  Quantum computing leverages the quantum resources of superposition and
entanglement to efficiently solve computational problems considered intractable
for classical computers. Examples include calculating molecular and nuclear
structure, simulating strongly-interacting electron systems, and modeling
aspects of material function. While substantial theoretical advances have been
made in mapping these problems to quantum algorithms, there remains a large gap
between the resource requirements for solving such problems and the
capabilities of currently available quantum hardware. Bridging this gap will
require a co-design approach, where the expression of algorithms is developed
in conjunction with the hardware itself to optimize execution. Here, we
describe a scalable co-design framework for solving chemistry problems on a
trapped ion quantum computer, and apply it to compute the ground-state energy
of the water molecule. The robust operation of the trapped ion quantum computer
yields energy estimates with errors approaching the chemical accuracy, which is
the target threshold necessary for predicting the rates of chemical reaction
dynamics.
