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

Understand

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.