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arXiv · 1911.11141

Cost-Reduced All-Gaussian Universality with the Gottesman-Kitaev-Preskill Code: Resource-Theoretic Approach to Cost Analysis

Hayata Yamasaki·Takaya Matsuura·Masato Koashi
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Abstract

The Gottesman-Kitaev-Preskill (GKP) quantum error-correcting code has emerged as a key technique in achieving fault-tolerant quantum computation using photonic systems. Whereas [Baragiola et al., Phys. Rev. Lett. 123, 200502 (2019)] showed that experimentally tractable Gaussian operations combined with preparing a GKP codeword $\lvert 0\rangle$ suffice to implement universal quantum computation, this implementation scheme involves a distillation of a logical magic state $\lvert H\rangle$ of the GKP code, which inevitably imposes a trade-off between implementation cost and fidelity. In contrast, we propose a scheme of preparing $\lvert H\rangle$ directly and combining Gaussian operations only with $\lvert H\rangle$ to achieve the universality without this magic state distillation. In addition, we develop an analytical method to obtain bounds of fundamental limit on transformation between $\lvert H\rangle$ and $\lvert 0\rangle$, finding an application of quantum resource theories to cost analysis of quantum computation with the GKP code. Our results lead to an essential reduction of required non-Gaussian resources for photonic fault-tolerant quantum computation compared to the previous scheme.

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Hayata Yamasaki, Takaya Matsuura, Masato Koashi. 2019-11-25. Cost-Reduced All-Gaussian Universality with the Gottesman-Kitaev-Preskill Code: Resource-Theoretic Approach to Cost Analysis. https://doi.org/10.1103/physrevresearch.2.023270

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