Single-shot GHZ characterization with connectivity-aware fanout constructions

We propose a practical recipe to transform any depth-L block of CNOTs that prepares n-qubit GHZ states into an n-qubit fanout gate (multitarget-CNOT) of depth 2L-1, without the need for ancilla qubits. Considering known logarithmic-depth circuits to prepare GHZ-states, this allows us to construct an n-qubit fanout gate with depth 2log₂(n)-1, reproducing previous ancillaless constructions. We employ our recipe to construct n-qubit fanout gates under heavy-hex connectivity restrictions, obtaining a depth of O\(n^1/2\), again reproducing previous complexity theory constructions. Using this recipe on the ibm_fez architecture yields a 156-qubit fanout construction with depth 33. Additionally, we show how to employ these n-qubit fanout constructions to measure complete sets of commuting observables from the n-body Pauli group with the same depth, allowing for efficient single-shot characterization of any GHZ-like state in a given known basis, e.g. fully characterizing a single copy of a 156-qubit GHZ state using circuit depth 33 in textit{ibm\_fez} (its preparation requires an additional depth of 17).