Scalable Experimental Bounds for Entangled Quantum State Fidelities

Journal Article · 17 December 2024 · ACM Transactions on Quantum Computing

DOI: https://doi.org/10.1145/3700885 · OSTI ID:2506987

Aktar, Shamminuj  ^[1]; Bärtschi, Andreas  ^[2]; Badawy, Abdel-Hameed A.  ^[1]; Eidenbenz, Stephan  ^[2]

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1. New Mexico State Univ., Las Cruces, NM (United States)
2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

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 et al.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 |$$D^{N}_{N/2}\rangle$$, 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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)
• Grant/Contract Number: 89233218CNA000001; AC05-00OR22725
• OSTI ID: 2506987
• Report Number(s): LA-UR--23-31364
• Journal Information: ACM Transactions on Quantum Computing, Journal Name: ACM Transactions on Quantum Computing Journal Issue: 4 Vol. 5; ISSN 2643-6809
• Publisher: Association for Computing MachineryCopyright Statement
• Country of Publication: United States
• Language: English