On the effect of quantum interaction distance on quantum addition circuits

ACM Journal on Emerging Technologies in Computing Systems

Volumn 7, Issue 3, 2011, Pages

  Choi, Byung Soo ^a   Van Rodney, Meter ^b  

^a University of Seoul   (South Korea)

^b KEIO UNIVERSITY   (Japan)

Author keywords

Depth lower bound; Graph embedding; Interaction distance; Quantum adder; Quantum architecture

Indexed keywords

GRAPH EMBEDDINGS; INTERACTION DISTANCES; LOWER BOUNDS; QUANTUM ADDERS; QUANTUM ARCHITECTURE;

COMPUTER ARCHITECTURE; ELECTRIC NETWORK ANALYSIS; LOGIC CIRCUITS; QUANTUM COMPUTERS; QUANTUM OPTICS; QUANTUM THEORY;

ADDERS;

EID: 80052003690     PISSN: 15504832     EISSN: 15504840     Source Type: Journal    
DOI: 10.1145/2000502.2000504     Document Type: Article

References (64)

1. ATHAS, W. C. AND SEITZ, C. L. 1988. Multicomputers: message-passing concurrent computers. IEEE Comput. 21, 9-24.
2. BACON, D. AND VAN DAM, W. 2010. Recent progress in quantum algorithms. Comm. ACM 53, 2, 84-93.
3. BECKMAN, D., CHARI, A. N., DEVABHAKTUNI, S., AND PRESKILL, J. 1996. Efficient networks for quantum factoring. Phys. Rev. A 54, 2, 1034-1063. (Pubitemid 126599992)
4. BEIN, W. T., LARMORE, L. L., SHIELDS, C. J., AND SUDBOROUGH, I. H. 2000. Three-dimensional embedding of binary trees. In Proceedings of the International Symposium on Parallel Architectures, Algorithms and Networks (I-SPAN). 140-147.
5. BENNET, C. H. 1973. Logical reversibility of computation. IBM J. Resear. Devel. 17, 525-532.
6. BONDERSON, P., FREEDMAN, M., AND NAYAK, C. 2008. Measurement-only topological quantum computation. Phys. Rev. Lett. 101, 1, 010501.
7. BROWNE, D. E., KASHEFI, E., AND PERDRIX, S. 2009. Computational depth complexity of measurementbased quantum computation. http://arxiv.org/abs/0909. 4673.
8. CALDERBANK, A. R. AND SHOR, P. W. 1996. Good quantum error-correcting codes exist. Phys. Rev. A 54, 2, 1098-1105. (Pubitemid 126599994)
9. CHEUNG, D., MASLOV, D., AND SEVERINI, S. 2007. Translation techniques between quantum circuit architectures. Poster Presentation, Workshop on Quantum Information Processing.
10. CIALDI, S., BRIVIO, D., AND PARIS, M. G. A. 2010. Demonstration of a programmable source of two-photon multiqubit entangled states. Phys. Rev. A 81, 4, 042322.
11. CLEVE, R. AND WATROUS, J. 2000. Fast parallel circuits for the quantum fourier transform. In Proceedings of the Annual Symposium on Foundations of Computer Science. 526-536. (Pubitemid 32075921)
12. CUCCARO, S. A., DRAPER, T. G., KUTIN, S. A., AND MOULTON, D. P. 2004. A new quantum ripple-carry addition circuit. http://arxiv.org/abs/quant-ph/ 0410184.
13. DIESTEL, R. 2005. Graph Theory 3rd Ed. Springer-Verlag.
14. DOUÇOT, B., IOFFE, L. B., AND VIDAL, J. 2004. Discrete non-abelian gauge theories in josephson-junction arrays and quantum computation. Phys. Rev. B 69, 21, 214501.
15. DRAPER, T. G. 2000. Addition on a quantum computer. http://arxiv.org/abs/ quant-ph/0008033.
16. DRAPER, T. G., KUTIN, S. A., RAINS, E. M., AND SVORE, K. M. 2006. A logarithmic-depth quantum carrylookahead adder. Quant. Inf. Computat. 6, 4-5, 351-369.
17. DÜR, W., BRIEGEL, H.-J., CIRAC, J. I., AND ZOLLER, P. 1999. Quantum repeaters based on entanglement purification. Phys. Rev. A 59, 1, 169-181. (Pubitemid 129680951)
18. ERCEGOVAC, M. D. AND LANG, T. 2003. Digital Arithmetic 1st Ed. Morgan Kaufmann Publishers.
19. FOWLER, A. G. AND GOYAL, K. 2009. Topological cluster state quantum computing. Quant. Inf. Computat. 9, 721.
