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Nigerian Journal of Applied Physics

Simulation Of Quantum Spin Systems For Qubit Applications

Iyanuoluwa Olaniyi Ajayi

Published Sep 22, 2026• 0 citations

Abstract

This study presents a numerical investigation of the dynamics of two coupled spin-1/2 quantum systems with emphasis on entanglement, quantum coherence, and state fidelity. The system is described by an isotropic Heisenberg Hamiltonian and investigated for exchange-coupling strengths J=−1, −0.5, 0, 0.5, and 11. Four representative initial states, comprising the Bell state, a partially entangled state with initial concurrence C (0) =0.8, and the separable states ∣01⟩and ∣++⟩are considered. Closed-system evolution is obtained using the unitary propagator, while environmental effects are modelled through a Lindblad master equation with local Markovian pure-dephasing channels for γ=0,0.1,0.5, and 11. The results show that the Bell state maintains maximal concurrence under closed Heisenberg evolution, while the partially entangled state retains its initial concurrence of 0.8 for all tested exchange couplings. In contrast, the initially separable ∣01⟩state develops strong transient entanglement through exchange interaction, reaching concurrence values essentially equal to unity for ∣J∣=0.5 and 11, whereas the ∣++⟩state remains separable to numerical precision. Under pure dephasing, concurrence and coherence decay progressively with increasing dephasing strength, while fidelity decreases toward its asymptotic value. The numerical calculations were further validated through normalization and Hermiticity checks, analytical dephasing benchmarks, and step-refinement convergence tests, with discrepancies remaining at machine-precision levels. The findings demonstrate that the preservation and generation of quantum correlations depend strongly on the initial state, exchange interaction, and environmental decoherence, providing validated numerical benchmarks for the study of coupled qubit dynamics.

DOI: 10.62292/njap-v2i3-2026-94

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The dynamics of two

1∕2

-spin qubits under the influence of a quantum Heisenberg

XY

-type spin-bath is studied. After the Holstein-Primakoff transformation, numerical polynomial scheme is used to give the time-evolution calculation of the center qubits initially prepared in a product state or a Bell state. Then the concurrence of the two qubits, the

z

-component moment of either of the subsystem spins, and the fidelity of the subsystem are shown; they exhibit sensitive dependence on the anisotropic parameter, the temperature, the coupling strength, and the initial state. It is found that (i) the larger the anisotropic parameter $\ensuremath{\gamma}$, the bigger the probability of maintaining the initial state of the two qubits; (ii) with increasing temperature

T

, the bath plays a stronger destroy effect on the dynamics of the subsystem, so does the interaction

{g}_{0}

between the subsystem and the bath; and (iii) the time evolution of the subsystem is dependent on the initial state. The revival of the concurrence does not always mean the restoration of the state. Further, the dynamical properties of the subsystem should be judged by the combination of concurrence and fidelity.

The decoherence and entanglement dynamics of two interacting qubits coupled through Heisenberg XY interactions to a spin bath in thermal equilibrium are studied. The exact form of the reduced density matrix is derived for finite and infinite numbers of environmental spins. It is shown that decoherence can be minimized at low bath temperatures and strong coupling between the qubits. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The relation between the fidelity and the concurrence is also investigated.

The dynamics of entanglement and fidelity for a subsystem of two separate spin-

1∕2

qubits prepared in Bell states is investigated. One of the subsystem qubit labeled

A

is under the influence of a Heisenberg

XY

spin bath, while another one labeled

B

is uncoupled with that. We discuss two cases: (i) the number of bath spins is infinite, $N\ensuremath{\rightarrow}\ensuremath{\infty}$, and (ii)

N

is finite,

N=40

. In both cases, the bath is initially prepared in a thermal equilibrium state. It is shown that the time dependence of the concurrence and the fidelity of the two subsystem qubits can be controlled by tuning the parameters of the spin bath, such as the anisotropic parameter, the temperature, and the coupling strength with qubit

A

. It is interesting to find that the dynamics of the concurrence is independent of four different initial Bell states and that of the fidelity is divided into two groups.