Leakage mitigation and correction techniques for topological surface codes

Abstract

A large scale quantum computer would be able to solve many problems that remain intractable for modern classical computers. In order to build such a machine, the quantum system must be protected from environmental influences that lead to errors that can destroy the fragile quantum information. Topological quantum error correction codes are a leading candidate for handling errors that occur during a computation. However, these codes can only handle errors within the computational subspace. Leakage is a particularly damaging error that occurs when the qubit leaves the defined computational space. Leakage errors limit the effectiveness of quantum error correcting codes by spreading additional errors to other qubits and corrupting syndrome measurements. Leakage errors are typically handled by implementing leakage reducing circuits (LRCs) which convert leakage errors into Pauli errors at the cost of additional overhead. How leakage is modeled greatly affects how much leakage reduction is needed and the cost of overhead can become quite expensive. Accurately describing the behavior of leakage errors is crucial when designing and implementing LRC’s in a system. The leakage model can affect qubit choice, syndrome extraction circuits and the most effective error correction code. In this dissertation, we shall discuss several different methods for handling and mitigating leakage in topological surface codes and address how the model of leakage impacts the basic building blocks of error correction.