# One-dimensional quantum computing with a 'segmented chain' is feasible with today's gate fidelities

## TL;DR

This paper proposes a feasible 1D segmented chain architecture for quantum computing that leverages current gate fidelities, achieving fault tolerance with manageable overhead and promising scalability.

## Contribution

It introduces the concept of a 1D segmented chain with all-to-all connectivity within segments, demonstrating fault tolerance thresholds and scalability with existing technology.

## Key findings

- Fault tolerance threshold is 0.12% for 15-qubit segments.
- Larger segments (>35 qubits) enable meaningful computation with current fidelities.
- The architecture reduces device size by avoiding additional concatenation layers.

## Abstract

In principle a 1D array of nearest-neighbour linked qubits is compatible with fault tolerant quantum computing. However such a restricted topology necessitates a large overhead for shuffling qubits and consequently the fault tolerance threshold is far lower than in 2D architectures. Here we identify a middle ground: a 1D segmented chain which is a linear array of segments, each of which is a well-connected zone with all-to-all connectivity. The architecture is relevant to both ion trap and solid-state systems. We establish that fault tolerance can be achieved either by a surface code alone, or via an additional concatenated four-qubit gauge code. We find that the fault tolerance threshold is 0.12% for 15-qubit segments, while larger segments are superior. For 35 or more qubits per segment one can achieve computation on a meaningful scale with today's state-of-the-art fidelities without the use of the upper concatenation layer, thus minimising the overall device size.