AlphaCNOT: Learning CNOT Minimization with Model-Based Planning

2026-04-15

AI Summary

Excessive CNOT gates in quantum circuits exacerbate error propagation on noisy devices, particularly under topological constraints that hinder optimization. This work addresses the CNOT minimization problem by formulating it for the first time as a model-driven planning task, integrating model-based reinforcement learning with Monte Carlo Tree Search (MCTS) to enable lookahead optimization. The proposed approach consistently outperforms existing techniques across both unconstrained settings and various 8-qubit topological constraints. In the synthesis of linear reversible circuits, it reduces CNOT gate count by up to 32% compared to the PMH baseline and maintains superior performance over state-of-the-art reinforcement learning methods.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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. In this work we introduce AlphaCNOT, a RL framework based on Monte Carlo Tree Search (MCTS) that address effectively the CNOT minimization problem by modeling it as a planning problem. In contrast to other RL- based solution, our method is model-based, i.e. it can leverage lookahead search to evaluate future trajectories, thus finding more efficient sequences of CNOTs. Our method achieves a reduction of up to 32% in CNOT gate count compared to PMH baseline on linear reversible synthesis, while in the constraint version we report a consistent gate count reduction on a variety of topologies with up to 8 qubits, with respect to state-of-the-art RL-based solutions. Our results suggest the combination of RL with search-based strategies can be applied to different circuit optimization tasks, such as Clifford minimization, thus fostering the transition toward the "quantum utility" era.

Problem

• CNOT minimization
• quantum circuit optimization
• topology-aware synthesis
• linear reversible synthesis
• quantum computing

Innovation

• CNOT minimization
• model-based reinforcement learning
• Monte Carlo Tree Search
• quantum circuit optimization
• topology-aware synthesis