Abstract
Many applications such as Element Distinctness, Triangle Finding, Boolean Satisfiability, Marked Subgraph problem can be solved by Quantum Walk, which is the quantum version of classical random walk without intermediate measurement. To design a quantum circuit for a given quantum algorithm, which involves Quantum Walk search, we need to define an oracle circuit specific to the given algorithm and the diffusion operator for amplification of the desired quantum state. In this paper, we propose a quantum circuit implementation for the oracle of the marked clique problem based on Quantum Walk approach. To the best of our knowledge, this is a first of its kind approach in regards to the quantum circuit synthesis of the marked clique oracle in binary quantum domain. We have performed the simulation of the proposed oracle circuit in Matlab.
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References
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Sci. Stat. Comput. 26, 1484 (1997). arXiv:quant-ph/9508027
Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of STOC’96, pp. 212–219. quant-ph/9605043
Ambainis, A.: Quantum walks and their algorithmic applications. Int. J. Quant. Inf. 1(4), 507–518 (2003). arXiv:quant-ph/0403120
Kempe, J.: Quantum Random Walks—an Introductory Overview. quant-ph/0303081
Childs, A.M., Farhi, E., Gutmann, S.: An Example of the Difference Between Quantum and Classical Random Walks. quant-ph/0103020
Bron, C., Kerbosch, J.: Algorithm 457: finding all cliques of an undirected graph. Commun. ACM (ACM) 16(9), 575–577 (1973). doi:10.1145/362342.362367
Ostergerd, P.: Discrete Appl. Math. 120, 195 (2002)
Dharwadker, A.: The Clique Algorithm. Amazon, pp. 48 (2011). ISBN:978-1466391215
Bojić, A.: Quantum Algorithm for Finding a Maximum Clique in an Undirected Graph. ISSN 1846-9418
Hillery, M., Reitzner, D., Buzek, V.: Searching via Walking: How to Find a Marked Subgraph of a Graph Using Quantum Walks. arXiv:0911.1102v1 [quant-ph]
Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walks. Phys. Rev. A 48, 1687 (1993)
Ambainis A.: Quantum Walk Algorithm for Element Distinctness. quant-ph/0311001
Magniez, F., Santha, M., Szegedy, M.: An O(\(n\,^{\sim \,} 1.3\)) Quantum Algorithm for the Triangle Problem. quant-ph/0310134
Quantum Verification of Matrix Products. arXiv.org/pdf/quantph/0409035
Krovi, H., Magniez, F., Ozols, M., Roland, J.: Quantum Walks Can Find a Marked Element on any Graph. quant-ph/1002.2419
Szegedy, M.: Quantum speedup of markov chain based algorithms. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS’04) 0272-5428/04
Aharonov, D., Ambainis, A., Kempe, J., Vazirani, U.: Quantum Walks on Graphs. arXiv:quant-ph/0012090v2
Chakrabarti, A., Lin, CC., Jha, NK.: Design of quantum circuits for random walk algorithms. In: 2012 IEEE Computer Society Annual Symposium on VLSI
MATLAB, R2012b, The MathWorks. Natick, MA (2012)
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Sanyal(Bhaduri), A., Saha, A., Gain, B., Mandal, S.B. (2017). Circuit Synthesis of Marked Clique Problem using Quantum Walk. In: Chaki, R., Saeed, K., Cortesi, A., Chaki, N. (eds) Advanced Computing and Systems for Security. Advances in Intelligent Systems and Computing, vol 567. Springer, Singapore. https://doi.org/10.1007/978-981-10-3409-1_3
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DOI: https://doi.org/10.1007/978-981-10-3409-1_3
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