恒定开销的神奇状态蒸馏

IF 18.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Adam Wills, Min-Hsiu Hsieh, Hayata Yamasaki
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引用次数: 0

摘要

大多数现实量子计算方案都需要进入所谓的魔法状态,以允许通用量子计算。由于制备过程可能存在噪声,因此需要状态蒸馏方法来提高其准确性并抑制任何潜在的误差。不幸的是,神奇状态蒸馏是资源密集型的,通常被认为是可扩展量子计算的瓶颈。在这里,成本是由开销定义的:噪声输入魔幻状态与干净输出的比率。这被称为\({\mathcal{O}}({\log }^{\gamma }(1/\epsilon ))\)为λ→0,其中λ是输出错误率,γ是某个常数。减少这种开销,对应于更小的γ,是消除瓶颈的迫切需要。然而,为了提取量子比特的神奇状态,确定可实现的最小指数γ被证明是具有挑战性的。在这里,我们通过演示具有最优指数γ = 0的协议来解决这个问题,因此对应于具有恒定开销的魔法状态蒸馏,并且我们表明这对于最重要的魔法状态(如\(\left\vert {\mathsf{T}}\right\rangle\)和\(\left\vert {\mathsf{CCZ}}\right\rangle\))是可以实现的。这是通过使用代数几何结构来构建第一个具有横向非clifford门的渐近良好量子码来实现的,为此我们还构造了一个具有线性解码半径的高效解码器。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Constant-overhead magic state distillation

Constant-overhead magic state distillation

Most schemes for realistic quantum computing require access to so-called magic states to allow universal quantum computing. Because the preparation process may be noisy, magic state distillation methods are needed to improve their accuracy and suppress any potential errors. Unfortunately, magic state distillation is resource-intensive and often considered a bottleneck to scalable quantum computation. Here, the cost is defined by the overhead: the ratio of noisy input magic states to cleaner outputs. This is known to scale as \({\mathcal{O}}({\log }^{\gamma }(1/\epsilon ))\) as ϵ → 0, where ϵ is the output error rate and γ is some constant. Reducing this overhead, corresponding to smaller γ, is highly desirable to remove the bottleneck. However, identifying the smallest achievable exponent γ for distilling magic states of qubits has proved challenging. Here, we resolve this problem by demonstrating protocols with the optimal exponent γ = 0, thus corresponding to magic state distillation with a constant overhead, and we show that this is achievable for the most important magic states such as \(\left\vert {\mathsf{T}}\right\rangle\) and \(\left\vert {\mathsf{CCZ}}\right\rangle\). This is achieved by using algebraic geometry constructions to build the first asymptotically good quantum codes with transversal non-Clifford gates, for which we also construct an efficient decoder with linear decoding radius.

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来源期刊
Nature Physics
Nature Physics 物理-物理:综合
CiteScore
30.40
自引率
2.00%
发文量
349
审稿时长
4-8 weeks
期刊介绍: Nature Physics is dedicated to publishing top-tier original research in physics with a fair and rigorous review process. It provides high visibility and access to a broad readership, maintaining high standards in copy editing and production, ensuring rapid publication, and maintaining independence from academic societies and other vested interests. The journal presents two main research paper formats: Letters and Articles. Alongside primary research, Nature Physics serves as a central source for valuable information within the physics community through Review Articles, News & Views, Research Highlights covering crucial developments across the physics literature, Commentaries, Book Reviews, and Correspondence.
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