Quantum homomorphic encryption from quantum codes

TL;DR

This paper introduces a quantum encryption scheme that is homomorphic for both classical and quantum circuits with limited non-Clifford gates, offering information-theoretic security unlike classical schemes.

Contribution

It presents the first quantum homomorphic encryption scheme with information-theoretic security for circuits with bounded non-Clifford gates.

Findings

Scheme is homomorphic for classical and quantum circuits with limited non-Clifford gates

Security is information-theoretic, not computational

Applicable to arbitrary classical and quantum circuits with constraints

Abstract

The recent discovery of fully-homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumptions that solving certain computation problems are intractable. Here we present a quantum encryption scheme which is homomorphic for arbitrary classical and quantum circuits which have at most some constant number of non-Clifford gates. Unlike classical schemes, the security of the scheme we present is information theoretic and hence independent of the computational power of an adversary.