Cost-reduced all-Gaussian universality with the Gottesman-Kitaev-Preskill code: Resource-theoretic approach to cost analysis - Hayata Yamasaki; Takaya Matsuura; Masato Koashi (Physical Review Research, 2020)
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)PRLTAO0031-900710.1103/PhysRevLett.123.200502] showed that experimentally tractable Gaussian operations combined with preparing a GKP codeword |0〉 suffice to implement universal quantum computation, this implementation scheme involves a distillation of a logical magic state |H〉 of the GKP code, which inevitably imposes a trade-off between implementation cost and fidelity. In contrast, we propose a scheme of preparing |H〉 directly and combining Gaussian operations only with |H〉 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 |H〉 and |0〉, 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.