Abstract
We present a mathematical theory for a new type of quantum computer called a duality quantum computer that is similar to one that has recently been proposed. We discuss the nonunitarity of certain circuits of a duality quantum computer. We then discuss the relevance of this work to quantum operations and their convexity theory. This discussion is based upon isomorphism theorems for completely positive maps.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brooks, M.: Quantum Computing and Communications. Springer, London (1999)
Choi, M.D.: Completely positive linear maps on complex matrices. Linear Algebra Appl. 10, 285–290 (1975)
Gruska, J.: Quantum Computing. McGraw-Hill, London (1999)
Gudder, S.: Quantum mechanics on finite groups. Found. Phys. 36, 1160–1192 (2006)
Gudder, S.: Mathematical theory of duality quantum computers. Quant. Inf. Proc. 6, 37–48 (2007)
Hirvensalo, M.: Quantum Computing. Springer, Berlin (2001)
Long, G.L.: The general quantum interference principle and the duality computer. arxiv: quant-ph/0512120 (2005)
Long, G.L.: Mathematical theory of the duality computer in the density matrix formalism. arxiv: quant-ph/0605087 (2006)
Nielsen, M., Chuang, J.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Shiekh, A.Y.: The role of quantum interference in quantum computing. Int. J. Theor. Phys. 45, 1646–1648 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gudder, S. Duality Quantum Computers and Quantum Operations. Int J Theor Phys 47, 268–279 (2008). https://doi.org/10.1007/s10773-007-9512-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-007-9512-1