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arXiv:2602.11839

Single-shot GHZ characterization with connectivity-aware fanout constructions

Giancarlo Gatti

quant-phSubmitted Feb 12, 2026• Announced Feb 13, 2026• 0 citations
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Abstract

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 $2\log_2(n)-1$, 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 \textit{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 $17$).

Comments
7 pages, 3 figures

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Mid-circuit measurements with feedforward reduce the optimal worst-case quantum depth for exact nnn-qubit unitary synthesis from Θ(n)Θ(n)Θ(n) to O(1)O(1)O(1), using arbitrary one- and two-qubit gates and unrestricted ancillary space. Measurements and resets without feedforward remain subject to the circuit causal-cone bound. Our deterministic construction uses single-qubit measurements, O(1)O(1)O(1) rounds of parity feedforward, and O(n4nlog⁡(n+2))O(n4^n\log(n+2))O(n4nlog(n+2)) total qubits, with all ancillas starting and ending in ∣0⟩|0\rangle∣0⟩. Classical processing is not counted in quantum depth. We teleport only the matrix error of an approximation by Nehoran and Yuen. An exactly prepared ancillary state encodes this error, whose action is added back by coherent interference. At operator-norm error 2−n2^{-n}2−n, one step of amplitude amplification suffices. Coherent fanout circuits achieve the same constant-depth bound, while circuits using only one- and two-qubit gates attain depth Θ(n)Θ(n)Θ(n) with O(4nlog⁡2(n+2))O(4^n\log^2(n+2))O(4nlog2(n+2)) gates. Generic targets require Ω(4n/(h+1))Ω(4^n/(h+1))Ω(4n/(h+1)) qubits at depth hhh, even under unrestricted classical control. Our depth-width trade-offs meet this bound within a factor O(n2)O(n^2)O(n2) for 1≤h≤2n1\le h\le2^n1≤h≤2n.
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