Braiding Majorana zero modes (MZMs) is the key procedure toward topological quantum computation. We show such braiding can be well performed in a parallel semiconductor-superconductor nanowire structure. Considering the fact that the low-energy Andreev bound states (ABSs) usually mix with the MZMs in the present setup, we further investigate the braiding properties of MZMs when an ABS is presented. Our numerical simulation suggests that ABS can be regarded as a pair of weakly coupled MZMs. The dynamical hybridization of MZMs plus the non-Abelian braiding of MZMs would induce an arbitrary rotation on the Bloch sphere of a single qubit. Remarkably, such rotation is manipulable since the rotation parameters could be individually modulated. Thus, the dynamic evolution can be eliminated and the non-Abelian braiding statistics, independent of the braiding time, retrieves.Braiding Majorana zero modes (MZMs) is the key procedure toward topological quantum computation. We show such braiding can be well performed in a parallel semiconductor-superconductor nanowire structure. Considering the fact that the low-energy Andreev bound states (ABSs) usually mix with the MZMs in the present setup, we further investigate the braiding properties of MZMs when an ABS is presented. Our numerical simulation suggests that ABS can be regarded as a pair of weakly coupled MZMs. The dynamical hybridization of MZMs plus the non-Abelian braiding of MZMs would induce an arbitrary rotation on the Bloch sphere of a single qubit. Remarkably, such rotation is manipulable since the rotation parameters could be individually modulated. Thus, the dynamic evolution can be eliminated and the non-Abelian braiding statistics, independent of the braiding time, retrieves.

arXiv:2005.00735Physical review. B./Physical review. BFeb 9, 202218 citations

Non-abelian Majoranas and braiding in inhomogeneous spin ladders

Fabio L. Pedrocchi, Suhas Gangadharaiah, Stefano Chesi +1 more

Apr 13, 20120 citations

Three-Majorana cotunneling interferometer for non-Abelian braiding and topological quantum gate implementation

Zhen Chen, Yijia Wu, X. C. Xie

We propose a scheme for performing Majorana zero mode (MZM) braiding utilizing cotunneling processes in a three-MZM system incorporating reference arms. This approach relies on the interference between cotunneling paths through the MZMs and reference arms, establishing an effective, tunable coupling between the MZMs. The strength and sign of this coupling can be manipulated via the reference arms and applied magnetic flux. Notably, the introduction of a half-quantum flux reverses the coupling sign, enabling an echolike protocol to eliminate dynamic phases during braiding. Our setup, requiring only three MZMs, represents a minimal platform for demonstrating non-Abelian braiding statistics. We demonstrate that this system facilitates the implementation of Clifford gates via braiding and, significantly, permits the realization of non-Clifford gates, such as the $T$ gate, by geometric phase, thereby offering a potential pathway toward universal topological quantum computation.We propose a scheme for performing Majorana zero mode (MZM) braiding utilizing cotunneling processes in a three-MZM system incorporating reference arms. This approach relies on the interference between cotunneling paths through the MZMs and reference arms, establishing an effective, tunable coupling between the MZMs. The strength and sign of this coupling can be manipulated via the reference arms and applied magnetic flux. Notably, the introduction of a half-quantum flux reverses the coupling sign, enabling an echolike protocol to eliminate dynamic phases during braiding. Our setup, requiring only three MZMs, represents a minimal platform for demonstrating non-Abelian braiding statistics. We demonstrate that this system facilitates the implementation of Clifford gates via braiding and, significantly, permits the realization of non-Clifford gates, such as the $T$ gate, by geometric phase, thereby offering a potential pathway toward universal topological quantum computation.

arXiv:2506.03553Physical review. B./Physical review. BSep 15, 20250 citations

Reading the quantum state change of Majorana braiding

Chun-Xiao Liu, Ching‐Kai Chiu

Bulletin of the American Physical SocietyMar 4, 20190 citations

Teleportation-based quantum information processing with Majorana zero modes

Sagar Vijay, Liang Fu

We present a measurement-based scheme for performing braiding operations on Majorana zero modes in mesoscopic superconductor islands and for detecting their non-Abelian statistics without moving or hybridizing them. In our scheme for ``braiding without braiding'', the topological qubit encoded in any pair of well-separated Majorana zero modes is read out from the transmission phase shift in electron teleportation through the island in the Coulomb-blockade regime. We propose experimental setups to measure the teleportation phase shift via conductance in an electron interferometer or persistent current in a closed loop.We present a measurement-based scheme for performing braiding operations on Majorana zero modes in mesoscopic superconductor islands and for detecting their non-Abelian statistics without moving or hybridizing them. In our scheme for ``braiding without braiding'', the topological qubit encoded in any pair of well-separated Majorana zero modes is read out from the transmission phase shift in electron teleportation through the island in the Coulomb-blockade regime. We propose experimental setups to measure the teleportation phase shift via conductance in an electron interferometer or persistent current in a closed loop.

arXiv:1609.00950Physical review. B./Physical review. BDec 29, 2016164 citations

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gate, by geometric phase, thereby offering a potential pathway toward universal topological quantum computation.