# Classical Homomorphic Encryption for Quantum Circuits

arXiv: https://arxiv.org/abs/1708.02130 · HTML: https://mlsanity.com/paper/1708.02130/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2017.

## Built on by (most cited first, 6 of 6)

- [Quantum delegated and federated learning via quantum homomorphic encryption](https://mlsanity.com/paper/2409.19359/) (2024)
- [QuMoS: A Framework for Preserving Security of Quantum Machine Learning Model](https://mlsanity.com/paper/2304.11511/) (2023)
- [PristiQ: A Co-Design Framework for Preserving Data Security of Quantum Learning in the Cloud](https://mlsanity.com/paper/2404.13475/) (2024)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [Trustworthy Quantum Machine Learning: A Roadmap for Reliability, Robustness, and Security in the NISQ Era](https://mlsanity.com/paper/2511.02602/) (2025)
- [Encryptability As a Coordinate Choice: Depth-One Homomorphic Federated Learning of Quantum Neural Networks](https://mlsanity.com/paper/2609.30581/) (2026)

## Abstract (arXiv)

We present the first leveled fully homomorphic encryption scheme for quantum circuits with classical keys. The scheme allows a classical client to blindly delegate a quantum computation to a quantum server: an honest server is able to run the computation while a malicious server is unable to learn any information about the computation. We show that it is possible to construct such a scheme directly from a quantum secure classical homomorphic encryption scheme with certain properties. Finally, we show that a classical homomorphic encryption scheme with the required properties can be constructed from the learning with errors problem.