Quantitative Evaluation of Quantum/Classical Neural Network Using a Game Solver Metric

TL;DR

The paper tackles the challenge of benchmarking quantum versus classical neural networks on real tasks by introducing a game-based framework that uses Elo ratings to compare engine performance in tic-tac-toe. It embeds a client–server quantum communication model to quantify overhead and evaluates 54 engines across classical, quantum, and hybrid architectures, finding that hybrid classical–quantum networks approach or exceed classical performance while current quantum-only engines lag behind due to hardware limits. The work demonstrates the viability of game-based benchmarks for assessing quantum advantage and shows that incorporating noisy quantum communication incurs only modest overhead in many configurations, providing a foundation for scalable, hybrid quantum applications. Together, these results advocate for standardized, task-based benchmarking in quantum computing and highlight avenues for improving quantum architectures and communication protocols in near-term devices.

Abstract

To evaluate the performance of quantum computing systems relative to classical counterparts and explore the potential, we propose a game-solving benchmark based on Elo ratings in the game of tic-tac-toe. We compare classical convolutional neural networks (CCNNs), quantum or quantum convolutional neural networks (QNNs, QCNNs), and hybrid classical-quantum neural networks (Hybrid NNs) by assessing their performance based on round-robin matches. Our results show that the Hybrid NNs engines achieve Elo ratings comparable to those of CCNNs engines, while the quantum engines underperform under current hardware constraints. Additionally, we implement a QNN integrated with quantum communication and evaluate its performance to quantify the overhead introduced by noisy quantum channels, and the communication overhead was found to be modest. These results demonstrate the viability of using game-based benchmarks for evaluating quantum computing systems and suggest that quantum communication can be incorporated with limited impact on performance, providing a foundation for future hybrid quantum applications.

Figures (15)

• Figure 1: The game solver initially runs on the client, receiving the board state and selecting the next move using a classical, quantum, or hybrid neural network. In the Quantum Internet setup, a noisy quantum communication (Q-comm) channel connects the client and server. The client processes the input with a classical neural network, encodes the output into qubits, and sends them through the quantum channel. The server then applies a quantum neural network and returns either classical measurement results or unmeasured qubits. The client uses the received data to determine the next move.
• Figure 2: Tic-Tac-Toe game board consisting of 9 squares. 2 players place O and X alternately in the squares. The first player to place O or X in a vertical, horizontal, or diagonal line wins the game. If neither of them is aligned, the game ends in a tie.
• Figure 3: Schematic diagram of agent–environment interaction in reinforcement learning. At each time step $i$, the environment provides the current board state $s_i$ and reward $r_i$ to the agent. The agent then selects an action $a_i$ based on this input. The environment updates the board accordingly and returns the next state $s_{i+1}$ and reward $r_{i+1}$. This cycle is repeated throughout the game.
• Figure 4: Structure of a quantum neural network (QNN). A typical QNN consists of three components: (1) Embedding – classical data is encoded into quantum states $\vert \psi_k \rangle$; (2) Ansatz – parameterized quantum circuits optimized via classical computation; and (3) Measurement – quantum states are measured to produce classical outputs.
• Figure 5: Relationship between rating difference and winning rate.