High-Performance Exact Synthesis of Two-Qubit Quantum Circuits

TL;DR

This paper introduces a highly efficient exact synthesis method for two-qubit quantum circuits over the Clifford+$T$ gate set, optimizing T-count with a novel search and canonicalization approach.

Contribution

It presents a new synthesis framework that combines algebraic canonicalization, meet-in-the-middle algorithms, and pruning to produce optimal two-qubit circuits efficiently.

Findings

Significantly improved synthesis speed and accuracy.

Creates a lookup table for optimal implementations.

Enables practical, exact synthesis of two-qubit circuits.

Abstract

Exact synthesis provides unconditional optimality and canonical structure, but is often limited to small, carefully scoped regimes. We present an exact synthesis framework for two-qubit circuits over the Clifford+$T$ gate set that optimizes $T$-count exactly. Our approach exhausts a bounded search space, exploits algebraic canonicalization to avoid redundancy, and constructs a lookup table of optimal implementations that turns synthesis into a query. Algorithmically, we combine meet-in-the-middle ideas with provable pruning rules and problem-specific arithmetic designed for modern hardware. The result is an exact, reusable synthesis engine with substantially improved practical performance.