Recent experimental demonstrations: logical memory and an error-suppressed magic state with superconducting qubits

In the pursuit of fault-tolerant quantum computation, recent hardware progress and improvements in control electronics, have provided new capabilities for performing real-time feedback useful to quantum error correction applications. In this talk we review two recent demonstrations on superconducting qubits in a heavy-hexagon lattice. In the first, we performed several rounds of fault-tolerant syndrome measurements on a distance three logical qubit. Comparing the performance of matching and maximum likelihood decoders, we observe logical error per round as low as ∼0.04 for the matching decoder and as low as ∼0.035 for the maximum likelihood decoder – underscoring the importance of improving decoders alongside quantum experiment. Next we focus on preparation of high-fidelity magic states, a necessary component for universal fault-tolerant computation that is experimentally hampered by the large resource overhead of distilling magic states in pre-fault tolerant quantum devices. In this work, we decrease this overhead by reducing the error rate of the physical system at the initial preparation step of a distillation protocol. Drawing on key properties of an error-detecting code, we propose and demonstrate a protocol to suppress the state-preparation error of a two-qubit magic state, that we call the 'CZ state'. We highlight how this error-suppressed magic-state preparation protocol further benefits from reduced resource cost by the addition of a single classically controlled unitary operation.