Scalable Experimental Bounds for Dicke and GHZ States Fidelities

2022-10-06

ACM International Conference on Computing Frontiers

AI Summary

Scalable fidelity estimation of large-scale entangled states—specifically Dicke and GHZ states—on NISQ devices is hindered by the exponential resource cost of full quantum tomography. To address this, we propose a scalable experimental method for estimating lower bounds on state fidelity. Leveraging the Quantinuum H1 trapped-ion platform, our approach integrates symmetric-state preparation circuits with optimized Pauli measurement strategies. We experimentally achieve fidelity lower-bound estimates for all Dicke states up to $N leq 10$ and all GHZ states up to $N leq 20$, marking the first such demonstration. The resulting bounds surpass the precision of full-fidelity measurements performed on small-scale states in superconducting platforms and represent the largest-scale fidelity lower bounds reported to date for Dicke and GHZ states. By circumventing exponential resource scaling, our work establishes a new paradigm for efficient, practical benchmarking of high-dimensional entangled states in the NISQ era.

Abstract

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. 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.

Problem

• Quantum Devices
• Entangled States
• Measurement Accuracy

Innovation

• Quantinuum H1 Quantum Computer
• Large-scale Dicke and GHZ States
• Enhanced Quantum Circuit Efficiency