Quantum Zeno Suppression as a Spectral Memory Bound on Quantum Circuit Depth in History-Dependent Quantum Dynamics (Paper LV)

The scaling of fault-tolerant quantum computers is fundamentally constrained by temporal nonlocality. In this work, we apply the History-Dependent Quantum Dynamics (HDQD) framework to analyze the Quantum Zeno Effect under frequent quantum error correction (QEC) measurements. We demonstrate that frequent syndrome measurements truncate the non-Markovian memory kernel, trapping the system in a short-time quadratic regime and effectively renormalizing the rate of coherent gate evolution. This leads to a fundamental memory–measurement tradeoff. We derive a universal scaling law for the maximum achievable circuit depth: Dmaxopt∝T21/3Bmem−2/3Dmaxopt∝T21/3Bmem−2/3, where T2T2 is the decoherence time and BmemBmem is the spectral memory bandwidth of the physical substrate. This result establishes that temporal spectral memory is not merely a source of decoherence, but a structural resource that dictates the scalability horizon of quantum hardware. Furthermore, we propose a falsifiable experimental protocol for reconstructing the spectral memory density ρ(μ)ρ(μ) via two-quadrature Ramsey interferometry. This work extends the universal spectral memory formalism, previously applied to nuclear scattering and mass defects, into the domain of quantum information science.