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# Error-protected qubits in a silicon photonic chip

## Abstract

General-purpose quantum computers can, in principle, entangle a number of noisy physical qubits to realize composite qubits protected against errors. Architectures for measurement-based quantum computing intrinsically support error-protected qubits and are the most viable approach for constructing an all-photonic quantum computer. Here we propose and demonstrate an integrated silicon photonic scheme that both entangles multiple photons, and encodes multiple physical qubits on individual photons, to produce error-protected qubits. We realize reconfigurable graph states to compare several schemes with and without error-correction encodings and implement a range of quantum information processing tasks. We observe a success rate increase from 62.5% to 95.8% when running a phase-estimation algorithm without and with error protection, respectively. Finally, we realize hypergraph states, which are a generalized class of resource states that offer protection against correlated errors. Our results show how quantum error-correction encodings can be implemented with resource-efficient photonic architectures to improve the performance of quantum algorithms.

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## Data availability

The data that support the plots within this paper and other findings of this study are available at https://doi.org/10.6084/m9.figshare.11903427.

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## Acknowledgements

We thank R. Santagati, A. E. Jones, J. F. Bulmer, R. Shaw, D. D. Roberts, J. F. Tasker, N. Maraviglia, J. W. Silverstone, W. A. Murray, Z. Raissi, C. Gogolin and P. Skrzypczyk for useful discussions and technical assistance. We acknowledge support from the Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC) and European Commission (EC) funded grants PICQUE, BBOI, QUCHIP, QuPIC, QITBOX, VILLUM FONDEN, QUANPIC (ref. 00025298), the Center of Excellence, Denmark SPOC (ref DNRF123) and ERA-NET cofund initiatives QuantERA within the European Union’s Horizon 2020 research and innovation programme grant agreement 731473 (project SQUARE). We acknowledge support from the EPSRC Hubs in Quantum Computing and Simulation (EP/T001062/1) and Networked Quantum Information Technologies (EP/N509711/1). Fellowship support from EPSRC is acknowledged by A.L. (EP/N003470/1).

## Author information

Authors

### Contributions

C.V., S.P., Y.D., J.W., D.B., M.G.T. and A.L. designed the experiment. J.W. and S.P. designed the integrated circuit. Y.D. fabricated the silicon photonics device. C.V. and S.P. performed the experiment and analysed the data, with theoretical support from J.C.A. and S.M.-S. C.V., S.P., J.C.A. and A.L. wrote the manuscript with feedback from all authors. L.K.O., M.G.T., J.G.R. and A.L. managed the project.

### Corresponding authors

Correspondence to Yunhong Ding, Jianwei Wang or Anthony Laing.

## Ethics declarations

### Competing interests

M.G.T. is involved in developing quantum photonic technologies at PsiQuantum Corporation. The remaining authors declare no competing interests.

Peer review information Nature Physics thanks the anonymous reviewers 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.

## Supplementary information

### Supplementary Information

Supplementary Sections 1–12, Figs. 1–16 and Tables 1–12.

## Rights and permissions

Reprints and Permissions

Vigliar, C., Paesani, S., Ding, Y. et al. Error-protected qubits in a silicon photonic chip. Nat. Phys. 17, 1137–1143 (2021). https://doi.org/10.1038/s41567-021-01333-w

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• DOI: https://doi.org/10.1038/s41567-021-01333-w

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