Many-body Majorana braiding without an exponential Hilbert space

Abstract

Qubits built out of Majorana zero modes (MZMs) constitute the primary path towards topologically protected quantum computing. Simulating the braiding process of multiple MZMs corresponds to the quantum dynamics of a superconducting many-body system. It is crucial to study the Majorana dynamics both in the presence of all other quasiparticles and for reasonably large system sizes. We present a method to calculate arbitrary many-body wavefunctions as well as their expectation values, correlators and overlaps from time evolved single-particle states of a superconductor, allowing for significantly larger system sizes. We calculate the fidelity, transition probabilities, and joint parities of Majorana pairs to track the quality of the braiding process. We show how the braiding success depends on the speed of the braid. Moreover, we demonstrate the topological CNOT two-qubit gate as an example of two-qubit entanglement. Our work opens the path to test and analyze the many theoretical implementations of Majorana qubits. Moreover, this method can be used to study the dynamics of any non-interacting superconductor.

arXiv commentv2: revised version, including the demonstration of CNOT gate via braiding

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• Effect of impurities and disorder on the braiding dynamics of Majorana zero modes
• Characterizing Dynamic Majorana Hybridization for Universal Quantum Computing
• Transient effects in quantum dots contacted via topological superconductor
• Preparation and readout of Majorana qubits in magnet-superconductor hybrid systems
• Altermagnet-Superconductor Heterostructure: a Scalable Platform for Braiding of Majorana Modes
• Transport of Majorana Bound State in the presence of telegraph noise
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Nonadiabatic braiding of Majorana modes
• Majorana braiding simulations with projective measurements
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Quantifying the non-Abelian property of Andreev bound states in inhomogeneous Majorana nanowires