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# Integrated optical multi-ion quantum logic

### Subjects

A Publisher Correction to this article was published on 19 January 2021

## Abstract

Practical and useful quantum information processing requires substantial improvements with respect to current systems, both in the error rates of basic operations and in scale. The fundamental qualities of individual trapped-ion1 qubits are promising for long-term systems2, but the optics involved in their precise control are a barrier to scaling3. Planar-fabricated optics integrated within ion-trap devices can make such systems simultaneously more robust and parallelizable, as suggested by previous work with single ions4. Here we use scalable optics co-fabricated with a surface-electrode ion trap to achieve high-fidelity multi-ion quantum logic gates, which are often the limiting elements in building up the precise, large-scale entanglement that is essential to quantum computation. Light is efficiently delivered to a trap chip in a cryogenic environment via direct fibre coupling on multiple channels, eliminating the need for beam alignment into vacuum systems and cryostats and lending robustness to vibrations and beam-pointing drifts. This allows us to perform ground-state laser cooling of ion motion and to implement gates generating two-ion entangled states with fidelities greater than 99.3(2) per cent. This work demonstrates hardware that reduces noise and drifts in sensitive quantum logic, and simultaneously offers a route to practical parallelization for high-fidelity quantum processors5. Similar devices may also find applications in atom- and ion-based quantum sensing and timekeeping6.

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## Data availability

The raw data generated during this study are available from the corresponding author on reasonable request.

## Code availability

The analysis code employed in this study is available from the corresponding author on reasonable request.

## Change history

• ### 10 December 2020

This Article was amended to remove a minor typographical error in the main text

• ### 19 January 2021

A Correction to this paper has been published: https://doi.org/ 10.1038/s41586-020-03097-4

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## Acknowledgements

We thank D. Marchenko, D. Geuzebroek and A. Leinse at LioniX International for fabrication of the devices and for discussions during design; V. Negnevitsky and Matteo Marinelli for their work on the experimental control system and software used for these experiments; S. Miller for assistance in characterization of fabricated photonic devices; F. Gürkaynak at ETH for support with CAD software; the ETH FIRST cleanroom staff; and E. Schlatter for helpful advice on epoxies. We acknowledge funding from the Swiss National Fund grant number 200020165555, NCCR QSIT, ETH Zürich, the EU Quantum Flagship, and an ETH Postdoctoral Fellowship.

## Author information

Authors

### Contributions

K.K.M. conceived the work, and designed, characterized and assembled the trap devices. K.K.M., C.Z. and M.M. performed the trapped-ion experiments in an apparatus with substantial contributions from C.Z., M.M., T.-L.N. and M.S. KKM analysed the data. J.P.H. supervised the work, and K.K.M. wrote the manuscript with input from all authors.

### Corresponding author

Correspondence to Karan K. Mehta.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Jungsang Kim and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Design layout.

a, Mask images for device fabrication across a four-inch wafer. b, Individual 2.2 × 2.2 cm2 reticle, showing trap designs as well as independent optics test structures. c, Trap design used in ion experiments presented here. In all images, SiN features are shown in red, the top trap electrode layer in grey and the ground plane in blue. The eight waveguides coupled to the fibre array are labelled at the left, with inputs 1 and 8 forming a loop structure used to align the fibre V-groove array.

### Extended Data Fig. 2 Fibre attachment.

Fibre attachment process schematic and measured single-pass fibre–waveguide coupling losses inferred from a loop-back structure on-chip; solid line is a guide to the eye.

### Extended Data Fig. 3 Ramsey coherence measurements.

We apply two π/2 pulses separated by a variable wait time, and the fringe contrast on scanning the phase of the second pulse relative to the first is plotted to assess $${T}_{2}^{\ast }$$. Data are shown using the same light guided through the in-cryostat fibres and integrated couplers (black points and fit) or through free space (red points and fit). The fit to the data observed with the integrated coupler was used to infer laser noise parameters relevant to gate infidelity calculation; the observation of markedly faster decoherence when driving with the free-space beam (red points/fit) using the same 729-nm source indicates the integrated beam path’s advantage in insensitivity to cryostat vibrations. Error bars on points represent 68% confidence intervals on fit contrasts.

### Extended Data Fig. 4 Readout histograms.

Histogram of photomultiplier tube (PMT) counts observed in detection events over all points in the parity scan of Fig. 4, fitted to a sum of three Poissonian distributions. Each distribution corresponds to counts obtained during a 250-μs detection period from events with either 0, 1 or 2 ions in the bright state.

### Extended Data Fig. 5 Cross-talk characterization.

a, b, Rabi oscillations at zone 3 with light coupled to the port directly addressing this zone (input 3) (a), and with light coupled to the port intended to address zone 2 (input 5) (b). Fits to Rabi oscillations with a Gaussian envelope decay indicate π-times of 2.4 μs (a) and 2.6 ms (b).

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Mehta, K.K., Zhang, C., Malinowski, M. et al. Integrated optical multi-ion quantum logic. Nature 586, 533–537 (2020). https://doi.org/10.1038/s41586-020-2823-6

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