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Recent work has dramatically reduced the gate complexity required to quantumsimulate chemistry by using linear combinations of unitaries based methods toexploit structure in the plane wave basis Coulomb operator. Here, we show thatone can achieve similar scaling even for arbitrary basis sets (which can behundreds of times more compact than plane waves) by using qubitized quantumwalks in a fashion that takes advantage of structure in the Coulomb operator,either by directly exploiting sparseness, or via a low rank tensorfactorization. We provide circuits for several variants of our algorithm (whichall improve over the scaling of prior methods) including one with$\widetilde{\cal O}(N^{3/2} \lambda)$ T complexity, where $N$ is number oforbitals and $\lambda$ is the 1-norm of the chemistry Hamiltonian. We deployour algorithms to simulate the FeMoco molecule (relevant to Nitrogen fixation)and obtain circuits requiring about seven hundred times less surface codespacetime volume than prior quantum algorithms for this system, despite ususing a larger and more accurate active space.

Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization