Fast equivalence-checking for quantum circuits

Quantum Information and Computation

Volumn 10, Issue 9-10, 2010, Pages 721-734

  Yamashita, Shigeru ^a   Markov, Igor L ^b  

^a RITSUMEIKAN UNIVERSITY   (Japan)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Circuit simplification; Equivalence checking; Quantum circuit; Reversible miters

Indexed keywords

QUANTUM THEORY; TIMING CIRCUITS;

EQUIVALENCE CHECKING; ORDERS OF MAGNITUDE; QUANTUM ALGORITHMS; QUANTUM CIRCUIT; REVERSIBLE CIRCUITS; REVERSIBLE MITERS; VERIFICATION METHODOLOGY; VERIFICATION TECHNIQUES;

FORMAL VERIFICATION;

EID: 78649516790     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. S. A. Cuccaro et al. A new quantum ripple-carry addition circuit. http://xxx.lanl.gov/abs/quant-ph/0410184, Los Alamos e-print, 2004.
2. A. G. Fowler, S. J. Devitt and L. C. L. Hollenberg. Implementation of Shor's algorithm on a linear nearest neighbour qubit array. Quantum Information and Computation, 4(4):237-251, July 2004.
3. L. Grover. Quantum mechanics helps in searching for a needle in a haystack. Physical Review Letters, 79(2):325-328, July 1997.
4. D. Hanneke et al. J. P. Home, J. D. Jost, J. M. Amini, D. Leibfried, D. J. Wineland Realisation of a programmable two-qubit quantum processor. Quantum Physics pre-print ARXIV.ORG:0908.3031, National Inst. of Standards and Technology, August 2009.
5. K. Iwama, Y. Kambayashi and S. Yamashita. Transformation Rules for Designing CNOT-based Quantum Circuits. DAC, pp. 419-424, 2002.
6. R. C. Johnson. NIST scales up quantum computing. EE Times, 6 Aug. 2009.
7. B. P. Lanyon, T. J. Weinhold, N. K. Langford, M. Barbieri, D. F. V. James, A. Gilchrist and A. G. White. Experimental Demonstration of a Compiled Version of Shor's Algorithm with Quantum Entanglement. Physical Review Letters, 99, 250505, Dec. 2007.
8. 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. Physical Review Letters, 99, 250504, Dec. 2007.
9. D. Maslov. Linear depth stabilizer and quantum Fourier transformation circuits with no auxiliary qubits in finite-neighbor quantum architectures. Physical Review A 76, 052310, Nov. 2007.
10. D. Maslov, G. W. Dueck, D. M. Miller and C. Negrevergne. Quantum circuit simplification and level com- paction. IEEE Trans. on CAD, 27(3):436-444, Mar. 2008.
11. R. Van Meter, K. M. Itoh, "Fast quantum modular exponentiation," Physical Review A 71(052320), May 2005.
12. D. M. Miller and M. A. Thornton. QMDD: A decision diagram structure for reversible and quantum circuits. IEEE Int'l Symp. on Multiple-Valued Logic, p.30, May 2006.
13. A. Mishchenko, S. Chatterjee, R. Brayton, N. Een. Improvements to combinational equivalence checking. ICCAD, pp. 836-843, 2006.
14. M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
15. A. Politi, J. C. F. Matthews and J. L. O'Brien. Shor's Quantum Factoring Algorithm on a Photonic Chip. Science 4, 325(5945):1221, Sept. 2009.
16. A. K. Prasad, V. V. Shende, K. N. Patel, I. L. Markov and J. P. Hayes. Algorithms and data structures for simplifying reversible circuits. ACM J. of Emerging Technologies in Computing, 2(4):277-293, Oct. 2006.
17. P. W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum com- puter. SIAM Journal on Computing, 26(5):1484-1509, 1997.
18. K. M. Svore, A. V. Aho, A. W. Cross, I. L. Chuang, I. L. Markov, "A Layered Software Architecture for Quantum Computing Design Tools," IEEE Computer 39(1): 74-83, 2006.
19. R. R. Tucci. Q. C. Paulinesia. http://xxx.lanl.gov/abs/quant-ph/0407215, Los Alamos e-print, 2004.
20. G. F. Viamontes, I. L. Markov, and J. P. Hayes. Improving gate-level simulation of quantum circuits. Quantum Information Processing, 2(5):347-380, 2003.
21. G. F. Viamontes, I. L. Markov, and J. P. Hayes. Equivalence checking of quantum circuits and states. ICCAD, pp. 69-74, 2007.
22. J. Yoshida. 35 people, places and things that will shape the future. EE Times, February 29, 2008.
23. The ABC Home Page. http://www.eecs.berkeley.edu/alanmi/abc/.
24. The MiniSat Home Page. http://minisat.se/MiniSat.html.