Constant-optimized quantum circuits for modular multiplication and exponentiation

Quantum Information and Computation

Volumn 12, Issue 5-6, 2012, Pages 361-394

  Markov, Igor L ^a   Saeedi, Mehdi ^b  

^a The Department of Civil and Environmental Engineering   (United States)

^b AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Modular exponentiation; Modular multiplication; Quantum circuits; Shor's quantum factoring algorithm

Indexed keywords

EID: 84858047569     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. D. Aharonov, Z. Landau, and J. Makowsky, "The Quantum FFT can be Classically Simulated," quant-ph/0611156
2. M. Arabzadeh, M. Saeedi, M. Saheb Zamani. "Rule-Based Optimization of Reversible Circuits," Asia and South Pacific Design Autom. Conf., pp. 849-854, 2010.
3. Avizienis, "Signed-Digit Number Representations for Fast Parallel Arithmetic," IRE Trans. on Electronic Computers, Vol. EC-10, No. 3, pp. 389-400, Sept. 1961.
4. Barenco et al., "Elementary Gates for Quantum Computation," Phys. Rev. A, 1995.
5. D. Beckman, A. N. Chari, S. Devabhaktuni, J. Preskill, "Efficient Networks for Quantum Factoring," Phys. Rev. A 54:1034-1063, 1996.
6. R. P. Brent, P. Zimmermann, "Modern Computer Arithmetic," Cambridge Univ. Press, 2010.
7. -4 in a Trapped Ion," Phys. Rev. A, pp. 84:030303, 2011.
8. F. Buscemi, "Shor's Quantum Algorithm using Electrons in Semiconductor Nanostructures," Phys. Rev. A 83, 012302 (2011) quant-ph/arXiv:1011.2628.
9. S. A. Cuccaro, T. G. Draper, S. A. Kutin, and D. P. Moulton, "A New Quantum Ripple-Carry Addition Circuit," quant-ph/0410184, 2004.
10. G. Fowler, S. J. Devitt, L. C. L. Hollenberg, "Implementation of Shor's Algorithm on a Linear Nearest Neighbour Qubit Array," Quantum Information and Computation 4, pp. 237-251, 2004.
11. P. Lanyon et al., "Experimental Demonstration of a Compiled Version of Shor's Algorithm with Quantum Entanglement," Phys. Rev. Lett. 99:250505, 2007.
12. C.-Y. Lu, D. E. Browne, T. Yang, and J.-W. Pan, "Demonstration of a Compiled Version of Shor's Quantum Factoring Algorithm Using Photonic Qubits," Phys. Rev. Lett. 99:250504, 2007.
13. L. Markov and Y.-Y. Shi, "Simulating Quantum Computation by Contracting Tensor Networks," SIAM J, on Computing, Vol. 38, No. 3, pp. 963-981, June 2008.
14. D. Maslov and M. Saeedi, "Reversible Circuit Optimization via Leaving the Boolean Domain," IEEE Trans. CAD, Vol. 30, No. 6, pp. 806-816, 2011.
15. M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, 2000.
16. Politi, J. C. F. Matthews, J.L. O'Brien, "Shor's Quantum Factoring Algorithm on a Photonic Chip," Science, Vol. 325, No. 4, September 2009.
17. M. Saeedi and I. L. Markov, "Synthesis and Optimization of Reversible Circuits - A Survey," ACM Computing Surveys, 2012.
18. V. V. Shende and I. L. Markov, "On the CNOT-cost of TOFFOLI Gates," Quantum Information and Computation, Vol. 9, No. 5-6, pp. 461-486, May 2009.
19. Y. Takahashi, S. Tani, N. Kunihiro, "Quantum Addition Circuits and Unbounded Fan-out," Quantum Information and Computation, Vol. 10 No. 9&10, pp. 872-890, 2010
20. R. Van Meter, K. Itoh, "Fast Quantum Modular Exponentiation," Phys. Rev. A 71:052320, 2005.
21. R. Van Meter, "Architecture of a Quantum Multicomputer Optimized for Shor's Factoring Algorithm," Ph.D. Thesis, Keio University, 2006. http://arxiv.org/abs/quant-ph/0607065
22. V. Vedral, A. Barenco, A. Ekert, "Quantum Networks for Elementary Arithmetic Operations," Phys. Rev. A, Vol. 54(1), pp. 147-153, 1996.
23. G. F. Viamontes, I. L. Markov, J. P. Hayes, "Quantum Circuit Simulation," Springer 2009.
24. N. Yoran and A. Short. "Efficient Classical Simulation of the Approximate Quantum Fourier Transform," Phys. Rev. A, 76:042321, 2007.
25. R. Wille and R. Drechsler. "BDD-based Synthesis of Reversible Logic for Large Functions," Design Autom. Conf., pp. 270-275, 2009.