Scalable Experimental Bounds for Dicke and GHZ States Fidelities

Estimating the state preparation fidelity of highly entangled states on noisy intermediate-scale quantum (NISQ) devices is an important task for benchmarking and application considerations. Unfortunately, exact fidelity measurements quickly become prohibitively expensive, as they scale exponentially as O(3N) for N-qubit states, using full state tomography with measurements in all Pauli bases combinations. However, Somma et al. [20] established that the complexity could be drastically reduced when looking at fidelity lower bounds for states that exhibit symmetries, such as Dicke States and GHZ States. For larger states, these bounds still need to be tight enough to provide reasonable estimations on NISQ devices.