https://doi.org/10.1140/epjp/s13360-025-06369-y
Tutorial
Quantum state evolution in spin–orbit coupled systems through analytical and computational perspectives into electron dynamics and phonon interactions
Department of Computer Sc. & App., Dr. APJ Abdul Kalam Gov. College, Dokmardi, Silvassa, UT of Dadra and Nagar Haveli & Daman and Diu, India
a
shyams_sihare1979@rediffmail.com
Received:
20
December
2024
Accepted:
25
April
2025
Published online:
29
May
2025
This research provides a coherent theoretical framework to study quantum error robustness in spin–orbit–phonon-coupled systems across electron, trapped-ion, and photonic qubit platforms. Evading conventional error model constraints, the work combines path integral formulations with spin–orbit coupling to handle non-Markovian decoherence, nonlinear error spreading, and platform-dependent noise correlations. In electron qubits, the model includes frequency-dependent 1⁄f noise spectra and decoherence induced by phonons, evading static noise approximations. Trapped-ion platforms are handled by multi-mode phonon correlation functions handling cross-talk for fast entangling gates, whereas photonic qubits enjoy the first triply time-ordered error correlation model, addressing unusual photon statistics in boson sampling experiments. Nonlinear error propagators and security measures are introduced through diamond norm fidelity, converting physical error processes into cryptographic thresholds. Experimental test cases exhibit predictive accuracy, recovering phonon-assisted spatial error patterns in quantum dots subjected to acoustic excitation, fidelity decay in ion-trap entanglement processes, and sub-Poissonian photon statistics in optical systems. Bounding quantum information theory, condensed matter physics, and quantum optics, the research provides a cross-platform framework for estimating error dynamics, providing design principles for fault-tolerant architectures and secure quantum networks. Results counter intuitive Pauli channel approximations by pointing out environmental noise filtering, spatial separation of qubits, and gate-induced spectral modulation of errors in suppressing errors. Such a unification enables co-design approaches to quantum hardware and error correction, removing scalability limitations from next-generation quantum technologies.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjp/s13360-025-06369-y.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
