Agentic Pipelines for Mapping Topological Codes to Quantum Hardware

Abstract

Mapping a prescribed many-body Hamiltonian to a particular quantum hardware is generally an approximate process, resulting in both intended and unwanted quantum dynamics. We introduce an AI-agent-assisted workflow that uses Lean to establish whether an effective device Hamiltonian retains the intended low-energy subspace of the target many-body Hamiltonian. We demonstrate this approach with topological quantum error correction (QEC), providing, to our knowledge, the first Lean-verified pipeline connecting a code space to low-energy states of a device model. Starting from qubits and parity checks, the pipeline constructs the ideal Hamiltonian whose lowest energy states form the intended code space, and determines the excitation gap that protects that code space. It then tests if the device retains the required number of isolated low-energy states and quantifies how closely their subspace matches the intended code space. We compare three bounds on unwanted energy shifts obtained by: summing the interaction strengths, grouping the anticommuting Pauli interactions, and diagonalizing the Hamiltonian. Pauli grouping yields a bound that is tighter than the conventional sum and closer to the diagonalization result, avoiding overly conservative compensation requirements. The workflow also identifies the strongest unwanted interactions and the qubits they affect, providing specific targets for improving device couplings and controls. We demonstrate our framework using an eight-qubit toric-code array on a superconducting device, where the same driven device generates both the required four-qubit interactions as well as unwanted dynamics. An AI agent identifies viable device parameters within a prescribed leakage budget, and Lean verifies four isolated low-energy states close to the ideal code space. Our workflow supports predictive hardware engineering for analog implementations of QEC codes.