Quantum Circuit Pre-Synthesis: Learning Local Edits to Reduce $T$-count

TL;DR

This paper introduces Q-PreSyn, a reinforcement learning-based method that learns local circuit edits to optimize quantum circuit synthesis, significantly reducing T-counts in fault-tolerant quantum computing.

Contribution

It presents a novel RL-driven approach for learning local circuit modifications to improve T-count reduction in quantum circuit synthesis.

Findings

Achieves up to 20% T-count reduction on circuits with up to 25 qubits.

Integrates with existing synthesis algorithms without adding approximation errors.

Demonstrates effectiveness of learned local edits in quantum circuit optimization.

Abstract

Compiling quantum circuits into Clifford+$T$ gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, $T$ gates will dominate the cost of fault tolerant implementations, and any reduction in the number of such expensive gates could mean the difference between being able to run a circuit or not. While exact synthesis is exponentially hard in the number of qubits, local synthesis approaches are commonly used to compile large circuits by decomposing them into substructures. However, composing local methods leads to suboptimal compilations in key metrics such as $T$-count or circuit depth, and their performance strongly depends on circuit representation. In this work, we address this challenge by proposing \textsc{Q-PreSyn}, a strategy that, given a set of local edits preserving circuit equivalence, uses a RL agent to identify effective sequences of such actions and thereby obtain circuit representations that yield a reduced $T$-count upon synthesis. Experimental results of our proposed strategy, applied on top of well-known synthesis algorithms, show up to a $20\%$ reduction in $T$-count on circuits with up to 25 qubits, without introducing any additional approximation error prior to synthesis.