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

Dominic Berry
Yuval Sanders
Ian Kivlichan
Artur Scherer
Annie Wei
Peter Love
Alán Aspuru-Guzik
Quantum Science and Technology, vol. 3 (2017), pp. 015006


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).