arXiv subjects

Arpita Sanyal

Publications and source records attributed to Arpita Sanyal.

2 recordsLinked to original sources

arXiv2022

Robust Quantum Circuit for Clique Problem with Intermediate Qudits

Clique problem has a wide range of applications due to its pattern matching ability. There are various formulation of clique problem like $k$-clique problem, maximum clique problem, etc. The $k$-Clique problem, determines whether an arbitrary network has a clique or not whereas maximum clique problem finds the largest clique in a graph. It is already exhibited in the literature that the $k$-clique or maximum clique problem (NP-problem) can be solved in an asymptotically faster manner by using quantum algorithms as compared to the conventional computing. Quantum computing with higher dimensions is gaining popularity due to its large storage capacity and computation power. In this article, we have shown an improved quantum circuit implementation for the $k$-clique problem and maximum clique problem (MCP) with the help of higher-dimensional intermediate temporary qudits for the first time to the best of our knowledge. The cost of state-of-the-art quantum circuit for $k$-clique problem is colossal due to a huge number of $n$-qubit Toffoli gates. We have exhibited an improved cost and depth over the circuit by applying a generalized $n$-qubit Toffoli gate decomposition with intermediate ququarts (4-dimensional qudits).

cs.ET↗

arXiv2021

Circuit Design for Clique Problem and Its Implementation on Quantum Computer

Finding cliques in a graph has several applications for its pattern matching ability. $k$-clique problem, a special case of clique problem, determines whether an arbitrary graph contains a clique of size $k$, has already been addressed in quantum domain. A variant of $k$-clique problem that lists all cliques of size $k$, has also popular modern-day applications. Albeit, the implementation of such variant of $k$-clique problem in quantum setting still remains untouched. In this paper, apart from theoretical solution of such $k$-clique problem, practical quantum gate-based implementation has been addressed using Grover's algorithm. This approach is further extended to design circuit for the maximum clique problem in classical-quantum hybrid architecture. The algorithm automatically generates the circuit for any given undirected and unweighted graph and any given $k$, which makes our approach generalized in nature. The proposed approach of solving $k$-clique problem has exhibited a reduction of qubit cost and circuit depth as compared to the state-of-the-art approach, for a small $k$ with respect to a large graph. A framework that can map the automated generated circuit for clique problem to quantum devices is also proposed. An analysis of the experimental results is demonstrated using IBM's Qiskit.

cs.DS↗