# Simulations of Quantum Turing Machines by Quantum Multi-Stack Machines

- Published: 29 Jan 2005

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[12] T. Yamakami, A Foundation of Programming a Multi-Tape Quantum Turing Machine, in: MFCS'99, Lecture Notes in Computer Science, Vol.1672, Springer-Verlag, Berlin, 1999, pp. 430-441. More precisely, we show that VσM2 is a unitary operator on l2(CM2) = HQ2⊗H[0,r−1]Z⊗HN. For any (qi,ni1,ni2) ∈ Q2 × [0,r − 1]Z × N, i = 1,2, n(q, n1, n2, . . . , nr) : q ∈ Q, ni ∈ N, i = 1, 2, . . . , r, Pir=−11 ni ≤ 1o and therefore, Vσ is a linear operator on l2(CM2 ) where CM2 = n|qi|n1i|n2i . . . |nri : q ∈ Q, ni ∈ N, i = 1, 2, . . . , r, Pjr=−11 nj ≤ 1o, that is, l2(CM2 ) = HQ ⊗ (H{0,1})⊗(r−1) ⊗ HN. [OpenAIRE]