Tableau-Based Framework for Efficient Logical Quantum Compilation

Abstract: Quantum computing holds the promise of solving problems intractable for classical computers, but practical large-scale quantum computation requires error correction to protect against errors. Fault-tolerant quantum computing (FTQC) enables reliable execution of quantum algorithms, yet they often demand substantial physical qubit overhead. Resource-efficient FTQC architectures minimize the number of physical qubits required, saving more than half compared to other architectures, but impose constraints that introduce up to 4.7$\times$ higher runtime overhead. In this paper, we present TQC, a \underline{T}ableau-based \underline{Q}uantum \underline{C}ompiler framework that minimizes FTQC runtime overhead without requiring additional physical qubits. By leveraging operation reorderability and latency hiding through parallel execution, TQC reduces FTQC runtime overhead by \textbf{2.57$\times$} on average. Furthermore, FTQC circuits often contain millions of gates, leading to substantial compilation overhead. To address this, we optimize the core data structure, the tableau, used in stabilizer formalism. We provide two tailored versions of the Tableau data type, each designed for different usage scenarios. These optimizations yield an overall performance improvement of more than \textbf{1000$\times$} compared to state-of-the-art FTQC optimization tools.