Zhenyu Cai

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 $\mathcal{O}(d)$ in conventional surface code lattice surgery to constant time. We present explicit protocols for these operations and demonstrate that access to a transversal $S$ 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.

Many quantum computing platforms are based on a two-dimensional physical layout. Here we explore a concept called looped pipelines which permits one to obtain many of the advantages of a 3D lattice while operating a strictly 2D device. The concept leverages qubit shuttling, a well-established feature in platforms like semiconductor spin qubits and trapped-ion qubits. The looped pipeline architecture has similar hardware requirements to other shuttling approaches, but can process a stack of qubit arrays instead of just one. Even a stack of limited height is enabling for diverse schemes ranging from NISQ-era error mitigation through to fault-tolerant codes. For the former, protocols involving multiple states can be implemented with a space-time resource cost comparable to preparing one noisy copy. For the latter, one can realise a far broader variety of code structures; as an example we consider layered 2D codes within which transversal CNOTs are available. Under reasonable assumptions this approach can reduce the space-time cost of magic state distillation by two orders of magnitude. Numerical modelling using experimentally-motivated noise models verifies that the architecture provides this benefit without significant reduction to the code's threshold.