Recorded 28 November 2023. Roman Lutchyn of Microsoft Research presents "Topological Quantum Computation with Majorana zero-energy modes" at IPAM's Topology, Quantum Error Correction and Quantum Gravity Workshop. Abstract: Research in quantum computing has offered many new physical insights and a potential to exponentially increase the computational power that can be harnessed to solve important problems in science and technology. The largest fundamental barrier to building a scalable quantum computer is errors caused by decoherence. Topological quantum computing overcomes this barrier by exploiting topological materials which, by their nature, limit errors. In this talk, I will discuss how to engineer topological superconductors supporting Majorana zero-energy modes at the interface of a conventional superconductor (Aluminum) and a semiconductor with spin-orbit interaction (Indium Arsenide). I will present recent results by the Microsoft Quantum team consistent with the emergence of topological superconductivity in proximitized semiconductor nanowires. Finally, I will discuss a proposal for scalable quantum computing involving topological qubits which comprise of superconducting islands in a Coulomb blockade regime hosting aggregates of four or more Majorana zero modes. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iv-topology-quantum-error-correction-and-quantum-gravity/