Zero-level $CCZ$ Distillation
- URL: http://arxiv.org/abs/2605.21867v1
- Date: Thu, 21 May 2026 01:22:28 GMT
- Title: Zero-level $CCZ$ Distillation
- Abstract summary: Magic state distillation is a key component of fault-tolerant quantum computation.<n>We propose a zero-level distillation protocol that efficiently generates a high-fidelity logical $CCZ magic state.<n>The proposed method improves the logical error rate by approximately one and two orders of magnitude at $p = 10-3$ and $p = 10-4$, respectively.
- Score: 2.6945797019995363
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Magic state distillation is a key component of fault-tolerant quantum computation, as it enables the implementation of non-Clifford gates such as the $T$ gate and the $CCZ$ gate via gate teleportation. However, conventional distillation protocols require a large number of logical qubits and introduce substantial spatial and temporal overhead, posing a significant bottleneck for scalable fault-tolerant quantum computation. In this work, we propose a zero-level distillation protocol that efficiently generates a high-fidelity logical $CCZ$ magic state using only physical qubits on a two-dimensional square lattice with nearest-neighbor interactions. Our method leverages the transversal $T/T^\dagger$ operation of the $[[ 8,3,2 ]]$ code to fault-tolerantly encode the state $\overline{CCZ}|+++\rangle$, which is subsequently teleported to three surface-code logical qubits via lattice surgery. To enable teleportation between codes with different distances, we introduce adaptively initialized teleportation (AIT), a tailored initialization procedure for the surface code. Numerical simulations demonstrate that the logical error rate scales as $p_L \simeq 300 \times p^2$ with respect to the physical error rate $p$. For example, the proposed method improves the logical error rate by approximately one and two orders of magnitude at $p = 10^{-3}$ and $p = 10^{-4}$, respectively, compared to conventional seven-$T$-gate approaches. The distillation circuit requires only 22 physical qubits, 3 logical qubits, and a circuit depth of 24, reducing the space-time overhead by a factor of approximately 5-10 compared to previous methods. This result highlights the practicality of $CCZ$-state distillation in early fault-tolerant quantum computation and offers a new direction toward resource-efficient physical-level magic state distillation beyond conventional $T$-state generation.
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