DFS-Qubit Error Modeling with Gauge-Averaged Tensor Network Simulations

A central challenge in quantum information processing is understanding how microscopic noise processes map onto effective qubit error models. For decoherence-free subsystem (DFS) qubits, this task is further complicated by subsystem structure: the three-spin exchange-only DFS qubit includes a gauge degree of freedom that makes the characterization of encoded dynamics and leakage processes nontrivial. We introduce a gauge-averaging formalism that resolves this issue and provides a consistent framework for defining error models in the encoded qubit. The utility of this framework is demonstrated through tensor network simulations of coherent spin dynamics with realistic 1/f noise. This enables direct evaluation of encoded and leakage error rates and provides an efficient route to simulating randomized benchmarking. Furthermore, we highlight the broader advantages of tensor networks for studying correlated noise and leakage in DFS qubits, including efficient error-rate extraction and the ability to exploit structural decompositions for simulation.