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, it is known [Somma et.al. 2006] that the complexity can 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 have so far not been tight enough to provide reasonable estimations on today's (2022) NISQ devices. In this work, 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. For example, we give state preparation fidelity lower bounds of (i) 0.46 for the Dicke State |D10,5> and (ii) 0.73 for the GHZ State |G20>. These match or exceed exact fidelity records recently achieved on superconducting systems for the much smaller states |D6,3> and |G5>, respectively. Furthermore, we provide evidence that for large Dicke States |DN,N/2>, we can resort to a GHZ-based approximate state preparation to achieve better fidelity.
翻译:估计高度纠缠的中间级量子(NISQ)装置的国家准备准确性是衡量基准和应用因素的一项重要任务。 不幸的是,精确的准确性测量很快变得过于昂贵,因为对于Nqubit 国家来说,它们以O(3 ⁇ N)指数成倍的缩放,使用所有保利基地的测量组合进行完全的状态透析。然而,[Somma 和al. 2006]众所周知,如果对显示对齐的中间级量子(NISQSQ)装置的准确性较低界限,其复杂性可以大幅降低。对于较大的国家来说,这些精确度测量值很快变得太紧,对于今天(20°N+Q)的准确性而言,这些约束值还不足以提供合理的估计值。