Explicit quantum-circuit simulation of nonlinear 1D fluid via second-order Carleman-linearized Boltzmann equation and QSVD Taylor ODE solver, with logarithmic scaling analysis.
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New SelectCopy architecture and qubit-constrained optimizations reduce QROM Toffoli cost from ~2N/λ to ~(1 + 1/b)N/λ while preserving the ability to trade dirty qubits for lower gate count.
Constructs quantum filtered oracle for Valiant-Vazirani theorem reducing SAT to UNIQUE SAT, enabling polynomial-time NP solution via torsion nonlinearity in noise-free limit but not #P.
Presents LCNU-plus-embedding data loading for any polynomial Carleman-linearized autonomous system and applies it to the 3D LBE, yielding Ns ~ O(α²Q²) terms and explicit T-gate resource estimates for two solvers.
A quantum solver for PDEs is introduced via flexible matrix product operator representations with mid-circuit measurements and state-dependent norm correction to handle non-unitary dynamics.
Demonstration of quantum circuit implementation for 2D obstacle flow via Carleman-linearized LBM solved with QSVT, achieving logarithmic qubit and gate scaling with lattice points.
Adiabatic solver slightly outperforms shortcut when solution norm unknown; shortcut significantly better for non-Hermitian matrices when norm known.
A comprehensive review of scaling paths for superconducting quantum computers, with resource and sensitivity analyses for utility-scale applications under realistic error distributions.
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