# Two-bit gates are universal for quantum computation

- Published: 01 Feb 1995
- Publisher: American Physical Society (APS)

- IBM (United States) United States

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[1] See, e.g., P. Benioff, “Quantum mechanical Hamiltonian models of Turing machines”, J. Stat. Phys. 29, 515 (1982). Ref. [26] has a complete set of references.

[2] D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation”, Proc. Roy. Soc. Lond. A 439, 554 (1992).

[3] E. Bernstein and U. Vazirani, “Quantum complexity theory”, Proceedings of the 25th Annual ACM Symposium on the Theory of Computing, 1993, p. 11.

[4] P. W. Shor, “Algorithms for quantum computation: discrete log and factoring”, Proceedings of the 26th Annual ACM Symposium on the Theory of Computing, 1994 (to be published).

[5] D. R. Simon, “On the power of quantum computation”, Proceedings of the 26th Annual ACM Symposium on the Theory of Computing, 1994 (to be published).

[6] D. Coppersmith, “An approximate Fourier transform useful in quantum factoring”, preprint (1994); and unpublished.

[7] See, e.g., S. Washburn and R. A. Webb, “Aharonov-Bohm effect in normal metal quantum coherence and transport”, Adv. Phys. 35, 375 (1986). [OpenAIRE]

[8] Using the electron spin as a computational degree of freedom has been discussed by S. Bandyopadhyay, B. Das, and A. E. Miller, “Supercomputing with spin-polarized single electrons in a quantum coupled architecture”, submitted to Nanotechnology (1994). There are other, largely unexplored, possibilities of using natural Ising-spin systems for computation; see, e.g., W. P. Wolf, “Anisotropic interactions between magnetic ions”, J. Phys. 32, C1-26 (1970).

[9] R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+ : Y2SiO5”, Phys. Rev. Lett. 72, 2179 (1994).

[10] C. S. Lent, P. D. Tougaw, W. Porod, and G. H. Bernstein, “Quantum cellular automata”, Nanotechnology 4, 49 (1993).

[11] D. M. Eigler, C. P. Lutz, and W. E. Rudge, “An atomic switch realized with the scanning tunneling microscope”, Nature 352, 600 (1991). [OpenAIRE]

[15] S. Lloyd, “A potentially realizable quantum computer”, Science, 261, 1569 (1993); “Envisioning a quantum supercomputer”, Science, 263, 695 (1994).

[16] K. Obermayer, W. G. Teich and G. Mahler, “Structural basis of multistationary quantum systems. I. Effective single-particle dynamics”, Phys. Rev. B 37, 8096 (1988); W. G. Teich, K. Obermayer and G. Mahler, “Structural basis of multistationary quantum systems. II. Effective few-particle dynamics”, Phys. Rev. B 37, 8111 (1988). [OpenAIRE]

[17] G. P. Berman, G. D. Doolen, D. D. Holm, and V. I. Tsifrinovich, “Quantum computer on a class of one-dimensional Ising systems”, LANL preprint LA-UR-94-1404 (1994).

[18] J. W. Negele and H. Orland, Quantum Many-Particle Systems, (Addison-Wesley, 1988), Eq. (2.11).

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