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.
Quantum Information Processing – Springer Journals
Published: May 8, 2011
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