20. FOWLER, A. G., DEVITT, S. J., AND HOLLENBERG, L. C. L. 2004. Implementation of Shor's algorithm on a linear nearest neighbor qubit array. Quant. Info. Computat. 4, 4, 237-251. (Pubitemid 39080445)
21. GOTTESMAN, D. 2000. Fault tolerant quantum computation with logical gates. J. Mod. Opt. 47, 2/3, 333-345. (Pubitemid 35392916)
22. GROVER, L. K. 1996. A fast quantum mechanical algorithm for database search. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing. ACM, New York, NY, 212-219.
23. HÄFFNER, H., HÄNSEL, W., ROOS, C. F., BENHELM, J., CHEK-AL KAR, D., CHWALLA, M., KÖRBER, T., RAPOL, U., RIEBE, M., SCHMIDT, P. O., BECHER, C., GÜHNE, O., DÜR, W., AND BLATT, R. 2005. Scalable multi-particle entanglement of trapped ions. Nature 438, 643-646. (Pubitemid 41740570)
24. HECKMANN, R., KLASING, R., MONIEN, B., AND UNGER, W. 1991. Optimal embedding of complete binary trees into lines and grids. In Proceedings of the International Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, vol. 570. Springer Verlag, 25-35.
25. HELMER, F., MARIANTONI, M., FOWLER, A. G., VON DELFT, J., SOLANO, E., AND MARQUARDT, F. 2007. Two-dimensional cavity grid for scalable quantum computation with superconducting circuits. http://arxiv.org/abs/0706.3625.
26. HENNESSY, J. L. AND PATTERSON, D. A. 2006. Computer Architecture: A Quantitative Approach 4th Ed. Morgan Kaufman.
27. JONES, N. C., VAN METER, R., FOWLER, A. G., MCMAHON, P. L., KIM, J., LADD, T. D., AND YAMAMOTO, Y. 2010. A layered architecture for quantum computing using quantum dots. http://arxiv.org/abs/1010.5022.
28. KANE, B. E. 1998. A silicon-based nuclear spin quantum computer. Nature 393, 133-137. (Pubitemid 28242245)
29. KEH, H.-C. AND LIN, J.-C. 1997. Embedding a complete binary tree into a faulty supercube. In Proceedings of the International Conference on Algorithms and Architectures for Parallel Processing (ICAPP). 323-330.
30. KLEINJUNG, T., AOKI, K., FRANKE, J., LENSTRA, A. K., THOMÉ, E., BOS, J. W., GAUDRY, P., KRUPPA, A., MONTGOMERY, P. L., OSVIK, D. A., TE RIELE, H. J. J., TIMOFEEV, A., AND ZIMMERMANN, P. 2010. Factorization of a 768-bit rsa modulus. In Proceedings of CRYPTO. Lecture Notes in Computer Science, vol. 6223. 333-350.
31. KNUTH, D. E. 1998. The Art of Computer Programming 2nd Ed. Addison-Wesley Professional.
32. KUTIN, S. A. 2007. Shor's algorithm on a nearest-neighbor machine. http://arxiv.org/abs/quant-ph/0609001.
33. LAFOREST, M., SIMON, D., BOILEAU, J.-C., BAUGH, J., DITTY, M. J., AND LAFLAMME, R. 2007. Using error correction to determine the noise model. Phys. Rev. A 75, 1, 012331.
34. LIN, Q. AND HE, B. 2010. Efficient generation of universal two-dimensional cluster states with hybrid systems. Phys. Rev. A 82, 2, 022331.
35. MASLOV, D. 2007. Linear depth stabilizer and quantum fourier transformation circuits with no auxiliary qubits in finite-neighbor quantum architectures. Phys. Rev. A 76, 5, 052310.
36. MASLOV, D., FALCONER, S. M., AND MOSCA, M. 2008. Quantum circuit placement. IEEE Trans. Comput.-Aid. Des. Integr. Circ. Syst. 27, 4, 752-763. (Pubitemid 351470942)
37. MOSCA, M. 2008. Quantum algorithms. http://arxiv.org/abs/0808.0369.
38. MÖTTÖNEN, M. AND VARTIAINEN, J. J. 2006. Decompositions of general quantum gates. http://arxiv.org/abs/0504100.
39. NAYAK, C., SIMON, S. H., STERN, A., FREEDMAN, M., AND DAS SARMA, S. 2008. Non-abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 3, 1083-1159.
