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

Recent work has dramatically reduced the gate complexity required to quantum simulate chemistry by using linear combinations of unitaries based methods to exploit structure in the plane wave
basis Coulomb operator. Here, we show that one can achieve similar scaling even for arbitrary basis
sets (which can be hundreds of times more compact than plane waves) by using qubitized quantum
walks in a fashion that takes advantage of structure in the Coulomb operator, either by directly
exploiting sparseness, or via a low rank tensor factorization. We provide circuits for several variants
of our algorithm (which all improve over the scaling of prior methods) including one with O(N^{3/2} λ)
T complexity, where N is number of orbitals and λ is the 1-norm of the chemistry Hamiltonian. We
deploy our algorithms to simulate the FeMoco molecule (relevant to Nitrogen fixation) and obtain
circuits requiring almost one thousand times less surface code spacetime volume than prior quantum
algorithms for this system, despite us using a larger and more accurate active space.

• Quantum Computing