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The geometric phase (GP) was first introduced by Michael Berry in 1984 and describes the global, gauge-invariant information acquired by a quantum state during adiabatic, cyclic, Abelian, and unitary evolution. Since then, generalizations such as the Aharonov–Anandan phase for nonadiabatic evolution have extended their applicability to various physical systems.

In this work, we compute the GP induced by Rashba spin–orbit coupling (SOC), a key interaction in spintronics and hole-spin qubits. The first concerns the GP of entangled electron pairs transported through a non-Abelian system. An L-shaped electron-pair device with intrinsic Rashba SOC enables non-commutative transport. The second part focuses on Rashba and Dresselhaus SOC. We investigate how the GP of spin pairs is affected by different propagation angles and by varying the ratio α/β , where α denotes the Rashba and β denotes the Dresselhaus coupling strength. Finally, we extend to mixed-state GPs and discuss the application of GP in quantum computing.