Fault-tolerant Quantum Computation without Distillation on a 2D Device

TL;DR

This paper demonstrates a method for fault-tolerant quantum computation on a 2D device using looped pipeline architectures, highlighting the potential for improvements in decoder performance to reduce resource costs.

Contribution

It introduces a novel approach for implementing non-Clifford gates in 2D surface codes without distillation, emphasizing the importance of decoder optimization.

Findings

Shuttling schedule complexity is comparable to standard surface code implementation.

Current resource costs favor magic state distillation over the proposed method.

Decoder performance significantly impacts the efficiency of non-Clifford gate implementation.

Abstract

We show how looped pipeline architectures - which use short-range shuttling of physical qubits to achieve a finite amount of non-local connectivity - can be used to efficiently implement the fault-tolerant non-Clifford gate between 2D surface codes described in (Sci. Adv. 6, eaay4929 (2020)). The shuttling schedule needed to implement this gate is only marginally more complex than is required for implementing the standard 2D surface code in this architecture. We compare the resource cost of this operation with the cost of magic state distillation and find that, at present, this comparison is heavily in favour of distillation. The high cost of the non-Clifford gate is almost entirely due to the relatively low performance of the just-in-time decoder used as part of this process, which necessitates very large code distances in order to achieve suitably low logical error rates. We argue that, as very little attention has previously been given to the study and optimisation of these decoders, there are potentially significant improvements to be made in this area.