### Abstract

We present a quantum algorithm for the simulation of molecular systems that is asymptotically
more efficient than all previous algorithms in the literature in terms of the main problem parameters.
As in previous work [Babbush et al., New Journal of Physics 18, 033032 (2016)], we employ a
recently developed technique for simulating Hamiltonian evolution, using a truncated Taylor series
to obtain logarithmic scaling with the inverse of the desired precision. The algorithm of this paper
involves simulation under an oracle for the sparse, first-quantized representation of the molecular
Hamiltonian known as the configuration interaction (CI) matrix. We construct and query the CI
matrix oracle to allow for on-the-fly computation of molecular integrals in a way that is exponentially
more efficient than classical numerical methods. Whereas second-quantized representations of the
wavefunction require O(N) qubits, where N is the number of single-particle spin-orbitals, the CI
matrix representation requires O(η) qubits where η ≪ N is the number of electrons in the molecule
of interest. We show that the gate count of our algorithm scales at most as O(η^2 N^3 t).