Density matrix formalism of duality quantum computer and the solution of zero-wave-function paradox

  • Authors:

  • Jingxin Cui;Tao Zhou;Gui Lu Long

  • Affiliations:

  • State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, China 100084;State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, China 100084;State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, China 100084 and Tsinghua National Laboratory for Information Science and Technolog ...

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2012

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Abstract

Duality quantum computer can accommodate both unitary and non-unitary operations. In this paper, we derive the mathematical theory of duality quantum computer in terms of density matrix using the duality mode of quantum computers. We give a solution to the `zero-wave-function' paradox of duality quantum computer raised by Zou et al. (Quantum Inf Process 8:37---50 2009) where in duality quantum computer the final wave function may be zero, which contradicts the general understanding of an normalized wave function for a quantum system. We show that it is natural for zero wave function to occur in duality quantum computer because we only consider a part of the wave function in duality quantum computer. In addition, the conditions for zero wave function are presented in both pure state formalism and mixed state formalism.