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Quantifying the properties of evolutionary quantum states of the XXZ spin model using quantum computing

M. P. Tonne, Kh. P. Gnatenko

TL;DR

This work addresses the problem of quantifying entanglement distance and dynamical speed in a two-spin XXZ system initialized in generic separable states. It combines analytic derivations with quantum-protocol implementations executed on the AerSimulator to compute Pauli expectations and state overlaps, enabling measurement of the entanglement distance $E^{ED}$ and the evolution speed $v$. The key contributions are explicit analytic expressions for $E^{ED}$ and $v$, together with validated quantum-computation results that closely match theory across varied initial-state and coupling parameters. Overall, the study demonstrates the feasibility of using quantum computing to probe entanglement geometry and dynamical efficiency in simple spin models, providing a benchmark framework for scaling to larger systems.

Abstract

The entanglement distance of evolutionary quantum states of a two-spin system with the XXZ model has been studied. The analysis has been conducted both analytically and using quantum computing. An analytical dependence of the entanglement distance on the values of the model coupling constants and the parameters of the initial states has been obtained. The speed of evolution of a two-spin system has been investigated. The analysis has been performed analytically and using quantum computing. An explicit dependence of the speed of evolution on the coupling constants and on the parameters of the initial state has been obtained. The results of quantum computations are in good agreement with the theoretical predictions.

Quantifying the properties of evolutionary quantum states of the XXZ spin model using quantum computing

TL;DR

This work addresses the problem of quantifying entanglement distance and dynamical speed in a two-spin XXZ system initialized in generic separable states. It combines analytic derivations with quantum-protocol implementations executed on the AerSimulator to compute Pauli expectations and state overlaps, enabling measurement of the entanglement distance and the evolution speed . The key contributions are explicit analytic expressions for and , together with validated quantum-computation results that closely match theory across varied initial-state and coupling parameters. Overall, the study demonstrates the feasibility of using quantum computing to probe entanglement geometry and dynamical efficiency in simple spin models, providing a benchmark framework for scaling to larger systems.

Abstract

The entanglement distance of evolutionary quantum states of a two-spin system with the XXZ model has been studied. The analysis has been conducted both analytically and using quantum computing. An analytical dependence of the entanglement distance on the values of the model coupling constants and the parameters of the initial states has been obtained. The speed of evolution of a two-spin system has been investigated. The analysis has been performed analytically and using quantum computing. An explicit dependence of the speed of evolution on the coupling constants and on the parameters of the initial state has been obtained. The results of quantum computations are in good agreement with the theoretical predictions.
Paper Structure (5 sections, 27 equations, 10 figures)

This paper contains 5 sections, 27 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Analytical consideration of entanglement distance of quantum states of a spin system with XXZ model
  3. Quantifying the entanglement distance of quantum state with quantum calculations
  4. Speed of evolution of quantum states of a two-spin system with the XXZ model
  5. Conclusions

Figures (10)

  • Figure 1: Quantum protocol for calculating the mean value of operator $\sigma^x$
  • Figure 2: Quantum protocol for calculating the mean value of operator $\sigma^y$
  • Figure 3: Quantum protocol for calculating the mean value of operator $\sigma^z$
  • Figure 4: Entanglement distance of qubit $q[0]$ with other qubits in state \ref{['eq:evolution_state']} for different values of $\theta_0$ and $\theta_1$. The surface corresponds to the analytical result. Results of quantifying on AerSimulator are marked with dots.
  • Figure 5: Entanglement distance of qubit $q[0]$ with other qubits in state \ref{['eq:evolution_state']} for different values of $\phi_0$ and $\phi_1$. The surface corresponds to the analytical result. Results of quantifying on AerSimulator are marked with dots.
  • ...and 5 more figures