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Decoherence is the operative crisis of quantum computing——every architecture confronts it, and every proposed remedy carries a hidden cost in overhead, gap requirement, or temperature constraint. This paper derives, in full algebraic detail and without unexplained transitions, a holographic decoherence-suppression mechanism rooted in the AdS$_3$/CFT$_2$ correspondence, showing that the bulk--boundary geometry of three-dimensional anti-de Sitter space acts as a geometric filter that exponentially screens environmental noise from qubit degrees of freedom encoded in the helical edge modes of topological insulators and in trapped-ion chains. Starting from the chiral Luttinger liquid Hamiltonian of a quantum spin Hall edge, we derive the Virasoro algebra with central charge $c$, identify the bosonic density fluctuation $\delta\rho(x,t)$ as the boundary trace of a bulk dilaton field $\phi(z,x,t)$, solve the dilaton equation of motion step by step to obtain the bulk-to-boundary propagator, and couple it to the Lindblad master equation to derive the modified decoherence rate:\[ \gamma_{\text{holo}} = \gamma_{\text{std}} \exp\!\left(-\frac{2\pi \Delta_n}{c}\frac{l}{\xi}\right), \qquad \frac{T_{\text{std}}^{\text{holo}}}{T_{\text{std}}^{\text{std}}} = \exp\!\left(\frac{\xi}{6}\ln\frac{l}{\xi}\right). \]. Every intermediate numerical estimate in the paper is anchored to independently measured material parameters: Fermi velocity \(v_{\mathrm{F}}\), bulk gap \(\Delta_{\mathrm{gap}}\), and coherence length \(\xi = \hbar v_{\mathrm{F}} / \Delta_{\mathrm{gap}}\). We derive explicit density--density correlation functions, dynamical structure factors, and out-of-time-order correlators (OTOCs), each carrying logarithmic holographic corrections testable by scanning tunneling microscopy, angle-resolved photoemission spectroscopy (ARPES), and Ramsey interferometry. Gate fidelities exceeding \(99.9\%\) are shown to be achievable for Majorana-based qubits when the geometric ratio satisfies \[L/\xi \gtrsim 15 \quad \text{with} \quad c \geq 2. \] Three experimental platforms are analyzed quantitatively: \(\mathrm{Bi}_2\mathrm{Se}_3\) topological insulator edges, \(\mathrm{HgTe}/\mathrm{CdTe}\) quantum wells, and \(^{171}\mathrm{Yb}^+\) trapped-ion chains, with detailed measurement protocols for each.