# Quantum homomorphic encryption for polynomial-sized circuits

arXiv: https://arxiv.org/abs/1603.09717 · HTML: https://mlsanity.com/paper/1603.09717/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2016.

## Built on by (most cited first, 4 of 4)

- [STIQ: Safeguarding Training and Inferencing of Quantum Neural Networks from Untrusted Cloud](https://mlsanity.com/paper/2405.18746/) (2024)
- [Enigma: Application-Layer Privacy for Quantum Optimization on Untrusted Computers](https://mlsanity.com/paper/2311.13546/) (2023)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [Ents: An Efficient Three-party Training Framework for Decision Trees by Communication Optimization](https://mlsanity.com/paper/2406.07948/) (2024)

## Abstract (arXiv)

We present a new scheme for quantum homomorphic encryption which is compact and allows for efficient evaluation of arbitrary polynomial-sized quantum circuits. Building on the framework of Broadbent and Jeffery and recent results in the area of instantaneous non-local quantum computation, we show how to construct quantum gadgets that allow perfect correction of the errors which occur during the homomorphic evaluation of T gates on encrypted quantum data. Our scheme can be based on any classical (leveled) fully homomorphic encryption (FHE) scheme and requires no computational assumptions besides those already used by the classical scheme. The size of our quantum gadget depends on the space complexity of the classical decryption function -- which aligns well with the current efforts to minimize the complexity of the decryption function. Our scheme (or slight variants of it) offers a number of additional advantages such as ideal compactness, the ability to supply gadgets "on demand", circuit privacy for the evaluator against passive adversaries, and a three-round scheme for blind delegated quantum computation which puts only very limited demands on the quantum abilities of the client.