Circuit Design Of Clique Problem And Its Implementation On NISQ Using Combinatorial Approach Of Classical-Quantum Hybrid Model

In the Maximum Clique Problem, the objective is to find a clique whose size is maximum among all the cliques of an arbitrary undirected and unweighted graph. Maximum Clique Problem resembles with minimum vertex cover problem, independent set problem. As it is an NP-hard problem, no polynomial time algorithms can be found. As these problems have several important practical applications such as information retrieval, community detection in network, spatial data mining etc, it is of great interest to try to synthesis the circuit of Maximum Clique Problem. In classical computing any brute-force solution to the Maximum Clique Problem requires an exponential increase of time with the size of the problem (i.e., with time complexity of $O(2^n)$ ). In this paper, Maximum Clique Problem has been solved using combinatorial approach of Grover's search algorithm. An algorithm has been proposed that auto-generates the circuit for any given undirected and unweighted graph which makes the approach generalized in nature for Maximum Clique Problem. Computational speed up is achieved by using our approach with the help of quantum mechanical effect that is quantum superposition. We have simulated the proposed circuit using IBM's QISkit platform and verified its correctness.In the Maximum Clique Problem, the objective is to find a clique whose size is maximum among all the cliques of an arbitrary undirected and unweighted graph. Maximum Clique Problem resembles with minimum vertex cover problem, independent set problem. As it is an NP-hard problem, no polynomial time algorithms can be found. As these problems have several important practical applications such as information retrieval, community detection in network, spatial data mining etc, it is of great interest to try to synthesis the circuit of Maximum Clique Problem. In classical computing any brute-force solution to the Maximum Clique Problem requires an exponential increase of time with the size of the problem (i.e., with time complexity of $O(2^n)$). In this paper, Maximum Clique Problem has been solved using combinatorial approach of Grover's search algorithm. An algorithm has been proposed that auto-generates the circuit for any given undirected and unweighted graph which makes the approach generalized in nature for Maximum Clique Problem. Computational speed up is achieved by using our approach with the help of quantum mechanical effect that is quantum superposition. We have simulated the proposed circuit using IBM's QISkit platform and verified its correctness.

Mar 10, 20200 citations

Robust quantum circuit for clique problem with intermediate qudits

Arpita Sanyal, Amit Saha, Banani Saha +1 more

arXiv:2211.07947Nano Communication NetworksJun 16, 20231 citation

Circuit design for clique problem and its implementation on quantum computer

Arpita Sanyal, Amit Saha, Banani Saha +1 more

Abstract Finding cliques in a graph has a wide range of applications due to its pattern matching ability. The k ‐clique problem, a subset of the clique problem, determines whether or not an arbitrary network has a clique of size k . Modern‐day applications include a variation of the k ‐clique problem that lists all cliques of size k . However, the quantum implementation of such a variation of the k ‐clique problem has not been addressed yet. In this work, apart from the theoretical solution of such a k ‐clique problem, practical quantum‐gate‐based implementation has been addressed using Grover's algorithm. In a classical‐quantum hybrid architecture, this approach is extended to build the circuit for the maximum clique problem. Our technique is generalised since the program automatically builds the circuit for any given undirected and unweighted graph and any chosen k . For a small k with regard to a big graph, the proposed solution to addressing the k ‐clique issue has shown a reduction in qubit cost and circuit depth when compared to the state‐of‐the‐art approach. A framework is also presented for mapping the automated generated circuit for clique problems to quantum devices. Using IBM's Qiskit, an analysis of the experimental results is demonstrated.Abstract Finding cliques in a graph has a wide range of applications due to its pattern matching ability. The k ‐clique problem, a subset of the clique problem, determines whether or not an arbitrary network has a clique of size k . Modern‐day applications include a variation of the k ‐clique problem that lists all cliques of size k . However, the quantum implementation of such a variation of the k ‐clique problem has not been addressed yet. In this work, apart from the theoretical solution of such a k ‐clique problem, practical quantum‐gate‐based implementation has been addressed using Grover's algorithm. In a classical‐quantum hybrid architecture, this approach is extended to build the circuit for the maximum clique problem. Our technique is generalised since the program automatically builds the circuit for any given undirected and unweighted graph and any chosen k . For a small k with regard to a big graph, the proposed solution to addressing the k ‐clique issue has shown a reduction in qubit cost and circuit depth when compared to the state‐of‐the‐art approach. A framework is also presented for mapping the automated generated circuit for clique problems to quantum devices. Using IBM's Qiskit, an analysis of the experimental results is demonstrated.

