Optimal diabatic dynamics of Majorana-based quantum gates

摘要

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 arbitrarilysmall by performing the process more slowly. To enhance the performance of quantum information processingwith Majorana zero modes, we apply the theory of optimal control to the diabatic dynamics of Majorana-basedqubits. While we sacrifice complete topological protection, we impose constraints on the optimal protocol totake advantage of the nonlocal nature of topological information and increase the robustness of our gates. Byusing the Pontryagin’s maximum principle, we show that robust equivalent gates to perfect adiabatic braidingcan be implemented in finite times through optimal pulses. In our implementation, modifications to the deviceHamiltonian are avoided. Focusing on thermally isolated systems, we study the effects of calibration errors andexternal 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 ofthe adiabatic scheme, our fast optimal protocols exhibit remarkable stability to noise and have the potential tosignificantly enhance the practical performance of Majorana-based information processing.