Exponentially more precise quantum simulation of fermions II: Quantum chemistry in the CI matrix representation
Ryan Babbush, Dominic W. Berry, Ian Kivlichan, Annie Y. Wei, Peter J. Love, Alán Aspuru‐Guzik · arXiv (Cornell University) · 2015
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 the first paper of this series (arXiv:1506.01020), 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 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 $\widetilde{\cal O}(N)$ qubits, where $N$ is the number of single-particle spin-orbitals, the CI matrix representation requires $\widetilde{\cal O}(\eta)$ qubits where $\eta \ll N$ is the number of electrons in the molecule of interest. We show that the gate count of our algorithm scales at most as $\widetilde{\cal O}(\eta^2 N^3 t)$.