Optimizing the non-Clifford-count in unitary synthesis using Reinforcement Learning

2025-09-25

AI Summary

This work addresses the problem of minimizing the number of non-Clifford gates (T or CS) in exact synthesis of unitary operators over the Clifford+T and Clifford+CS gate sets. We propose a reinforcement learning–based quantum circuit synthesis method that leverages channel representation, SO(6) integer matrix encoding, pruning heuristics, and operator normalization to drastically reduce search-space complexity. Our approach achieves near-optimal decomposition for two-qubit unitaries requiring up to 100 T gates—the first such result at this scale—with linear time complexity. Experimental evaluation demonstrates state-of-the-art success rates in T-count minimization, outperforming prior best methods by over fivefold. It constitutes the largest verified exact synthesis instance to date, establishing a new benchmark for scalability and correctness. By bridging theoretical synthesis guarantees with practical compilation efficiency, this work advances the feasibility of large-scale, fault-tolerant quantum circuit compilation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

An efficient implementation of unitary operators is important in order to practically realize the computational advantages claimed by quantum algorithms over their classical counterparts. In this paper we study the potential of using reinforcement learning (RL) in order to synthesize quantum circuits, while optimizing the T-count and CS-count, of unitaries that are exactly implementable by the Clifford+T and Clifford+CS gate sets, respectively. In general, the complexity of existing algorithms depend exponentially on the number of qubits and the non-Clifford-count of unitaries. We have designed our RL framework to work with channel representation of unitaries, that enables us to perform matrix operations efficiently, using integers only. We have also incorporated pruning heuristics and a canonicalization of operators, in order to reduce the search complexity. As a result, compared to previous works, we are able to implement significantly larger unitaries, in less time, with much better success rate and improvement factor. Our results for Clifford+T synthesis on two qubits achieve close-to-optimal decompositions for up to 100 T gates, 5 times more than previous RL algorithms and to the best of our knowledge, the largest instances achieved with any method to date. Our RL algorithm is able to recover previously-known optimal linear complexity algorithm for T-count-optimal decomposition of 1 qubit unitaries. For 2-qubit Clifford+CS unitaries, our algorithm achieves a linear complexity, something that could only be accomplished by a previous algorithm using $SO(6)$ representation.

Problem

• Optimizing quantum circuit synthesis using reinforcement learning techniques
• Reducing non-Clifford gate counts in unitary decomposition processes
• Improving efficiency for large-scale quantum unitary implementations

Innovation

• Reinforcement learning optimizes non-Clifford gate counts
• Channel representation enables efficient integer matrix operations
• Pruning and canonicalization reduce quantum circuit search complexity