Reverse Delegated Training and Private Inference via Perfectly-Secure Quantum Homomorphic Encryption

TL;DR

The paper tackles privacy in cloud quantum machine learning by employing a perfectly-secure quantum homomorphic encryption scheme (QHE) based on quantum one-time pad encryption and a Clifford+$T$ gate framework. It demonstrates efficient, non-interactive homomorphic evaluation of quantum neural networks, specifically quantum convolutional neural networks (QCNN), and analyzes the complexity, showing linear scaling with the number of $T$ gates $M$, i.e., $M$-quasi-compactness. Two practical use cases are explored: reverse delegated training, where encrypted data from multiple providers trains a user’s QCNN via federated aggregation, and private inference, where encrypted inputs are processed by a server’s private quantum network. Simulations implemented with the CQC-QHE toolchain illustrate feasibility, including data privacy via quantum one-time pads and partial server circuit privacy through Pauli concealment; the work highlights a practical privacy-utility trade-off and paves the way for securely deployed multi-party quantum learning. The results indicate that perfectly-secure QHE can be a viable framework for protecting data in multi-party quantum ML, with potential impact on privacy-preserving quantum cloud services and federated quantum learning ecosystems.

Abstract

Quantum machine learning in cloud environments requires protecting sensitive data while enabling remote computation. Here we demonstrate the first realistic implementations of a perfectly-secure quantum homomorphic encryption (QHE) scheme applied to quantum neural networks (QNN). Using efficient Clifford+$T$ decomposition, we implement quantum convolutional neural networks for two complementary scenarios: (i) reverse delegated training, where encrypted data from multiple providers trains a user's network via federated aggregation; (ii) private inference, where users process encrypted data with remote quantum networks. Moreover, analysis of server circuit privacy reveals probabilistic model protection through Pauli gate concealment. These results establish perfectly-secure QHE as a practical framework for multi-party quantum machine learning.

Figures (11)

• Figure 1: (a) Homomorphic evaluation scheme for a T gate using quantum teleportation. (b) Circuit corresponding to SERVER’s operations, including Bell-pair creation and swap. (c) CLIENT's decryption procedure, including a Bell measurement after the correction of the $S$ error.
• Figure 2: General workflow of a quantum neural network training process. At each iteration, the initial state $\left|\psi_\mathbf{x}\right>$ representing the data is fed to the quantum network, processed by a parameterized quantum circuit $U(\boldsymbol{\theta})$ of the ansatz, and measured to produce classical outputs used for calculating the result $f(\mathbf{x},\boldsymbol{\theta})$. With this, the loss and its gradient are calculated, and finally the weights $\boldsymbol{\theta}$ are updated on a classical computer.
• Figure 3: Example of the structure of the quantum convolutional neural network ansatz for a system with eight qubits. In this case there are three layers of convolutional and pooling operations. After the pooling operations, the number of effective qubits is reduced by half. The dashed line in a convolutional unit means that it connects with the opposite qubit in the circuit.
• Figure 4: Subunit circuits for the QCNN ansatz. (a) General $SU(4)$ unitary operator, where $U3(\theta_1,\theta_2,\theta_3) \sim R_Z(\theta_2)HS^\dagger HR_Z(\theta_1)HSHR_Z(\theta_3)$. (b) General $SO(4)$ unitary operator. (c) Simple subunit used for pooling.
• Figure 5: Decomposition of the controlled rotation gates of the pooling subunit in Figure \ref{['F:Pooling']} into $R_Z$ gates.