# Unitary Synthesis with AlphaZero via Dynamic Circuits

## TL;DR

This paper introduces a reinforcement learning approach inspired by AlphaZero for exact quantum unitary synthesis, capable of handling dynamic circuits with measurements and conditional gates, improving efficiency and versatility.

## Contribution

It presents a novel RL-based method for quantum unitary synthesis that extends to dynamic circuits with non-unitary operations, enabling efficient subroutine synthesis.

## Key findings

- Achieves low inference time for unitary synthesis.
- Versatile across different gate sets and qubit connectivities.
- Effective in synthesizing quantum subroutines for complex algorithms.

## Abstract

Unitary synthesis is the process of decomposing a target unitary transformation into a sequence of quantum gates. This is a challenging task, as the number of possible gate combinations grows exponentially with the circuit depth. In this manuscript, we propose an approach using an AlphaZero-inspired reinforcement-learning agent for the exact compilation of unitaries using discrete sets of logic gates. The approach achieves low inference time and proves versatile across different gate sets, and qubit connectivities. Leveraging this flexibility, we explore unitary synthesis with dynamic circuits -- circuits that contain non-unitary operations such as measurements and conditional gates -- and discover unusual implementations of logical quantum gates. Although the direct synthesis of complete algorithms is intractable, our approach is well suited for efficiently synthesizing subroutines. This may have a significant impact when these subroutines are invoked repeatedly during algorithm execution.

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Source: https://tomesphere.com/paper/2508.21217