School of Physics - Theses
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ItemTopological quantum computing with magnet-superconductor hybrid systems( 2023-11)Developing a practical general purpose quantum computer is this eras moonshot project, enabling fundamental advances in simulating quantum many-body systems, as well as promising new classical-computer-beating algorithms with applications in cryptography, meteorology, economics, and logistics. Current quantum processors struggle with short coherence times --- meaning that the fragile quantum bits (qubits) break down --- resulting in high error rates. Thus complicated or long calculations are prohibitive to run on current devices. Quantum error correction could be the solution, however, many physical qubits are required to encode a single logical qubit. Thus a massive scaling up of hardware is required to realise even a modest number of fault-tolerant logical qubits. Over the past twenty years the idea of engineering an inherently fault-tolerant, or topological, quantum computer has been developed. In principle, these fault-tolerant qubits do not decohere due to a topological protection; the information is distributed across a physical system such that local perturbations do not damage the whole information encoding. Majorana zero-modes, characteristic quasiparticles in topological superconductors, have emerged as a leading candidate for the building blocks of a fault-tolerant qubit. Many experimental platforms which might yield Majorana zero-modes have been proposed, but as of writing unambiguous evidence for Majorana zero-modes and topological superconductivity has not been presented in any experiment. Here I study magnet-superconductor hybrid (MSH) systems, which involve networks of magnetic adatoms assembled on a superconducting surface via lateral atom manipulation using a scanning tunneling microscope tip. These systems are clean and crystalline, and thus are an ideal platform for experiments. I present compelling theoretical and experimental evidence for topological superconductivity in Mn and Fe chains on Nb(110). However, the systems investigated so far experimentally have long localisation lengths, resulting in hybridised Majorana modes. Because these modes cannot be used to build a fault-tolerant qubit, I theoretically investigate several extensions to these experiments. I propose constructing quasi one-dimensional chains consisting of several rows of magnetic adatoms, with ferromagnetic order in one crystalline direction and antiferromagnetic in the other. I also suggest engineering the Nb(110) surface with an alloy to dramatically increase the Rashba splitting. Both of these proposals are readily accessible in experiment, and could yield non-hybridised Majorana zero-modes. Having established the viability of the platform, I introduce a numerical apparatus for studying many-body nonequilibrium superconducting physics. While this is generic and can be applied to any superconducting problem, here I use it to study topological quantum computing on a MSH platform. I first show that quantum gates can indeed be implemented via braiding Majorana zero-modes. I then show how single-molecule magnets can be use to initialise and readout MSH qubits. I build on this protocol and introduced a dressed Majorana qubit, which combines an MSH network with single-molecule magnets. These could be easier to initialise and readout than a conventional Majorana qubit.