Quantum Algorithm for Open-System Battery Cathodes by Modeling Multiple Strongly Coupled Holstein Polarons with Chain-Mapped Caldeira-Leggett Dynamics

Cathode lithiation occupies a chemical regime of tightly localized orbitals, narrow bandwidths, and strong electron-lattice coupling. The defining electrochemical observables (open-circuit voltage and differential capacity) are open-system, reservoir-equilibration quantities that closed-Hamiltonian quantum simulation cannot produce, set by exchange with electron, Li^+, and phonon baths. We present a fault-tolerant quantum algorithm that recovers them through a unitary chain-mapped Caldeira-Leggett embedding, rendering the baths Trotterizable. The resulting fourth-order Trotter step has a T-gate count polynomial in system size, validating its open-system dynamics against hierarchical equations of motion (HEOM) at strong coupling and the Lindblad limit at weak coupling. For single-carrier olivine LiFePO₄, a single voltage anchor on an otherwise DFT-fixed Hamiltonian places the differential-capacity peak within the pm5 mV reproducibility of the experimental plateau. For multi-carrier spinel LiMn₂O₄, whose 1{:}1 Mn³⁺/Mn⁴⁺ filling makes the inter-site Coulomb repulsion dynamically active, the same kernel yields a two-plateau voltage curve with a 125 mV split, within 17\% of the observed 150 mV. We deliver an end-to-end fault-tolerant resource estimate for such a multi-carrier, three-reservoir observable: 368 logical qubits and sim3times10⁵ T-gates per step, or sim1.7times10¹² T-gates for a full voltage curve parallelizable over $sim10³$ trajectories, leaving the production-scale dynamical run as a milestone for future hardware. The same kernel reproduces macroscopic quantum coherence, two-band superconductivity, and the Mikheyev-Smirnov-Wolfenstein resonance without modification, placing dynamical battery chemistry and similar Hamiltonians within scope for fault-tolerant quantum simulation.