Mid-circuit measurements cut the cost of a quantum logic workhorse

Multi-controlled Toffoli gates underpin quantum arithmetic but are expensive to compile into hardware-native operations. By splitting execution into adaptive stages — measuring ancilla qubits partway through and applying corrections conditioned on those results — the authors reduce both the number of entangling gates and the T-count relative to standard static decompositions. Relative-phase variants of primitive gates absorb some overhead that fixed circuits cannot. The gains scale with the number of controls, making the approach relevant for near-term and fault-tolerant devices alike.