Resource overheads and attainable rates for trapped-ion lattice surgery

TL;DR

This paper estimates the ion resource requirements and achievable lattice surgery rates for fault-tolerant trapped-ion quantum computing, highlighting the need for faster ion coupling methods to enable scalable quantum systems.

Contribution

It provides the first detailed estimates of ion overheads and communication rates for lattice surgery in trapped-ion systems, considering realistic cycle times and technological constraints.

Findings

Hundreds to hundreds of thousands of ions needed depending on cycle time

Limited ion coupling rates are the main bottleneck for scalability

Optical coupling improvements are urgently needed for large-scale trapped-ion quantum computers

Abstract

We present estimates for the number of ions needed to implement fault-tolerant lattice surgery between spatially separated trapped-ion surface codes. Additionally, we determine attainable lattice surgery rates given a number of dedicated ``communication ions" per logical qubit. Because our analysis depends heavily on the rate that syndrome extraction cycles take place, we survey the state-of the art and propose three possible cycle times between $10$ and $1000 \mu s$ that we could reasonably see realised provided certain technological milestones are met. Consequently, our numerical results indicate that hundreds of resource ions will be needed for lattice surgery in the slowest case, while close to a hundred thousand will be needed in the fastest case. The main factor contributing to these prohibitive estimates is the limited rate that ions can be coupled across traps. Our results indicate an urgent need for optical coupling to improve by one or more orders of magnitude for trapped-ion quantum computers to scale.