Constant sized support state distillation with qubit recycling
Abstract
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 → 1 protocol for |T⟩ 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.
Related
- The limits of magic-state distillation
- Correlation-sensitive magic-state distillation from spin-squeezed neutral atoms
- Quantum Knowledge Distillation: State-of-the-art, Applications and Open Problems
- Transversal Gates and Magic State Distillation in an Optimally Synthesized Spin-Qubit Shuttling Bus
- χc1(4010) as a D*±D∓ Molecular State: Mass, Decay Constant, and Width
BibTeX
@misc{barizien2026constant,
title = {{Constant sized support state distillation with qubit recycling}},
author = {Victor Barizien},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17044},
eprint = {2609.17044},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17044},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constant sized support state distillation with qubit recycling
AU - Victor Barizien
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17044
UR - https://arxiv.org/abs/2609.17044
AB - 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 → 1 protocol for |T⟩ 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.
ER -