Background

The Schrodinger equation governs the dynamics of quantum systems. In chemistry, solving the Schrodinger equation for the electrons in a molecule is key to understand both reactivity (Is a reaction possible? Energetically favorable?) and ground-state behaviour of molecule (What resting shape does a molecule take? How does it non-covalently interact with other molecules). And since chemistry is involved in basically everything we practically care about, efficient, quick and scalable solution to this equation is key for bottom-up understanding of troves of phenomena, including what we understand as biology (as it runs on [macro]molecules interacting) and upward.

Unfortunately, even with sophisticated methods like DFT, huge computational expense are necessary for all but the simplest systems, using classical computers.

One of the fairly well-established upcoming use of quantum computer is the efficient solution to these system. Indeed, what better than a quantum system to simulate another one? A myriad of work exists today on elegant and efficient way to map chemical problem to quantum computer gateware. They are however not practically applicable to relevant quantum chemistry problem in the NISQ era.

The fine print

Quantum advantage: The quantum computer returns the same answers (interaction energy) as the classical method in less than one tenth the time of the classical computer (or computer cluster) for the whole problem set. Both the classical and quantum method are left to implementer's choice, given the below criteria are fulfilled.

Cost criteria: The quantum and classical computer total unit monetary cost are within one order of magnitude (10x) of each other. Neither the classical computer/cluster nor the quantum computer need to be off-the-shelf commercial product, but both should be in-theory duplicable at the given unit cost level. (This is to avoid a deliberately weak classical computer to ensure practical relevance)

Time: real-life, wall clock time.

Problem set: the S66 benchmark set (ref 1), or at-least-as-hard future benchmark set, as determined by a person skilled in the art.

Accuracy level: Compared to the CCSD(T)/CBS result on the S66 set, up to 0.2 kcal/mol RMSE error - both for the chosen classical and quantum code. If future benchmark set, less than the RMSE of the CCSD(T) CBS on that set.

Tolerance: up to 0.2 kcal/mol RMSE error between the classically-computed and quantum-computer-computed energies over the problem set.

Year: Year of first peer-reviewed, high ranking journal publication (overall high ranking, or high ranking in computer chemistry), available as ASAP online article.

(ref 1) https://pubs.acs.org/doi/10.1021/ct2002946

Resolves N/A if no quantum advantage demonstrated before 2030. Does not resolves (yet) if the problem set is not S66 and there is disagreement between persons skilled in the art as to whether the benchmark set is at least as difficult; or the set is judged less hard; or if the high ranking character of the publishing journal is in dispute among person skilled in the art.