Leveraging Zero-Level Distillation to Generate High-Fidelity Magic States

Abstract

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 $p_{\mathrm{phys}}=10^{-4}$ ($10^{-3}$) and targeting an error rate for the magic state within $[5\times 10^{-17},10^{-11}]$ ($[5\times 10^{-11},10^{-8}]$), (0+1)-level distillation reduces the spatiotemporal overhead by more than 63% (61%) compared to the (15-to-1)$\times$(15-to-1) protocol and more than 43% (44%) compared to the (15-to-1)$\times$(20-to-4) protocol, offering a substantial efficiency gain over the traditional protocols.

11 pages, 19 figures. This work has been submitted to the IEEE for possible publication

References in corpus (12)

• Quantum Computing in the NISQ era and beyond
• Fault-tolerant quantum computation by anyons
• Quantum algorithm for solving linear systems of equations
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Simulated Quantum Computation of Molecular Energies
• Surface code quantum computing by lattice surgery
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Magic State Distillation: Not as Costly as You Think
• Efficient magic state factories with a catalyzed |CCZ> to 2|T> transformation
• A unified framework for magic state distillation and multi-qubit gate-synthesis with reduced resource cost
• Shorter quantum circuits via single-qubit gate approximation
• Lattice Surgery Translation for Quantum Computation

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