Curator's Take
AI Commentary
This article shows that magic‑state distillation can be carried out with a fixed number of logical qubits by recycling idle qubits, dramatically shrinking the space‑time volume needed for high‑fidelity non‑Clifford gates. By extending code‑doubling techniques to every level of the Clifford hierarchy, it recovers known efficient protocols and introduces ultra‑compact $111\to1$ T‑state distillation at distance 7, a clear step toward practical fault‑tolerant quantum processors where qubit resources are scarce. The result dovetails with recent efforts to lower overhead in surface‑code architectures, though the schemes still rely on sufficiently low physical error rates to achieve the promised distances.
— Mark Eatherly
Summary
In order to circumvent that no universal set of gates can be achieved on a given quantum error-correcting codes, additional gates can be performed through magic state injection. This however requires to have access to high fidelity magic state, which can be obtained by the distillation of low quality states to fewer higher quality ones. In this paper, we provide a family of distillation protocols able to produce diagonal states at every level of the Clifford hierarchy. This family is obtained recursively using code doubling techniques and leveraging qubit recycling, the fact that some idle qubits of the protocols can be measured and re-used. At a given level of the Clifford hierarchy, we show that the protocols we derive can be performed at arbitrary high distance on a fix number of logical qubits. This family recovers many known efficient protocols, and uncovers new ones, such as a $111 \to 1$ protocol for $|T\rangle$ state distillation at distance $7$, which are the most compact in term of volume. Finally, we discuss possible extension of this framework for distillation protocols producing more than one output state.