Hybrid algorithm classically diagonalizes Hamiltonian tensor factors to construct block-encodings for quantum simulation via QSVD, with extensions for commuting time-dependent cases.
Before proceeding to the final step, we invoke the following Lemma: Lemma III.3.[[45] Theorem 56] Suppose thatUis an(α, a, ϵ)-encoding of a Hermitian matrixA
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Hybrid Quantum-Classical Algorithm for Hamiltonian Simulation
Hybrid algorithm classically diagonalizes Hamiltonian tensor factors to construct block-encodings for quantum simulation via QSVD, with extensions for commuting time-dependent cases.