Quantum Formulas: A Lower Bound and Simulation

We show that Nechiporuk’s method [26] for proving lower bounds for Boolean formulas can be extended to the quantum case. This leads to an Ω(n/ log n) lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas [27] states that the majority function does not have a linear–size quantum formula. We also show that quantum formulas can be simulated by Boolean circuits of almost the same size.