Below Threshold Logical Quantum Computation at Quantinuum

We review some of the recent break-even experimental QEC demonstrations on Quantinuum's trapped-ion quantum computers and their scalability. Results will include a break-even quantum memory using a [[10,1,4]] DFS code, which extends the coherence time by an order of magnitude beyond physical qubits. We review the passive and active protection provided by this code and its improved performance compared to physical [[2,1,1]] DFS pairs. We also discuss a new fault-tolerant magic state preparation protocol used in a break-even experimental demonstration of a non-Clifford gate, the controlled-Hadamard, using the [[6,2,2]] code and how to scale this protocol via code-concatenation. Finally, new experimental QEC demonstrations on Helios, Quantinuum's 98 qubit trapped-ion quantum computer, will also be discussed.