arXiv subjects

Tomohiro Itogawa

Publications and source records attributed to Tomohiro Itogawa.

4 recordsLinked to original sources

arXiv2026

Efficient magic state cultivation with lattice surgery

Magic state distillation plays a crucial role in fault-tolerant quantum computation and represents a major bottleneck. In contrast to traditional logical-level distillation, physical-level distillation offers significant overhead reduction by enabling direct implementation with physical gates. Magic state cultivation is a state-of-the-art physical-level distillation protocol that is compatible with the square-grid connectivity and yields high-fidelity magic states. However, it relies on the complex grafted code, which incurs substantial spacetime overhead and complicates practical implementation. In this work, we propose an efficient cultivation-based protocol compatible with the square-grid connectivity. We reduce the spatial overhead by avoiding the grafted code and further reduce the average spacetime overhead by utilizing code expansion and enabling early rejection. Numerical simulations show that, with a color code distance of 3 and a physical error probability of $10^{-3}$, our protocol achieves a logical error probability for the resulting magic state comparable to that of magic state cultivation ($\approx 3 \times 10^{-6}$), while requiring about half the spacetime overhead. Our work provides an efficient and simple distillation protocol suitable for megaquop use cases and early fault-tolerant devices.

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arXiv2026

Zero-level $CCZ$ Distillation

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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arXiv2025

Efficient Magic State Distillation by Zero-Level Distillation

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 incurs a large spatiotemporal overhead, which is one of the major bottlenecks for the realization of fault-tolerant quantum computers (FTQCs). Here we propose zero-level distillation, which prepares a high-fidelity logical magic state at the physical level, namely zero level, using physical qubits and nearest-neighbor two-qubit gates on a square lattice. We develop a zero-level distillation circuit and show that distillation can be made even more efficient than the conventional sophisticated approaches with logical level distillations. The key idea involves the Knill et al.-type distillation using the Steane code and its careful mapping to the square-lattice architecture with error detection. The distilled magic state on the Steane-code state is then teleported or converted to surface codes. We numerically find that the error rate of the logical magic state scales as approximately $100 \times p^{2}$ 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 2 (1) orders of magnitude. This contributes to reducing both space and time overhead for early FTQC as well as full-fledged FTQC combined with conventional multilevel distillation protocols.

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arXiv2024

Leveraging Zero-Level Distillation to Generate High-Fidelity Magic States

Magic state distillation plays an important role in universal fault-tolerant quantum computing, and its overhead is one of the major obstacles to realizing fault-tolerant quantum computers. Hence, many studies have been conducted to reduce this overhead. Among these, Litinski has provided a concrete assessment of resource-efficient distillation protocol implementations on the rotated surface code. On the other hand, recently, Itogawa et al. have proposed zero-level distillation, a distillation protocol offering very small spatial and temporal overhead to generate relatively low-fidelity magic states. While zero-level distillation offers preferable spatial and temporal overhead, it cannot directly generate high-fidelity magic states since it only reduces the logical error rate of the magic state quadratically. In this study, we evaluate the spatial and temporal overhead of two-level distillation implementations generating relatively high-fidelity magic states, including ones incorporating zero-level distillation. To this end, we introduce (0+1)-level distillation, a two-level distillation protocol which combines zero-level distillation and the 15-to-1 distillation protocol. We refine the second-level 15-to-1 implementation in it to capitalize on the small footprint of zero-level distillation. Under conditions of a physical error probability of $p_{\mathrm{phys}} = 10^{-4}$ ($10^{-3}$) and targeting an error rate for the magic state within $[5 \times 10^{-17}, 10^{-11}]$ ($[5 \times 10^{-11}, 10^{-8}]$), (0+1)-level distillation reduces the spatiotemporal overhead by more than 63% (61%) compared to the (15-to-1)$\times$(15-to-1) protocol and more than 43% (44%) compared to the (15-to-1)$\times$(20-to-4) protocol, offering a substantial efficiency gain over the traditional protocols.

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