  Our previous work dealt with the zeta function for the interacting particle
system (IPS) including quantum cellular automaton (QCA) as a typical model in
the study of ``IPS/Zeta Correspondence". On the other hand, the absolute zeta
function is a zeta function over F_1 defined by a function satisfying an
absolute automorphy. This paper proves that a new zeta function given by QCA is
an absolute automorphic form of weight depending on the size of the
configuration space. As an example, we calculate an absolute zeta function for
a tensor-type QCA, and show that it is expressed as the multiple gamma
function. In addition, we obtain its functional equation by the multiple sine
function.
