platform. Our implementation is based on efficient circuits for the Grover and Shift operators. We verify the results about the one-shot hitting time of quantum walks on a hypercube as proved in [https://link.springer.com/article/10.1007/s00440-004-0423-2]. We extend the study to another family of cubelike graphs called the augmented cubes [https://onlinelibrary.wiley.com/doi/abs/10.1002/net.10033]. Based on our numerical study, we conjecture that for all families of cubelike graphs there is a linear relationship between the degree of a cubelike graph and its hitting time which holds asymptotically. That is, for any cubelike graph of degree $Δ$, the probability of finding the quantum random walk at the target node at time $\frac{πΔ}{2}$ approaches 1 as the degree $Δ$ of the cubelike graph approaches infinity.

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