arXiv:2004.10596IET Quantum CommunicationDec 9, 20218 citations

Resource-Efficient Bio-Molecular Docking on a NISQ-era Digital Quantum Computer

Tianqi Chen, Adrian M. Mak, Jianguo Li +3 more

Molecular docking is a vital computational task in drug discovery, wherein the objective is to efficiently identify optimal binding poses between a ligand and a target receptor protein. Due to the combinatorial explosion of possible binding configurations, docking of large and flexible molecules remains a computationally intensive problem, especially at scale. Early studies have revealed that the molecular docking can be re-cast as a maximum vertex-weighted clique problem (MVWCP) problem on a compatibility graph to be solved classically. In this work, we proposed a hybrid quantum-classical approach for molecular docking leveraging the MVWCP formalism with a variational full-basis encoding (FBE) strategy, which enables efficient encoding of classical binary variables with Bloch sphere vectors. We further prove that a global minimizer of the FBE objective can always be chosen to be a pure product state, thereby providing a rigorous justification for its optimization using a unitary variational circuit. The molecular docking problem is first mapped to a cost Hamiltonian that is minimized within a variational framework, optimized via a randomized imaginary time evolution (ITE)-inspired warm start, and gradient-based techniques. Finally, we also executed the circuit on an IBM quantum computer, underlying the feasibility and of quantum-assisted optimization for structure-based drug design and point towards the broader utility of advanced encoding techniques in quantum optimization for computational biology.Molecular docking is a vital computational task in drug discovery, wherein the objective is to efficiently identify optimal binding poses between a ligand and a target receptor protein. Due to the combinatorial explosion of possible binding configurations, docking of large and flexible molecules remains a computationally intensive problem, especially at scale. Early studies have revealed that the molecular docking can be re-cast as a maximum vertex-weighted clique problem (MVWCP) problem on a compatibility graph to be solved classically. In this work, we proposed a hybrid quantum-classical approach for molecular docking leveraging the MVWCP formalism with a variational full-basis encoding (FBE) strategy, which enables efficient encoding of classical binary variables with Bloch sphere vectors. We further prove that a global minimizer of the FBE objective can always be chosen to be a pure product state, thereby providing a rigorous justification for its optimization using a unitary variational circuit. The molecular docking problem is first mapped to a cost Hamiltonian that is minimized within a variational framework, optimized via a randomized imaginary time evolution (ITE)-inspired warm start, and gradient-based techniques. Finally, we also executed the circuit on an IBM quantum computer, underlying the feasibility and of quantum-assisted optimization for structure-based drug design and point towards the broader utility of advanced encoding techniques in quantum optimization for computational biology.

quant-pharXiv:2608.19868Aug 21, 20260 citations

Problem Solving using Quantum Computing and Quantum Clique Algorithm

Mandeep Kaur

May 1, 20070 citations

O(2^n)

). In this paper, Maximum Clique Problem has been solved using combinatorial approach of Grover's search algorithm. An algorithm has been proposed that auto-generates the circuit for any given undirected and unweighted graph which makes the approach generalized in nature for Maximum Clique Problem. Computational speed up is achieved by using our approach with the help of quantum mechanical effect that is quantum superposition. We have simulated the proposed circuit using IBM's QISkit platform and verified its correctness.