Federated learning with distributed fixed design quantum chips and quantum channels

TL;DR

The paper tackles privacy and communication challenges in federated learning by introducing a quantum FL framework in which fixed-design quantum chips are controlled by input quantum states sent from a central server. The server encodes a learning operator as a quantum state $|o\rangle$ and clients execute this operator on local data, returning gradients as quantum states for aggregation, enabling asynchronous updates without sharing full model parameters. It leverages block-encoding and a parameterized quantum circuit to realize a flexible learning model, while gradient estimation relies on the shift rule and superposition states to extract partial derivatives. The framework suggests potential improvements in privacy and communication efficiency through quantum channels and quantum-state data transfer, and outlines practical considerations, future directions, and real-world applicability in distributed quantum computing environments.

Abstract

The privacy in classical federated learning can be breached through the use of local gradient results combined with engineered queries to the clients. However, quantum communication channels are considered more secure because a measurement on the channel causes a loss of information, which can be detected by the sender. Therefore, the quantum version of federated learning can be used to provide better privacy. Additionally, sending an $N$-dimensional data vector through a quantum channel requires sending $\log N$ entangled qubits, which can potentially provide efficiency if the data vector is utilized as quantum states. In this paper, we propose a quantum federated learning model in which fixed design quantum chips are operated based on the quantum states sent by a centralized server. Based on the incoming superposition states, the clients compute and then send their local gradients as quantum states to the server, where they are aggregated to update parameters. Since the server does not send model parameters, but instead sends the operator as a quantum state, the clients are not required to share the model. This allows for the creation of asynchronous learning models. In addition, the model is fed into client-side chips directly as a quantum state; therefore, it does not require measurements on the incoming quantum state to obtain model parameters in order to compute gradients. This can provide efficiency over models where the parameter vector is sent via classical or quantum channels and local gradients are obtained through the obtained values these parameters.

Figures (3)

• Figure 1: A quantum circuit which runs the operations based on the input on the ancilla register $\left|o\right\rangle$ and can emulate the output of $O\left|\psi\right\rangle$ by using $\left|o\right\rangle = \left|vec(O)\right\rangle$. Note that nonunitary $O_i$s can be considered as block encoding circuits used in quantum signal processing and other similar works berry2015simulatinglow2017optimalchilds2012hamiltoniandaskin2012universal. Therefore, after writing them as a sum of $X$, $Z$, and $I$, the circuit can be rewritten in terms of unitary gates.
• Figure 2: Server-side parameterized quantum circuit (PQC): The circuit can be any parameterized model or a general purpose quantum chip. The output registers may be identical or different, depending on the considered learning model. The output states are sent to the client nodes through the quantum channel. The input $\left|\nabla_i\right\rangle$ represents the gradient from node $i$.
• Figure 3: The overall federated approach is as follows: Each client has a full-capacity quantum processing unit (QPU), which operates based on the input $\left|o\right\rangle$ sent by the server. It should be noted that $\left|o\right\rangle$ may be different or the same, depending on the chosen optimization approach. The input is considered as a superposition of the shifted states used to estimate gradients. The clients then apply the associated operator $O$ to their local data, represented by the data register $\left|d\right\rangle$. Finally, they evaluate their local gradients either classically or through quantum circuits and send the local gradient results $\left|\nabla_\theta\right\rangle$ to the server. The server aggregates these results to decide the next step in the optimization process.