FeMoco and quantum chemistry: how many resources would it take?

Short answer: FeMoco, the iron-molybdenum cofactor of the nitrogenase enzyme, is a standard example in quantum chemistry resource estimates. A 2016 paper reports that, with quantum error correction overhead included, the needed computations could run in reasonable time on small quantum computers. Those figures rest on assumed gate speeds, error rates and a good trial state. A later paper warns that conclusions should not be drawn from one widely used active space model.

What the estimates assume

A 2017 paper in PNAS estimates the cost of simulating two prototypical structures of FeMoco, chosen as an example of the complexity that would arise when probing the potential energy landscape of the complex. It first estimates run time assuming a quantum computer can perform a logical T gate every 10 ns or 100 ns, that Clifford circuits require negligible time, and that a good trial state for the ground state is available. The cost of preparing trial states is discussed in its supplementary appendix.

Fault-tolerant cost

The paper then determines the cost of doing the simulation fault-tolerantly using the surface code, with each physical gate taking 10 ns or 100 ns, including any time required by the decoder. It looks mainly at two cases. In the first, it considers error rates of 1 in 1,000 and 100-ns gates, which it calls a realistic estimate of where superconducting technology may be for near-term devices. In the second, it considers error rates of 1 in a million and 10-ns gates, which it calls an aspirational target for future generations of quantum computers. These are the authors' assumptions, not measured performance of any machine.

What the 2016 paper reports

An arXiv paper from 2016 uses the open problem of biological nitrogen fixation in nitrogenase as an example of how a quantum computer could be employed to elucidate reaction mechanisms in complex chemical systems. It discusses how quantum computers can augment classical-computer simulations to significantly increase accuracy and enable simulations that were intractable. Its abstract says detailed resource estimates show that, even when taking into account the substantial overhead of quantum error correction and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. That is the authors' conclusion from estimates, not a demonstration.

A caution about the model

A 2019 paper in the Journal of Chemical Physics reports that a recent active space model of the nitrogenase FeMo cofactor, proposed in the context of simulations on quantum computers, is not representative of the electronic structure of the FeMo cofactor ground state. It says a more representative model does not much affect certain resource estimates, such as the cost of a Trotter step, but strongly affects others, such as the cost of adiabatic state preparation. Its authors conclude that conclusions should not be drawn from the complexity of quantum or classical simulations of this system in that active space. They provide a different model active space that contains the basic open-shell qualitative character, and say it may be useful as a benchmark for resource estimates for classical and quantum computers.

What this does not tell you

This article summarises abstracts and introductions of three papers. None of them reports a quantum computer simulating FeMoco, and this article claims none. Resource estimates depend on assumptions that later work can change.

FAQ

What is FeMoco?

The FeMo cofactor of nitrogenase, an enzyme involved in biological nitrogen fixation, used as an example in the papers.

What gate speeds do the estimates assume?

The 2017 PNAS paper assumes a logical T gate every 10 ns or 100 ns, and for surface-code estimates physical gates of 10 ns or 100 ns including decoder time.

What error rates does it consider?

Two cases: error rates of 1 in 1,000 with 100-ns gates, which it calls realistic for near-term superconducting devices, and 1 in a million with 10-ns gates, which it calls aspirational.

Does the model choice matter?

A 2019 paper says it can: the cost of adiabatic state preparation changes strongly with the active space, while the cost of a Trotter step changes little.

Has FeMoco been simulated on a quantum computer?

None of the papers used here reports that. They are resource estimates.