Fidelity reduction in Majorana qubits by entanglement with environmental modes

Morten I. K. Munk, Reinhold Egger, Karsten Flensberg

Majorana qubits based on Majorana bound states (MBSs) are believed to be topologically protected and therefore robust to noise. However, when the MBSs are coupled to gapless modes, such as phonons or electromagnetic modes, the quantum information is stored in entangled MBS-environment states. Moreover, the combined system becomes gapless and even though the quantum information is still topologically protected, it is challenging to read out the quantum information when the measurement device only couples to the MBS. The paper discusses the readout errors that occur when performing projective measurement on the MBSs in this situation.

Sung Po Chao, Shih Hao Ho, Chung Hsien Chou +1 more

Eric Mascot, Themba Hodge, Daniel Crawford +3 more

Qubits built out of Majorana zero modes constitute the primary path toward topologically protected quantum computing. Simulating the braiding process of multiple Majorana zero modes 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 wave functions 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 Letter 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 noninteracting superconductor.

Mostafa Tanhayi Ahari, Gerardo Ortíz, Babak Seradjeh

Péter Boross, András Pályi

Topology-related ideas might lead to noise-resilient quantum computing. For example, it is expected that the slow spatial exchange (``braiding'') of Majorana zero modes in superconductors yields quantum gates that are robust against disorder. Here, we report our numerical experiments, which describe the dynamics of a Majorana qubit built from quantum dots controlled by time-dependent gate voltages. Our protocol incorporates nonprotected control, braiding-based protected control, and readout of the Majorana qubit. We use the Kitaev chain model for the simulations, and we focus on the case when the main source of errors is quasistatic charge noise affecting the hybridization energy splitting of the Majorana modes. We provide quantitative guidelines to suppress both diabatic errors and disorder-induced qubit dephasing, such that a fidelity plateau is observed as the hallmark of the topological quantum gate. Our simulations predict realistic features that are expected to be seen in future braiding experiments with Majorana zero modes and other topological qubit architectures.

Chang-Yu Hou, Fabian Hassler, Johan Nilsson +1 more