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arXiv:2203.13123 · PRX Quantum

Looped Pipelines Enabling Effective 3D Qubit Lattices in a Strictly 2D Device

Zhenyu Cai, Adam C. Siegel, Simon C. Benjamin

Published Jun 16, 2023• 24 citations
arXivHTMLPDF

Abstract

A proposed pipelining architecture processes a stack of qubit arrays and implements an effective 3D qubit lattice on a physical 2D hardware substrate, allowing the realization of a variety of code structures with the cost of magic state distillation reduced by 2 orders of magnitude.
DOI
10.1103/prxquantum.4.020345

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Qubit shuttling has become an indispensable ingredient for scaling leading quantum computing platforms, including semiconductor spin, neutral-atom, and trapped-ion qubits, enabling both crosstalk reduction and tighter integration of control hardware. Cai et al. (2023) proposed a scalable architecture that employs short-range shuttling to realize effective three-dimensional connectivity on a strictly two-dimensional device. Building on recent advances in quantum error correction, we show that this architecture enables the native implementation of folded surface codes on 2D hardware, reducing the runtime of all single-qubit logical Clifford gates and logical CNOTs within subsets of qubits from O(d)\mathcal{O}(d)O(d) in conventional surface code lattice surgery to constant time. We present explicit protocols for these operations and demonstrate that access to a transversal SSS gate reduces the spacetime volume of 8T-to-CCZ magic-state distillation by more than an order of magnitude compared with standard 2D lattice surgery approaches. Finally, we introduce a new "virtual-stack" layout that more efficiently exploits the quasi-three-dimensional structure of the architecture, enabling efficient multilayer routing on these two-dimensional devices.
Magic state distillation enables universal fault-tolerant quantum computation by implementing non-Clifford gates via the preparation of high-fidelity magic states. However, it comes at the cost of substantial logical-level overhead in both space and time. In this work, we propose a very low-cost magic state distillation scheme for biased-noise qubits. By leveraging the noise bias, our scheme enables the preparation of a magic state with a logical error rate of 3 × 10 −7 , using only 53 qubits and 5.5 error correction rounds, under a noise bias of η ≳ 5 × 10 6 and a phase-flip noise rate of 0.1%. This reduces the circuit volume by more than one order of magnitude relative to magic state cultivation for unbiased-noise qubits and by more than two orders of magnitude relative to standard magic state distillation. Moreover, our scheme provides three key advantages over previous proposals for biased-noise qubits. First, it only requires nearest-neighbor two-qubit gates on a 2D lattice. Second, the logical fidelity remains nearly identical even at a more modest noise bias of η ≳ 80, at the cost of a slightly increased circuit volume. Third, the scheme remains effective even at high physical phase-flip rates, in contrast to previously proposed approaches whose circuit volume grows exponentially with the error rate. Our construction is based on unfolding the X stabilizer group of the Hadamard 3D quantum Reed-Muller code in 2D, enabling distillation at the physical level rather than the logical level, and is therefore referred to as unfolded distillation.