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.
Highlights
Photonic quantum systems provide promising architectures toward implementing quantum computation [1,2,3]
The scalability is especially key to attaining high fault tolerance in quantum computation by means of quantum error correction [15,16,17,18], where quantum information of a logical qubit is redundantly encoded in a physical quantum system
Reference [26] has recently shown that if we can realize a light source that emits an optical mode prepared in a codeword |0 of a GKP code, experimentally tractable Gaussian operations combined with this light source suffice to implement universal quantum computation in a fault-tolerant way
Summary
Photonic quantum systems provide promising architectures toward implementing quantum computation [1,2,3]. Reference [26] has recently shown that if we can realize a light source that emits an optical mode prepared in a codeword |0 of a GKP code, experimentally tractable Gaussian operations combined with this light source suffice to implement universal quantum computation in a fault-tolerant way. While the state injection is well known in the qubit-based quantum computation, our key contribution is an essential reduction of non-Gaussian resources in implementing photonic fault-tolerant quantum computation. Notice that the cost reduction stems from the nature of photonic architecture that non-Gaussian |0 and |H of the GKP code are costly to prepare compared to performing Gaussian operations.
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