Quantum Homomorphic Encryption: Towards Practical and Private Computation on Untrusted Quantum Hardware

TL;DR

This paper introduces a universal quantum homomorphic encryption framework based on the Quantum One-Time Pad, enabling secure, non-interactive quantum computation on untrusted hardware with experimental validation.

Contribution

It presents a practical, information-theoretically secure quantum homomorphic encryption scheme supporting a broad class of quantum operations, bridging theory and near-term quantum hardware.

Findings

Supports homomorphic evaluation of Clifford+T circuits

Demonstrates correctness on simulated and real quantum devices

Maintains key secrecy under circuit noise and device constraints

Abstract

As quantum computing matures into a practical paradigm, the need for secure and private quantum computation on untrusted hardware becomes increasingly urgent. While classical fully homomorphic encryption has enabled computation over encrypted data in untrusted environments, a fully homomorphic and practically implementable quantum counterpart remains elusive. In this work, we propose a universal quantum homomorphic encryption (QHE) framework developed from the Quantum One-Time Pad (QOTP) scheme. Our approach (QOTPH) maintains information-theoretic security and supports a broad class of quantum operations on encrypted quantum states through a systematic set of homomorphic gate decompositions and key update rules. By leveraging the symmetric structure of QOTP and exploiting the transformation properties of quantum gates under Pauli encryption, we enable non-interactive homomorphic evaluation of arbitrary circuits expressible in the Clifford+T gate set, as well as controlled and parameterized operations relevant to variational quantum algorithms and delegated computation. We provide a formal specification of the proposed encryption model, detail its implementation procedure, and report the results obtained from both simulated environments and real quantum processors. Experimental validation demonstrates the correctness of the homomorphic operations and the preservation of key secrecy under circuit-level noise and real-device constraints. This work takes a step toward bridging the gap between theoretical quantum homomorphic encryption and practical realization on near-term quantum hardware, offering a scalable and symmetric cryptographic primitive for privacy-preserving quantum computation.