  Quantum chemistry provides key applications for near-term quantum computing,
but these are greatly complicated by the presence of noise. In this work we
present an efficient ansatz for the computation of two-electron atoms and
molecules within a hybrid quantum-classical algorithm. The ansatz exploits the
fundamental structure of the two-electron system, and treating the nonlocal and
local degrees of freedom on the quantum and classical computers, respectively.
Here the nonlocal degrees of freedom scale linearly with respect to basis-set
size, giving a linear ansatz with only $\mathcal{O}(1)$ circuit preparations
required for reduced state tomography. We implement this benchmark with error
mitigation on two publicly available quantum computers, calculating accurate
dissociation curves for 4- and 6- qubit calculations of ${\rm H}_\textrm{2}^{}$
and ${\rm H}_\textrm{3}^+$.
