  We introduce a polyadic analog of supersymmetry by considering the
polyadization procedure (proposed by the author) applied to the toy model of
one-dimensional supersymmetric quantum mechanics. The supercharges are
generalized to polyadic ones using the $n$-ary sigma matrices defined in
earlier work. In this way, polyadic analogs of supercharges and Hamiltonians
take the cyclic shift block matrix form, and they can describe multidegenerated
quantum states in a way that is different from the $N$-extended and multigraded
SQM. While constructing the corresponding supersymmetry as an $n$-ary Lie
superalgebra ($n$ is the arity of the initial associative multiplication), we
have found new brackets with a reduced arity of $2\leq m<n$ and a related
series of $m$-ary superalgebras (which is impossible for binary superalgebras).
In the case of even reduced arity $m$ we obtain a tower of higher order (as
differential operators) even Hamiltonians, while for $m$ odd we get a tower of
higher order odd supercharges, and the corresponding algebra consists of the
odd sector only.
