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Estimating the state preparation fidelity of highly entangled states on noisyintermediate-scale quantum (NISQ) devices is an important task for benchmarkingand application considerations. Unfortunately, exact fidelity measurementsquickly become prohibitively expensive, as they scale exponentially as $O(3^N)$for $N$-qubit states, using full state tomography with measurements in allPauli bases combinations. However, Somma and others [PhysRevA.74.052302]established that the complexity could be drastically reduced when looking atfidelity lower bounds for states that exhibit symmetries, such as Dicke Statesand GHZ States. For larger states, these bounds still need to be tight enoughto provide reasonable estimations on NISQ devices.  For the first time and more than 15 years after the theoretical introduction,we report meaningful lower bounds for the state preparation fidelity of allDicke States up to $N=10$, and all GHZ states up to $N=20$ on Quantinuum H1ion-trap systems using efficient implementations of recently proposed scalablecircuits for these states. Our achieved lower bounds match or exceed previouslyreported exact fidelities on superconducting systems for much smaller states.This work provides a path forward to benchmarking entanglement as NISQ devicesimprove in size and quality.

Scalable Experimental Bounds for Dicke and GHZ States Fidelities