Classical Homomorphic Encryption for Quantum Circuits

TL;DR

This paper introduces the first fully homomorphic encryption scheme for quantum circuits with classical keys, enabling secure delegation of quantum computations by classical clients.

Contribution

It constructs a leveled fully homomorphic encryption scheme for quantum circuits from classical homomorphic encryption based on learning with errors.

Findings

Enables blind delegation of quantum computations by classical clients.

Constructs a quantum-secure classical homomorphic encryption scheme from LWE.

Demonstrates the scheme's security against malicious servers.

Abstract

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.