  The depth of quantum circuits is a critical factor when running them on
state-of-the-art quantum devices due to their limited coherence times. Reducing
circuit depth decreases noise in near-term quantum computations and reduces
overall computation time, thus, also benefiting fault-tolerant quantum
computations. Here, we show how to reduce the depth of quantum sub-routines
that typically scale linearly with the number of qubits, such as quantum
fan-out and long-range CNOT gates, to a constant depth using mid-circuit
measurements and feed-forward operations, while only requiring a 1D line
topology. We compare our protocols with existing ones to highlight their
advantages. Additionally, we verify the feasibility by implementing the
measurement-based quantum fan-out gate and long-range CNOT gate on real quantum
hardware, demonstrating significant improvements over their unitary
implementations.
