Classical chemistry methods versus quantum computers: where a crossover might come

Short answer: Computational chemistry has long been named as a field quantum computers could transform, but classical methods keep improving too. A 2025 arXiv study that compares classical and quantum methods concludes that in many cases classical methods will likely stay superior for at least a couple of decades, with quantum computers most useful for highly accurate calculations on small to medium-sized molecules. These are the authors' projections, not measurements, and other researchers argue for advantages in particular systems.

Why chemistry is a target

A review article in a ScienceDirect journal explains that in chemistry the many-body entangled states underlying a molecule's electronic structure cannot be modelled fully even on today's most powerful computers, so numerous approximations are needed for larger molecules. These approximations can miss important electronic or electron-nuclear effects, especially in complicated systems such as complexes involving transition metals. The review says quantum algorithm development offers promising propositions in electronic structure, chemical quantum dynamics, spectroscopy and cheminformatics. It adds that physical quantum computers are still in their infancy and have yet to outperform classical computers for useful computations, and it summarizes progress in algorithms, hardware and software and the challenges that remain.

A comparison against classical methods

The 2025 arXiv paper says algorithmic advantages of fault-tolerant quantum computers for chemistry can be overwhelmed by other disadvantages, such as error correction and processor speed. To assess when quantum computing might be disruptive, the authors compare a wide range of classical methods with quantum methods, extending a framework from earlier work by Choi, Moses and Thompson, and account for both algorithms and hardware as they improve. Their findings, stated as likelihoods, are:

• In many cases classical methods will likely remain superior to quantum algorithms for at least the next couple of decades.
• For simulations with tens or hundreds of atoms, highly accurate methods such as Full Configuration Interaction and high-order Coupled Cluster are likely to be surpassed by quantum phase estimation in the coming decade.
• Where quantum phase estimation is most efficient, moderately accurate classical techniques such as Moller-Plesset could be surpassed in ten to fifteen years if technical advances are favourable.
• Overall, quantum computing will be most impactful for highly accurate computations on small to medium-sized molecules, while classical computers will likely remain the typical choice for larger molecules.

A more optimistic case for some systems

A conference talk abstract on finding quantum advantage in quantum chemistry says worst-case evaluation of molecular ground states is hard even for quantum computers, and that empirical studies suggest generic chemical systems show no exponential quantum advantage over standard classical algorithms. For strongly correlated electronic systems the speaker describes it differently, presenting quantum algorithms based on non-orthogonal methods, including a tensor network quantum eigensolver that allows calculations linear in system size. The abstract also mentions work proving classical simulation hardness of the corresponding circuits, which it says shows exponential speedups are possible with linear depth for important molecular systems. This is a speaker's description of their own work, and an abstract does not show the results themselves.

What this does not tell you

The projections depend on assumptions about hardware improvement and about which classical methods are used, and the authors present them as likely, not certain. None of these sources reports a quantum computer beating classical methods on a useful chemistry problem.

FAQ

Will quantum computers replace classical chemistry software?

The 2025 comparison says classical methods will likely remain superior in many cases for at least a couple of decades.

Where might quantum computers help first?

In highly accurate calculations on small to medium-sized molecules, per the same study.

Why is chemistry hard for classical computers?

Many-body entangled electronic states cannot be modelled fully, so approximations are used, according to the review.

Is there a case for advantage in strongly correlated systems?

A conference abstract describes algorithms it says offer advantages for such systems, but it is a summary of the speaker's own work.

Has a quantum computer beaten classical methods here?

The sources do not report that.