Previous work on parallel quantum algorithms has focused on minimizing the length of the critical path of the circuit (i.e., query span), motivated by the small decoherence times of qubits. In this paper, we study similar settings where queries to a quantum circuit can be made in parallel in each timestep. Rather than focus exclusively on query span, however, we are interested in also minimizing the total number of queries made across all parallel processes (i.e., query work). We give parallel quantum algorithms that solve the maxima set and convex hull problems for n lexicographically sorted points in the plane in \(\tilde{O}(\sqrt{n})\) query span and \(\tilde{O}(\sqrt{nh})\)  query work, where h is the size of the output. These results therefore resolve a natural question of whether we can use quantum computers in parallel to improve the depth of a quantum algorithm without requiring more work than a sequential algorithm. Also, note that our work bounds are sublinear when h is \(O(n^{1-\epsilon })\) , for a small constant, \(\epsilon >0\) .