Quantum Simulation of Finite TEBAC 9D/9D+ Topological Phases: Synthetic Dimensions, Spectral Gaps, Portal-Channel Diagnostics, and Local Qiskit Aer Execution

This preprint presents a finite-dimensional quantum-simulation framework for selected TEBAC 9D/9D+ topological phases, with emphasis on synthetic-dimensional encoding, spectral-gap diagnostics, portal-channel observables, and Qiskit-ready Hamiltonian construction. The manuscript formulates a finite-lattice simulation target for the internal TEBAC sector and encodes the model through Pauli-sum Hamiltonians suitable for NumPy exact diagonalization, Qiskit Aer simulation, and future IBM Runtime execution. The central simulation Hamiltonian is organized schematically as\[Hₛᵢₘ=HDirac(N)+Hgauge(N)+Hₜₒₚ(N)+Hchannel(N).\] The paper develops a concrete two-qubit benchmark v0.1 and a four-qubit finite-lattice sector v0.2. For the four-qubit sector, the manuscript gives an explicit Pauli decomposition, exact spectrum, spectral-gap diagnostic, topological proxy, link-sector markers, fidelity diagnostic, and determinant diagnostic. A key contribution of this version is the transition from a hardware-ready protocol to an executed local emulator report. The v0.2 four-qubit sector is evaluated through NumPy exact computation and local Qiskit Aer execution, including ideal sampling, readout-noisy sampling, and readout-mitigation recovery. For the topological proxy\[Q₄= ZZZZ,\]the reported values are:\[Q₄ᵉˣᵃᶜᵗ=0.986000,\]\[Q₄Aer,ideal=0.986572± 0.001805,\]\[Q₄Aer,noisy=0.775391± 0.006977,\]and\[Q₄ᵐⁱᵗⁱᵍᵃᵗᵉᵈ=0.993137± 0.008936.\] The manuscript also includes a Qiskit Aer / IBM Runtime execution skeleton, an error-mitigation roadmap, and a validation ledger. The included code package provides the Python scripts used for the NumPy and local Qiskit Aer runs. This preprint should be read as a companion algorithmic module to the TEBAC portal-channel preprint. The portal-channel preprint formulates the geometric and quantum-informational target model; the present manuscript formulates and partially executes a finite-dimensional quantum-simulation protocol for selected spectral, topological, and channel-level diagnostics. The RH and BSD modules of the broader TEBAC 9D/9D+ programme are discussed only methodologically. They are not used as physical inputs for quantum simulation. Their role is to motivate the common operator--spectrum--trace/determinant--comparison architecture used across the TEBAC programme. This version does not claim a laboratory realization of a physical TEBAC portal, a physical 9D/13D geometry on quantum hardware, or a remote IBM/Google hardware backend result. It reports a local NumPy and Qiskit Aer execution and provides a hardware-ready path toward future cloud-backend experiments.