# Exponentially More Precise Quantum Simulation of Fermions in the Configuration Interaction Representation

### Venue

Quantum Science and Technology, vol. 3 (2017), pp. 015006

### Publication Year

2017

### Authors

Ryan Babbush, Dominic Berry, Yuval Sanders, Ian Kivlichan, Artur Scherer, Annie Wei, Peter Love, Alán Aspuru-Guzik

### BibTeX

## 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).