40. PÉREZ-DELGADO, C. A., MOSCA, M., CAPPELLARO, P., AND CORY, D. G. 2006. Single spin measurement using cellular automata techniques. Phys. Rev. Lett. 97, 10, 100501.
41. RAUSSENDORF, R. AND BRIEGEL, H. J. 2001. A one-way quantum computer. Phys. Rev. Lett. 86, 22, 5188-5191. (Pubitemid 32527770)
42. RAUSSENDORF, R., BROWNE, D. E., AND BRIEGEL, H. J. 2003. Measurement-based quantum computation on cluster states. Phys. Rev. A 68, 2, 022312.
43. RAUSSENDORF, R., HARRINGTON, J., AND GOYAL, K. 2007. Topological fault-tolerance in cluster state quantum computation. New J. Phys. 9, 6, 199.
44. SEITZ, C. L. 1985. The cosmic cube. Comm. ACM 28, 22-33.
45. SHENDE, V. V., BULLOCK, S. S., AND MARKOV, I. L. 2006. Synthesis of quantum-logic circuits. IEEE Trans. Comput.-Aid. Des. Integr. Circ. Syst. 25, 6, 1000-1010.
46. SHENDE, V. V. AND MARKOV, I. L. 2009. On the CNOT-cost of TOFFOLI gates. Quant. Inf. Computat. 9, 5-6, 461-486.
47. SHOR, P. W. 1995. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, 4, R2493-R2496.
48. SHOR, P. W. 1997. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 5, 1484-1509. (Pubitemid 127613100)
49. STEANE, A. 1996a. Multiple-Particle Interference and Quantum Error Correction. Proc. Royal Soc. London Series A: Math. Physical Engin. Sci. 452, 1954, 2551-2577. (Pubitemid 126766262)
50. STEANE, A. M. 1996b. Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 5, 793-797. (Pubitemid 126625551)
51. SVORE, K. M., TERHAL, B. M., AND DIVINCENZO, D. P. 2005. Local fault-tolerant quantum computation. Phys. Rev. A 72, 2, 022317.
52. SZKOPEK, T., BOYKIN, P., FAN, H., ROYCHOWDHURY, V. P., YABLONOVITCH, E., SIMMS, G., GYURE, M., AND FONG, B. 2006. Threshold error penalty for fault-tolerant quantum computation with nearest neighbor communication. IEEE Trans. Nanotech. 5, 1, 42-49. (Pubitemid 43131853)
53. TAKAHASHI, Y. 2009. Quantum arithmetic circuits: A survey. IEICE Trans. Fund. Electron. Comm. Comput. Sci. E92. A, 5, 1276-1283.
54. TAKAHASHI, Y., KUNIHIRO, N., AND OHTA, K. 2007. The quantum fourier transform on a linear nearest neighbor architecture. Quant. Inf. Computat. 7, 4, 383-391.
55. TRISETYARSO, A. AND VAN METER, R. 2010. Circuit design for a measurement-based quantum carrylookahead adder. Int. J. Quant. Inf. 8, 5, 843-867.
56. Unger, W. 2008. private communication.
57. VALLONE, G., DONATI, G., CECCARELLI, R., AND MATALONI, P. 2010. Six-qubit two-photon hyperentangled cluster states: Characterization and application to quantum computation. Phys. Rev. A 81, 5, 052301.
58. VAN METER, R. 2004. Communications topology and distribution of the quantum fourier transform. In Proceedings of the Quantum Information Technology Symposium (QIT10). 2.
59. VAN METER, R. AND ITOH, K. M. 2005. Fast quantum modular exponentiation. Phys. Rev. A 71, 5, 052320.
60. VAN METER, R., LADD, T. D., FOWLER, A. G., AND YAMAMOTO, Y. 2010. Distributed quantum computation architecture using semiconductor nanophotonics. Int. J. Quant. Inf. 8, 295-323.
61. VAN METER III, R. D. 2006. Architecture of a quantum multicomputer optimized for Shor's factoring algorithm. Ph. D. thesis, Keio University. http://arxiv.org/abs/quant-ph/0607065.
62. VEDRAL, V., BARENCO, A., AND EKERT, A. 1996. Quantum networks for elementary arithmetic operations. Phys. Rev. A 54, 1, 147-153. (Pubitemid 126583488)
63. VOLLMER, H. 1999. Introduction to Circuit Complexity: A Uniform Approach. Springer-Verlag.
64. Weisstein, E. W. 2010. Binary tree. http://mathworld.wolfram.com/ BinaryTree.html.