  As was well known, in classical computation, Turing machines, circuits,
multi-stack machines, and multi-counter machines are equivalent, that is, they
can simulate each other in polynomial time. In quantum computation, Yao [11]
first proved that for any quantum Turing machines $M$, there exists quantum
Boolean circuit $(n,t)$-simulating $M$, where $n$ denotes the length of input
strings, and $t$ is the number of move steps before machine stopping. However,
the simulations of quantum Turing machines by quantum multi-stack machines and
quantum multi-counter machines have not been considered, and quantum
multi-stack machines have not been established, either. Though quantum counter
machines were dealt with by Kravtsev [6] and Yamasaki {\it et al.} [10], in
which the machines count with $0,\pm 1$ only, we sense that it is difficult to
simulate quantum Turing machines in terms of this fashion of quantum computing
devices, and we therefore prove that the quantum multi-counter machines allowed
to count with $0,\pm 1,\pm 2,...,\pm n$ for some $n>1$ can efficiently simulate
quantum Turing machines.
  Therefore, our mail goals are to establish quantum multi-stack machines and
quantum multi-counter machines with counts $0,\pm 1,\pm 2,...,\pm n$ and $n>1$,
and particularly to simulate quantum Turing machines by these quantum computing
devices.
