Compilation Pipeline for Predicting Algorithmic Break-Even in an Early-Fault-Tolerant Surface Code Architecture

Recent experimental progress in realizing surface code on hardware, including demonstrations of break-even logical memory on devices with up to hundreds of physical qubits, has materially advanced the prospects for fault-tolerant quantum computation. This progress creates urgency for the development of compilation workflows that directly target the forthcoming generation of devices with thousands of physical qubits, for which algorithm execution becomes practical. We develop a pipeline for compiling logical algorithms to physical circuits implementing lattice surgery on the surface code, and use this pipeline to identify the requirements for achieving algorithmic break-even - where quantum error correction improves the performance of a quantum algorithm - for two prominent quantum algorithms: the quantum approximate optimization algorithm (QAOA) and quantum phase estimation (QPE). Our pipeline integrates several open-source software tools, and leverages recent advances in error-aware unitary gate synthesis, high-fidelity magic state production, and the calculation of correlation surfaces in the surface code. We perform classical simulations of physical Clifford proxy circuits produced by our pipeline, and find that both 5-qubit QAOA and QPE can reach algorithmic break-even with 2517 physical qubits surface code distance $d=11$ at physical error rates of p=10^-3, or 1737 physical qubits $d=9$ at p=5times 10^-4. Our work thereby identifies conditions for achieving algorithmic break-even with near-term quantum hardware and paves the way towards an end-to-end compiler for early-fault-tolerant surface code architectures.