  An accurate description of electron transport at a molecular level requires a
precise treatment of quantum effects. These effects play a crucial role in
determining the electron transport properties of single molecules, such as
current-voltage curves, which can be challenging to simulate classically. Here
we introduce a quantum algorithm to efficiently calculate the electronic
current through single-molecule junctions in the weak-coupling regime. We show
that a quantum computer programmed to simulate vibronic transitions between
different charge states of a molecule can be used to compute sequential
electron transfer rates and electric current. In the harmonic approximation,
the algorithm can be implemented using Gaussian boson sampling devices, which
are a near-term platform for photonic quantum computing. We apply the algorithm
to simulate the current and conductance of a magnesium porphine molecule. The
simulations demonstrate quantum effects that are manifested as discrete steps
in the current and conductance, in agreement with experimental and theoretical
data.
