  Branching programs are quite popular for studying time-space lower bounds.
Bera et al. recently introduced the model of generalized quantum branching
program aka. GQBP that generalized two earlier models of quantum branching
programs. In this work we study a restricted version of GQBP with the
motivation of proving bounds on the query-space requirement of quantum-query
circuits. We show the first explicit query-space lower bound for our restricted
version. We prove that the well-studied OR$_n$ decision problem, given a
promise that at most one position of an $n$-sized Boolean array is a 1,
satisfies the bound $Q^2 s = \Omega(n^2)$, where $Q$ denotes the number of
queries and $s$ denotes the width of the GQBP. We then generalize the problem
to show that the same bound holds for deciding between two strings with a
constant Hamming distance; this gives us query-space lower bounds on problems
such as Parity and Majority. Our results produce an alternative proof of the
$\Omega(\sqrt{n})$-lower bound on the query complexity of any non-constant
symmetric Boolean function.
