Even more efficient magic state distillation by zero-level distillation

• URL: http://arxiv.org/abs/2403.03991v1
• Date: Wed, 6 Mar 2024 19:01:28 GMT
• Title: Even more efficient magic state distillation by zero-level distillation
• Authors: Tomohiro Itogawa, Yugo Takada, Yutaka Hirano, Keisuke Fujii
• Abstract summary: We propose zero-level distillation, which prepares a high fidelity logical magic state using physical qubits on a square lattice. The key idea behind is using the Steane code to distill a logical magic state by using noisy Clifford gates with error detection.
• Score: 0.8009842832476994
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Magic state distillation (MSD) is an essential element for universal fault-tolerant quantum computing, which distills a high fidelity magic state from noisy magic states using ideal (error-corrected) Clifford operations. For ideal Clifford operations, it needs to be performed on the logical qubits and hence takes a large spatiotemporal overhead, which is one of the major bottlenecks for the realization of fault-tolerant quantum computers (FTQC). Here we propose zero-level distillation, which prepares a high fidelity logical magic state using physical qubits on a square lattice using nearest-neighbor two-qubit gates without using multiple logical qubits. The key idea behind is using the Steane code to distill a logical magic state by using noisy Clifford gates with error detection. Then the Steane code state is teleported or converted to the surface codes. By carefully designing such circuits fault-tolerantly, the error rate of the logical magic state scales $\sim 100 \times p^2$ in terms of the physical error rate $p$. For example, with a physical error rate of $p=10^{-4}$ ($10^{-3}$), the logical error rate is reduced to $p_L=10^{-6}$ ($10^{-4}$), resulting in an improvement of two (one) orders of magnitude. This contributes to reducing both space and time overhead for early FTQC as well as full-fledged FTQC combined with conventional multi-level distillation protocols.

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