Simulations of Quantum Turing Machines by Quantum Multi-Counter Machines

We define quantum multi-stack machines (abbr. QMSMs) by generalizing quantum pushdown automata (abbr. QPDAs) dealt with before from one-stack to multi-stack, and the well-formedness (abbr. W-F) conditions for characterizing the unitary evolution are presented. Afterwards, by means of QMSMs we define quantum multi-counter machines (abbr. QMCMs) that are somewhat different from the quantum counter automata (abbr. QCAs) in the literature; as well, the W-F conditions are given for these defined devices. To simulate quantum Turing machines (abbr. QTMs), we deal with a number of simulations between QMCMs with different counters and different counts. In particular, we demonstrate the efficient simulations of QTMs in terms of QMSMs and QMSMs. To conclude, some remarks are included, and a number of issues are proposed for further considerations.