Scalable Experimental Bounds for Entangled Quantum State Fidelities

TL;DR

This paper introduces scalable methods to estimate lower bounds of entangled quantum state fidelities on NISQ devices, enabling efficient benchmarking of large Dicke and GHZ states with practical experimental results.

Contribution

It provides the first meaningful lower bounds for Dicke states up to 10 qubits and GHZ states up to 20 qubits on real quantum hardware, using scalable circuits and symmetry-based bounds.

Findings

Lower bounds match or surpass previous fidelities on smaller systems.

Efficient implementation of scalable circuits for large entangled states.

Approximate GHZ-based methods improve fidelity estimates for large Dicke states.

Abstract

Estimating the state preparation fidelity of highly entangled states on noisy intermediate-scale quantum (NISQ) devices is important for benchmarking and application considerations. Unfortunately, exact fidelity measurements quickly become prohibitively expensive, as they scale exponentially as $O(3^N)$ for $N$-qubit states, using full state tomography with measurements in all Pauli bases combinations. However, Somma and others [PhysRevA.74.052302] 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. These bounds must still be tight enough for larger states to 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 all Dicke States up to $N=10$ and all GHZ states up to $N=20$ on Quantinuum H1 ion-trap systems using efficient implementations of recently proposed scalable circuits for these states. Our achieved lower bounds match or exceed previously reported exact fidelities on superconducting systems for much smaller states. Furthermore, we provide evidence that for large Dicke States $D^N_{N/2}$, we may resort to a GHZ-based approximate state preparation to achieve better fidelity. This work provides a path forward to benchmarking entanglement as NISQ devices improve in size and quality.