A Unified Error Correction Code for Universal Quantum Computing with Identical Particles

We present a universal fault-tolerant quantum computing architecture based on identical particle qubits (IPQs), where we find that the first-order IPQ - bath interaction fundamentally differs from the conventional first-order qubit-bath interaction. This key distinction necessitates a redesign of existing strategies to fight decoherence. We propose that the simplest quantum error correction code can be realized directly within the physical qubit, provided that conventional correction and restoration are generalized beyond unitary operations to employ physically implementable reversal operations - naturally placing logical and physical qubits on equal footing. We further demonstrate that dynamical decoupling (DD) remains effective within this unified framework, and that a decoherence-free subspace (DFS) - like structure emerges. Unlike previous approximate treatments, our analytically solvable IPQ-Bath model enables rigorous testing of these strategies, with numerical simulations validating their effectiveness.