Quantum homomorphic encryption for polynomial-sized circuits

TL;DR

This paper introduces a compact quantum homomorphic encryption scheme capable of efficiently evaluating polynomial-sized quantum circuits, leveraging classical fully homomorphic encryption and quantum gadgets for error correction.

Contribution

It presents a novel quantum homomorphic encryption scheme that is compact, adaptable, and based on classical FHE, with minimal assumptions and enhanced privacy features.

Findings

Supports arbitrary polynomial-sized quantum circuits

Requires no additional computational assumptions beyond classical FHE

Offers advantages like circuit privacy and limited quantum client requirements

Abstract

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.