Optimal diabatic dynamics of Majorana-based quantum gates

Abstract

In topological quantum computing, unitary operations on qubits are performed by adiabatic braiding of non-Abelian quasiparticles, such as Majorana zero modes, and are protected from local environmental perturbations. In the adiabatic regime, with timescales set by the inverse gap of the system, the errors can be made arbitrarily small by performing the process more slowly. To enhance the performance of quantum information processing with Majorana zero modes, we apply the theory of optimal control to the diabatic dynamics of Majorana-based qubits. While we sacrifice complete topological protection, we impose constraints on the optimal protocol to take advantage of the nonlocal nature of topological information and increase the robustness of our gates. By using the Pontryagin's maximum principle, we show that robust equivalent gates to perfect adiabatic braiding can be implemented in finite times through optimal pulses. In our implementation, modifications to the device Hamiltonian are avoided. Focusing on thermally isolated systems, we study the effects of calibration errors and external white and $1/f$ (pink) noise on Majorana-based gates. While a noise-induced antiadiabatic behavior, where a slower process creates more diabatic excitations, prohibits indefinite enhancement of the robustness of the adiabatic scheme, our fast optimal protocols exhibit remarkable stability to noise and have the potential to significantly enhance the practical performance of Majorana-based information processing.

8 pages, 5 figures

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• Approaching the adiabatic timescale with machine-learning
• Topological Quantum Computing Using Nanowire Devices
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• Error generation and propagation in Majorana-based topological qubits
• Non-Abelian Berry phase for open quantum systems: Topological protection vs geometric dephasing
• Demonstrating Majorana non-Abelian properties using fast adiabatic charge-transfer
• Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors
• Non-Abelian Geometric Dephasing
• Optimal noise-canceling shortcuts to adiabaticity: application to noisy Majorana-based gates
• Majorana bound state engineering via efficient real-space parameter optimization
• Transport probe of nonadiabatic transition caused by Majorana moving
• Optimal protocols for finite-duration quantum quenches in the Luttinger model
• Transport of Majorana Bound State in the presence of telegraph noise
• Transport and fusion of Majorana zero modes in the presence of nonadiabatic transitions
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Topological and geometric patterns in optimal bang-bang protocols for variational quantum algorithms: application to the $XXZ$ model on the square lattice
• Probing nontrivial fusion of Majorana zero modes via near-adiabatic coupling