Polylog-overhead highly fault-tolerant measurement-based quantum computation: all-Gaussian implementation with Gottesman-Kitaev-Preskill code
Polylog-overhead highly fault-tolerant measurement-based quantum computation: all-Gaussian implementation with Gottesman-Kitaev-Preskill code
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发表时间：
2020-06
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通讯作者：
H. Yamasaki;Kosuke Fukui;Yuki Takeuchi;S. Tani;M. Koashi
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作者：
H. Yamasaki;Kosuke Fukui;Yuki Takeuchi;S. Tani;M. Koashi
飞行光子量子系统在产生量子纠缠方面的可扩展性为实现大规模容错量子计算提供了可能，特别是通过基于测量的量子计算（MBQC）。然而，现有的MBQC协议在实现量子计算时不可避免地施加多项式开销成本，这是由于协议中使用的纠缠结构的几何约束，并且多项式开销潜在地抵消了量子计算中有用的多项式加速。为了实现量子计算，没有这种取消，我们构建了一个协议的光子MBQC，实现低的多对数开销，通过引入纠缠结构的低开销量子比特置换。基于此协议，我们设计了一个容错的光子MBQC协议，可以通过实验上易于处理的零差检测和高斯纠缠操作结合Gottesman-Kitaev-Preskill（GKP）量子纠错码，我们级联的$7$-qubit码。我们的容错协议达到阈值$7.8$ dB的GKP代码的压缩水平，优于$8.3$ dB的现有最好的协议的容错量子计算与GKP表面代码。因此，弥合MBQC的理论进展和光子实验实现MBQC之间的差距，我们的结果打开了一个新的方式实现一个大类的量子加速，包括这些多项式。
Scalability of flying photonic quantum systems in generating quantum entanglement offers a potential for implementing large-scale fault-tolerant quantum computation, especially by means of measurement-based quantum computation (MBQC). However, existing protocols for MBQC inevitably impose a polynomial overhead cost in implementing quantum computation due to geometrical constraints of entanglement structures used in the protocols, and the polynomial overhead potentially cancels out useful polynomial speedups in quantum computation. To implement quantum computation without this cancellation, we construct a protocol for photonic MBQC that achieves as low as poly-logarithmic overhead, by introducing an entanglement structure for low-overhead qubit permutation. Based on this protocol, we design a fault-tolerant photonic MBQC protocol that can be performed by experimentally tractable homodyne detection and Gaussian entangling operations combined with the Gottesman-Kitaev-Preskill (GKP) quantum error-correcting code, which we concatenate with the $7$-qubit code. Our fault-tolerant protocol achieves the threshold $7.8$ dB in terms of the squeezing level of the GKP code, outperforming $8.3$ dB of the best existing protocol for fault-tolerant quantum computation with the GKP surface code. Thus, bridging a gap between theoretical progress on MBQC and photonic experiments towards implementing MBQC, our results open a new way towards realization of a large class of quantum speedups including those polynomial.