Noisy quantum devices lie between uncontrolled many-body dynamics and fully fault-tolerant quantum computation. In this presentation, I will discuss two connected approaches to understanding and improving their scalability. First, I study error-mitigation thresholds in noisy random quantum circuits by mapping circuit-averaged second moments to a two-replica statistical model and simulating the resulting transfer process with fixed-bond-dimension matrix product states. This approach gives architecture-dependent threshold estimates for all-to-all, square-lattice, and heavy-hex geometries. Second, I discuss bosonic error correction for sequential photonic state generation in circuit QED, where cat and repetition-cat encodings, together with flag-assisted detection of emitter errors, aim to suppress error accumulation in generated photonic matrix-product states. Together, these directions address when mitigation fails and how encoded protocols can suppress errors at the hardware level.

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