Implementation of shor's algorithm on a linear nearest neighbour qubit array

Quantum Information and Computation

Volumn 4, Issue 4, 2004, Pages 237-251

  Fowler, A G ^a   Devitt, S J ^a   Hollenberg, L C L ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Linear nearest neighbour; Quantum circuit; Shor's algorithm

Indexed keywords

COMPUTER ARCHITECTURE; COMPUTER HARDWARE;

INTEGER-N; LEADING ORDERS; NEAREST NEIGHBOUR; NEAREST-NEIGHBOUR INTERACTIONS; QUANTUM CIRCUIT; QUBIT ARRAYS; SHOR'S ALGORITHMS; TIME POLYNOMIALS;

QUBITS;

EID: 4043121097     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. P. W. Shor (1994), Polynomial time algorithms for discrete logarithms and factoring on a quantum computer, Proc. Algorithmic Number Theory. First International Symposium, ANTS-I, p. 289
2. V. Subramaniam and P. Ramadevi (2002), Quantum computation of Jones' polynomials, quant-ph/0210095.
3. B. E. Kane (1998), A silicon-based nuclear spin quantum computer, Nature, Vol.393, pp. 133-137.
4. N.-J. Wu et al. (1999), Quantum computer using coupled quantum dot molecules, quant-ph/9912036.
5. R. Vrijen et al. (2000), Electron spin resonance transistors for quantum computing in silicon-germanium heterostructures, Phys. Rev. A, 62, 012306.
6. B. Golding and M. I. Dykman (2003), Acceptor-based silicon quantum computing, cond-mat/0309147.
7. E. Novais and A. H. Castro Neto (2003), Nuclear spin qubits in a pseudo-spin quantum chain, cond-mat/0308475.
8. L. C. L. Hollenberg et al (2003), Charge-based quantum computing using single donors in semiconductors, cond-mat/0306235.
9. L. Tian and P. Zoller (2003), Quantum computing with atomic josephson junction arrays, quant-ph/0306085.
10. K. Yang et al. (2003), Universal quantum gates based on both geometric and dynamic phases in quantum dots, Chinese Phys. Lett., Vol.20, pp. 991-994.
11. M. Feng et al. (2003), Spin-based quantum gating with semiconductor quantum dots by bichromatic radiation method, quant-ph/0304169.
12. J. K. Pachos and P. L. Knight (2003), Quantum computation with a one-dimensional optical lattice, Phys. Rev. Lett., 91, 107902.
13. M. Friesen et al. (2003), Practical design and simulation of silicon-based quantum dot qubits, Phys. Rev. B, 67, 121301.
14. L. M. K. Vandersypen et al. (2003), Quantum computing with electron spins in quantum dots, quant-ph/0207059.
15. P. Solinas et al. (2003), Semiconductor-based geometrical quantum gates, Phys. Rev. B, 67, 121307.
16. J. H. Jefferson et al. (2002), Two-electron quantum dots as scalable qubits, Phys. Rev. A, 66, 042328.
17. D. Petrosyan and G. Kurizki (2002), Scalable solid-state quantum processor using subradiant two-atom states, Phys. Rev. Lett., 89, 207902.
18. V. N. Golovach and D. Loss (2002), Electron spins in artificial atoms and molecules for quantum computing, Semicond. Sci. Tech., Vol.17, 355-366.
19. T. D. Ladd et al. (2002), An all silicon quantum computer, Phys. Rev. Lett., 89, 017901.
20. V. V'yurkov and L. Y. Gorelik (2000), Charge based quantum computer without charge transfer, quant-ph/0009099.
21. (2003), E. O. Kamenetskii and O. Voskoboynikov. On implementation of ferrite magnetostatic/magnetoelectric particles for quantum computation, cond-mat/0310558.
22. S. Beauregard (2003), Circuit for Shor's algorithm using 2n+3 qubits, Quantum Inform. Compu., Vol.3 No.2, pp. 175-185.
23. R. L. Rivest et al. (1978), A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, Vol.21 No.2, 120-126.
24. V. Vedral et al. (1996), Quantum networks for elementary arithmetic operations, Phys. Rev. A, 54, 147-153.
25. P. Gossett (1998), Quantum carry-save arithmetic, quant-ph/9808061.
26. C. Zalka (1998), Fast versions of Shor's quantum factoring algorithm, quant-ph/9806084.
27. A. G. Fowler and L. C. L. Hollenberg (2003), Scalability of Shor's algorithm with limited set of rotation gates, quant-ph/0306018.
28. J. Zhang et al (2003), Geometric theory of nonlocal two-qubit operations, Phys. Rev. A, 67, 042313.
29. M. J. Bremner et al. (2002), A practical scheme for quantum computation with any two-qubit entangling gate, Phys. Rev. Lett., 89, 247902.
30. C. D. Hill and H.-S. Goan (2003), Fast non-adiabatic two qubit gates for the Kane quantum computer, Phys. Rev. A, 68, 012321.
31. D. Coppersmith (1994), An Approximate Fourier Transform Useful in Quantum Factoring, IBM Research Report RC19642.
32. T. G. Draper (2000), Addition on a Quantum Computer, quant-ph/0008033.
33. A. G. Fowler, C. D. Hill, and L. C. L. Hollenberg (2004), Quantum error correction on linear nearest neighbor qubit arrays, Phys. Rev. A, 69, 042314.
34. S. Parker and M. B. Plenio (2000), Efficient factorization with a single pure qubit and log(n) mixed qubits, Phys. Rev. Lett., 85, pp. 3049-3052.