Finding Hidden Numbers with Majorana-based Topological Quantum Algorithms: Simulation of the Bernstein-Vazirani Algorithm

Executing a quantum code using Majorana zero modes - a major milestone for the field of topological quantum computing - requires a platform scalable to large quantum registers and controllable in real time and space, and a braiding protocol utilizing the unique properties of these exotic particles ideally. In this talk, I will present the successful simulation of the Bernstein-Vazirani algorithm in two-dimensional magnet-superconductor hybrid structures. Finding new possibilities in both the algorithm's initialization and read-out process, as well as advantages in its execution that stem from the Majorana zero modes' topological properties, I will demonstrate an optimized braiding protocol and a scalable architecture for its implementation with arbitrary numbers of qubits. Further, I will show how the algorithm protocol can be visualized in real time and space by computing the non-equilibrium density of states, which is proportional to the time-dependent differential conductance, and how its result can be read out by calculating the non-equilibrium charge density, which assigns a unique signature to each final state of the algorithm.