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

TL;DR

The paper introduces an automated end-to-end pipeline that compiles logical quantum circuits into physical circuits on a 2D surface-code architecture using lattice surgery, with execution-aware error budgeting and on-demand magic-state cultivation. By integrating rotation-synthesis in a $U3$-based framework, direct lattice-surgery compilation, and correlation-surface-aware decoding, the authors produce realistic Clifford proxy circuits for QPE and QAOA (LABS) and perform memory-noise simulations to predict algorithmic break-even. They demonstrate break-even at $d=11$ with $2517$ physical qubits at $p=10^{-3}$ or at $d=9$ with $1737$ qubits at $p=5\times 10^{-4}$, identifying practical resource targets for near-term EFT hardware. The work provides a concrete, automated path toward an end-to-end EFT surface-code compiler and establishes actionable guidance for achieving quantum advantage on early fault-tolerant devices.

Abstract

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 $p=5\times 10^{-4}$. 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.

Figures (7)

• Figure 1: (a) Pipe diagram representing a CNOT gate, which directly translates to the joint Pauli measurements implementation of the CNOT. The conditional Pauli gates are tracked in software. (b) The magic state injection circuit.
• Figure 2: The full pipeline. Raw inputs to the pipeline are indicated in orange. Intermediate representations, transformations, and metadata on the logical level (agnostic to the choice of error-correcting code) is indicated in blue, while data on the level of lattice surgery and physical qubit operations is indicated in green. (a) \ref{['sec:u3-transpilation']}: rotation merging and $U3$ compilation. (b) \ref{['sec:rotation-synthesis']}: execution-error-aware rotation synthesis. (c) \ref{['sec:t-normalization']}: $T$ sequence normalization. (d) \ref{['sec:t-injection']}: Magic state preparation and injection. (e) \ref{['sec:lattice-surgery-compilation']}: Clifford to lattice surgery. (f) \ref{['sec:physical-circuit']}: Lattice surgery to physical circuit. (g) \ref{['sec:results']}: Resource estimation based on physical-level simulation.
• Figure 3: Comparison of infidelity estimation by logical-level simulation, spacetime volume counting, and physical-level simulation.
• Figure 4: Performance of running the algorithm with the surface code versus directly, unencoded. Dashed lines indicate sampling error $\varepsilon$ obtained from the proxy Clifford simulations, without synthesis error.
• Figure 5: (a) Logical QAOA circuit for 5-bit LABS. (b) QPE logical circuit for 4-bit precision $R_Z(\pi/4)$.