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Quantum Simulation

Fingerprints of classical memory in quantum hysteresis

arXiv
Authors: Francesco Caravelli

Year

2026

Paper ID

3216

Status

Preprint

Abstract Read

~2 min

Abstract Words

131

Citations

N/A

Abstract

We present a simple framework for classical and quantum "memory" in which the Hamiltonian at time t depends on past values of a control Hamiltonian through a causal kernel. This structure naturally describes finite-bandwidth or filtered control channels and provides a clean way to distinguish between memory in the control and genuine non-Markovian dynamics of the state. We focus on models where H(t)=H0+int-inftytK(t-s) H1(s) ds, and illustrate the framework on single-qubit examples such as H(t)=σz+Φ(t)σx with Φ(t)=int-inftytK(t-s) u(s) ds. We derive basic properties of such dynamics, discuss conditions for unitarity, give an equivalent time-local description for exponential kernels, and show explicitly how hysteresis arises in the response of a driven qubit.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • We present a simple framework for classical and quantum "memory" in which the Hamiltonian at time t depends on past values of a control Hamiltonian through a causal kernel.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.20287 [2] arXiv https://arxiv.org/abs/2601.20287 [3] Publisher https://arxiv.org/abs/2601.20287

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