A heterogeneous mixture of topological and trivial superconducting domains in FeSe1-xTex explains why only some vortices host Majorana zero modes, with a domain-wall Majorana edge mode as the distinguishing signature.
Finding Hidden Numbers with Majorana-based Topological Quantum Algorithms: Simulation of the Bernstein-Vazirani Algorithm
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abstract
Executing quantum algorithms using Majorana zero modes - a major milestone for the field of topological quantum computing - requires a platform that can be scaled to large quantum registers, can be controlled in real time and space, and a braiding protocol that uses the unique properties of these exotic particles. Here, we demonstrate the first successful simulation of the Bernstein-Vazirani algorithm in two-dimensional magnet-superconductor hybrid structures from initialization to read-out of the final many-body state. Utilizing the Majorana zero modes' topological properties, we introduce an optimized braiding protocol for the algorithm and a scalable architecture for its implementation with an arbitrary number of qubits. We visualize the algorithm protocol in real time and space by computing the non-equilibrium density of states, which is proportional to the time-dependent differential conductance, and the non-equilibrium charge density, which assigns a unique signature to each final state of the algorithm.
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Majorana Zero Modes in a Heterogenous Structure of Topological and Trivial Domains in FeSe$_{1-x}$Te$_x$
A heterogeneous mixture of topological and trivial superconducting domains in FeSe1-xTex explains why only some vortices host Majorana zero modes, with a domain-wall Majorana edge mode as the distinguishing signature.