AlphaCNOT: Learning CNOT Minimization with Model-Based Planning
Summary: arXiv:2604.13812v1 Announce Type: new
Abstract
Quantum circuit optimization is a central task in Quantum Computing, as current Noisy Intermediate Scale Quantum devices suffer from error propagation that often scales with the number of operations. Among quantum operations, the CNOT gate is of fundamental importance, being the only 2-qubit gate in the universal Clifford+T set.
The problem of CNOT gates minimization has been addressed by heuristic algorithms such as the well-known Patel-Markov-Hayes (PMH) for linear reversible synthesis (i.e., CNOT minimization with no topological constraints), and more recently by Reinforcement Learning (RL) based strategies in the more complex case of topology-aware synthesis, where each CNOT can act on a subset of all qubits pairs.
Introduction of AlphaCNOT
In this work, we introduce AlphaCNOT, a Reinforcement Learning (RL) framework based on Monte Carlo Tree Search (MCTS) that effectively addresses the CNOT minimization problem by modeling it as a planning problem. Unlike other RL-based solutions, our method is model-based, enabling it to leverage lookahead search to evaluate future trajectories, thus finding more efficient sequences of CNOTs.
Performance and Results
Our method achieves a reduction of up to 32% in CNOT gate count compared to the PMH baseline on linear reversible synthesis. In the constraint version, we report a consistent gate count reduction across various topologies with up to 8 qubits, outperforming state-of-the-art RL-based solutions.
Implications for Quantum Computing
The results suggest that the combination of Reinforcement Learning with search-based strategies can be effectively applied to different circuit optimization tasks, such as:
- Clifford minimization
- Advanced quantum circuit synthesis
- Optimization of quantum algorithms
- Realization of more complex quantum operations
Such advancements are crucial for fostering the transition toward the “quantum utility” era, where quantum technologies can be harnessed for practical applications.
Conclusion
AlphaCNOT represents a significant step forward in the optimization of quantum circuits. By integrating model-based planning with Reinforcement Learning, this framework not only enhances the efficiency of CNOT gate minimization but also opens avenues for future research in quantum optimization. As quantum computing continues to evolve, techniques like AlphaCNOT will play a pivotal role in overcoming current limitations and enabling more complex quantum computations.