  Quantum formulas, defined by Yao [FOCS '93], are the quantum analogs of
classical formulas, i.e., classical circuits in which all gates have fanout
one. We show that any read-once quantum formula over a gate set that contains
all single-qubit gates is equivalent to a read-once classical formula of the
same size and depth over an analogous classical gate set. For example, any
read-once quantum formula over Toffoli and single-qubit gates is equivalent to
a read-once classical formula over Toffoli and NOT gates. We then show that the
equivalence does not hold if the read-once restriction is removed. To show the
power of quantum formulas without the read-once restriction, we define a new
model of computation called the one-qubit model and show that it can compute
all boolean functions. This model may also be of independent interest.
