Single-shot GHZ characterization with connectivity-aware fanout constructions

TL;DR

This paper introduces a practical method to transform depth-L CNOT blocks into efficient, ancilla-free n-qubit fanout gates, enabling scalable GHZ state characterization on quantum hardware with connectivity constraints.

Contribution

The authors present a novel recipe for converting CNOT circuits into fanout gates without ancillas, optimizing depth for hardware-limited quantum architectures.

Findings

Constructed 156-qubit fanout with depth 33 on ibm_fez.

Achieved single-shot GHZ state characterization with minimal circuit depth.

Reproduced known complexity bounds for fanout gate implementations.

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 $17$).