The Decoherence of Schrödinger’s State: A Quantitative Analysis of Fidelity in Noisy Quantum Simulations

• William Wallace Teodoro Rodrigues UTFPR
• João Fabrício Filho UTFPR

DOI: https://doi.org/10.5753/eradse.2025.16905

Resumo

The viability of algorithms on Noisy Intermediate-Scale Quantum (NISQ) computers is limited by operational errors and decoherence. To optimize execution, it is crucial to understand how circuit complexity (depth and number of gates), statistical sampling (shots), and result fidelity interact. This work investigates that relationship through large-scale simulations of 100,000 random circuits under a physically motivated noise model with temporal decoherence (T1/T2) and gate errors. The analysis shows a strong negative correlation between circuit complexity and Hellinger fidelity, revealing a “fidelity ceiling” where increasing shots reduces statistical error but cannot overcome noise. For complex circuits, the number of gates is identified as a stronger predictor of error than circuit depth.

Palavras-chave: Quantum Computing, Hellinger Fidelity, Decoherence, Statistical Sampling

Referências

L. Gyongyosi, “A survey on quantum computing technology,” Computer Science Review, vol. 31, pp. 51–71, 2019.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010.

J. Preskill, “Quantum Computing in the NISQ era and beyond,” Quantum, vol. 2, p. 79, 2018.

C. A. Fuchs and J. van de Graaf, “Cryptographic distinguishability and privacy of quantum states,” IEEE Transactions on Information Theory, vol. 45, no. 4, pp. 1216–1227, 1999.