Leveraging Zero-Level Distillation to Generate High-Fidelity Magic States
arxiv(2024)
摘要
Magic state distillation plays an important role in universal fault-tolerant
quantum computing, and its overhead is one of the major obstacles to realizing
fault-tolerant quantum computers. Hence, many studies have been conducted to
reduce this overhead. Among these, Litinski has provided a concrete assessment
of resource-efficient distillation protocol implementations on the rotated
surface code. On the other hand, recently, Itogawa et al. have proposed
zero-level distillation, a distillation protocol offering very small spatial
and temporal overhead to generate relatively low-fidelity magic states. While
zero-level distillation offers preferable spatial and temporal overhead, it
cannot directly generate high-fidelity magic states since it only reduces the
logical error rate of the magic state quadratically. In this study, we evaluate
the spatial and temporal overhead of two-level distillation implementations
generating relatively high-fidelity magic states, including ones incorporating
zero-level distillation. To this end, we introduce (0+1)-level distillation, a
two-level distillation protocol which combines zero-level distillation and the
15-to-1 distillation protocol. We refine the second-level 15-to-1
implementation in it to capitalize on the small footprint of zero-level
distillation. Under conditions of a physical error probability of
p_phys = 10^-4 (10^-3) and targeting an error rate for the
magic state within [5 × 10^-17, 10^-11] ([5 × 10^-11,
10^-8]), (0+1)-level distillation reduces the spatiotemporal overhead by
more than 63
more than 43
offering a substantial efficiency gain over the traditional protocols.
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