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 $O(3^N)$ 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. For larger states, these bounds still need to be tight enough 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. This work provides a path forward to benchmarking entanglement as NISQ devices improve in size and quality.

翻译：在含噪中等规模量子（NISQ）器件上估算高度纠缠态的制备保真度，是基准测试与应用考量中的重要任务。然而，精确保真度测量会迅速变得高得令人望而却步——对于$N$量子比特态，若采用所有泡利基组合的全状态层析成像，其复杂度呈$O(3^N)$指数增长。但Somma等人[PhysRevA.74.052302]指出，当关注Dicke态与GHZ态等具有对称性的态时，其保真度下界复杂度可大幅降低。对于较大规模的态，这些下界仍需足够紧致，方能在NISQ器件上提供合理估算。在理论提出逾15年后，我们首次报告了有意义的制备保真度下界：在Quantinuum H1离子阱系统中，采用近期提出的可扩展电路的高效实现方案，对$N\leq10$的所有Dicke态及$N\leq20$的所有GHZ态进行了实验验证。所得下界匹配或超越了此前在超导系统中针对更小规模态所报告的精确保真度。这项工作为随着NISQ器件规模与质量的提升而开展纠缠基准测试提供了可行路径。