Symmetry-aware spectral bounds for the electronic structure Hamiltonian

We present symmetry-aware spectral bounds to assess the query complexity of Hamiltonian oracles in quantum algorithms. Our numerical estimates indicate that these bounds are smaller than traditional ones for a variety of electronic structure systems, including exhibiting unique scaling behavior in thermodynamic and complete basis set limits. Our work highlights potential room for improvement in reducing the ₁ norm through tensor factorization and block-encoding methods, while also offering a critical evaluation of query complexity limits for quantum algorithms in physics and chemistry.