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Many-Body Majorana Braiding without an Exponential Hilbert Space
Eric Mascot1, Themba Hodge1, Dan Crawford1
1School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia.
Physical Review Letters
|November 13, 2023
Summary
This study introduces a new method for simulating Majorana zero modes, crucial for topological quantum computing. The approach enables analysis of larger systems and braiding dynamics, paving the way for developing Majorana qubits.
Area of Science:
- Condensed Matter Physics
- Quantum Computing
- Superconductivity
Background:
- Topologically protected quantum computing relies on qubits formed from Majorana zero modes.
- Simulating Majorana zero mode braiding is essential for understanding superconducting many-body system dynamics.
- Current methods are limited in system size and the inclusion of quasiparticles.
Purpose of the Study:
- To develop a method for calculating many-body wave functions and properties from single-particle states in superconductors.
- To enable the simulation of larger system sizes for Majorana dynamics.
- To analyze the fidelity and success of Majorana braiding processes.
Main Methods:
- Developed a computational method to derive many-body wave functions, expectation values, correlators, and overlaps from time-evolved single-particle states of a superconductor.
- Applied the method to simulate the braiding of Majorana zero modes.
- Calculated fidelity, transition probabilities, and joint parities to assess braiding quality.
Main Results:
- Successfully simulated Majorana dynamics for significantly larger system sizes than previously possible.
- Quantified the impact of braiding speed on the success of the braiding process.
- Demonstrated a topological CNOT two-qubit gate, showcasing two-qubit entanglement.
Conclusions:
- The presented method facilitates the analysis and testing of various theoretical implementations of Majorana qubits.
- This approach can be extended to study the dynamics of any noninteracting superconductor.
- Opens new avenues for understanding and advancing topological quantum computation.
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