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In order to establish the computational equivalence between quantum Turingmachines (QTMs) and quantum circuit families (QCFs) using Yao's quantum circuitsimulation of QTMs, we previously introduced the class of uniform QCFs based onan infinite set of elementary gates, which has been shown to be computationallyequivalent to the polynomial-time QTMs (with appropriate restriction ofamplitudes) up to bounded error simulation. This result implies that thecomplexity class BQP introduced by Bernstein and Vazirani for QTMs equals itscounterpart for uniform QCFs. However, the complexity classes ZQP and EQP forQTMs do not appear to equal their counterparts for uniform QCFs. In this paper,we introduce a subclass of uniform QCFs, the finitely generated uniform QCFs,based on finite number of elementary gates and show that the class of finitelygenerated uniform QCFs is perfectly equivalent to the class of polynomial-timeQTMs; they can exactly simulate each other. This naturally implies that BQP aswell as ZQP and EQP equal the corresponding complexity classes of the finitelygenerated uniform QCFs.Comment: 11page

Perfect computational equivalence between quantum Turing machines and finitely generated uniform quantum circuit families