Quantum Circuit Mapping Preserving Fault Tolerance

The patent applies preliminary action by performing multiple forward and backward traverses of the quantum circuit before final mapping. During these traverses, the algorithm pre-identifies and records the active states of data qubits, determining which qubits need to interact with ancilla qubits for error correction. This preliminary analysis enables the subsequent mapping step to preserve fault-tolerant characteristics by ensuring proper qubit placement and interaction timing, thus resolving the contradiction between hardware compatibility and fault tolerance.

The patent applies local quality by focusing the computational effort on specific critical regions of the quantum circuit rather than uniformly processing all qubits. During the forward and backward traverses, the algorithm identifies local patterns of qubit activation and interaction, particularly focusing on which data qubits become active and require error correction. This localized analysis approach enables efficient optimization across multiple mappings without requiring exhaustive computation of all possible qubit arrangements, thus resolving the contradiction between mapping optimization and computational complexity.