ИСТИНА

A quantum memristor is a quantum system with a dynamic internal state and hysteretic input- output characteristics, capable of performing operations with quantum information [1]. We study a three-level quantum memristor implemented on a single ultracold 171Yb ion confined in a Paul trap, where the input and output signals are determined by the populations of the energy levels, and the system is controlled by two resonant laser pulses with Gaussian envelopes [2]. We focus on the experimentally relevant regime where the two resonant pulses are significantly separated in time, so that during each pulse the other field envelope is negligible. Under these conditions, we derive explicit closed-form analytical expressions for the population dynamics and the memristor's input (x) and output (y) signals. The resulting dependences are expressed via the error-function integrals of Gaussian envelopes). The obtained analytical dependences for x and y are benchmarked against direct numerical integration of the original equations and show good agreement; for representative parameters used in the paper the reported relative standard deviation is below 0.03%. Within the memristor formalism, we introduce a control parameter (denoted as the reflection- coefficient analog R) and a feedback model with a sliding integration window,similar to photonic platform [3]. We demonstrate that the output-input hysteresis y(x) exhibits strong dependence on the window parameter T, which is essential for tuning the memristor response and implementing neuromorphic computing devices on the ion platform. We also compare the separated-pulses regime to the previously studied simultaneous-pulses configuration and observe that hysteresis persists, while the output variation range can change [4]. The developed analytical approach provides a consistent method for determining input and output signals, simplifying both experimental verification and the analytical simulation of ion- based quantum memristors for neuromorphic applications. This work was supported by the Russian Science Foundation (project no. 24-12-00415). References [1]. [2]. [3]. [4]. Chua L. O. IEEE Trans. Circuit Theory18, 507 (1971). Stremoukhov S., Forsh P., Khabarova K., Kolachevsky N. Entropy 25, 1134 (2023). Spagnolo M. et al. Nat. Photonics16, 318 (2022). Kovalishin I. A. et al., JETP Letters, 122 (12), 862–866 (2025).