Measurement-based long-range entangling gates in constant depth

The depth of quantum circuits is a critical factor when running them on state-of-the-art quantum devices owing to their limited coherence times. Reducing circuit depth decreases noise in near-term quantum computations and reduces overall computation time. This also benefits fault-tolerant quantum computations. Here, we show how to reduce the depth of quantum subroutines 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 feedforward 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.