Will Quantum Computers ever be useful for Chemistry?
In 1964, Peter Higgs used quantum mechanics to predict the existence of the “Higgs Boson” field, but it took 48 years (and a lot of money) to experimentally validate its existence. Quantum computing is following a similar path. Since its inception in the early 1980’s the mathematical formalism of quantum computing has become well established. Hundreds of textbooks have been written and the subject has been taught in universities for over two decades. The mathematics of quantum computing is just like any other mathematical system – learn the axioms and rules and play the game. It’s a game just like chess. But it does not necessarily represent physical reality.
Quantum Computing, Quantum Mechanics, and Nature
The axioms and rules of quantum computing (and, more generally, Quantum Information Science) were replicated from the axioms and rules of quantum mechanics, essentially as described by Paul Dirac in the late 1920’s [1]. The rationale was simple; quantum mechanics “describes the behaviour of nature” so we had better use quantum computing to perform computational simulations of Nature [2]. What a sweet, simple theory. But perhaps, naïve.
Quantum mechanics has helped discover numerous important technologies, but it is just a “calculation recipe” and, after almost 100 years, there is still no agreed interpretation of the underlying physical meaning of quantum mechanics (if any). All the technology achievements related to quantum mechanics (atomic bomb, lasers, transistors, MRI etc,) have been derived from simple applications of quantum mechanics to large ensembles of particles. Manipulating single particles as “qubits” is a far more challenging task. In addition, quantum mechanics has evolved significantly since its initial conception, with the refinements of Quantum Field Theory [3]. Whether quantum mechanics provides a true description of the behaviour of Nature is a complete unknown, and it is certain that new theories of Nature will evolve in future.
This is the nub of the problem with quantum computers. They are physical devices operating according to the laws of Nature within a very complex environment of laboratory, observers, and external influences such as heat, electromagnetic radiation, and gravity. The mathematical axioms and rules of quantum computing cannot account for all this complexity and hence there are errors generated in the computation process.
Reducing errors is a key requirement for quantum computers
It is fully accepted that errors are inevitable in quantum computers, just as they are in classical computers (but which are far fewer and more easily managed). Errors occur via physical qubit states decohering, failure of gate operations, crosstalk between channels, and failure of readout measurements. Physical qubits are very fragile objects and interaction with the outside world can easily disrupt them.
Error reduction involves two processes – mitigation (i.e., better hardware and control software to minimize errors) and error correction (fixing errors after they have occurred). Error correction is a wellestablished technique but can require up to 10,000 physical qubits to produce one stable “logical qubit”. Quite a large overhead! For very basic chemistry purposes a “useful” quantum computer needs at least 100 logical qubits, so this implies about 1 million physical qubits, versus today’s few hundred [4].
Renowned Israeli mathematician, Gil Kalai, has been a persistent critic of quantum computers, primarily based on error rates. He claims that, with today’s level of gate error rates (at best around 0.1%), it will never be possible to build adequate error correction protocols. His view is that gate error rates must be reduced to levels of 0.001%  a substantial engineering challenge [5]. Most people in the industry would agree that reducing the rate of errors is of primary importance and that this is one of the main engineering issues.
Qubit lifetime, scalability, connectivity, gate speed, RAM etc.
Errors are not the only issue. Today’s physical qubits have a very short lifetime before they decohere, typically microseconds or milliseconds. This is a very short time in which to perform operations on qubits. Much improvement is needed to build scalable systems capable of millions of qubits, ideally with known silicon fabrication techniques. We need to be able to connect multiples of qubits in flexible arrangements to be able to perform needed entanglement operations in algorithms, and we need to improve gate operation speeds which are presently orders of magnitude slower than classical GPUs. Finally, Quantum RAM is presently nonexistent. So overall, there are still quite a few engineering challenges in building a useful quantum computer.
Quantum Computing for Chemistry Applications
During the present NISQ era of quantum computing (Noisy Intermediate Scale Quantum computers) it is unlikely that quantum computers will offer any advantage for chemistry applications. Dozens of hybrid quantumclassical algorithms have been tried and none have generated any significant advantage versus classical computers. See, for example, [6]. The consensus agreement is that faulttolerant quantum computers (FTQC) with at least 100 logical qubits or more will be required for useful chemistry applications. Even this will not be enough for many drug discovery applications [7].
Key Conclusions
There is presently no proven advantage for the use of quantum computing in chemistry. It is all heuristic – try it and see. This situation is unlikely to change much during the next 5 years or so.
Large Industrial corporations should continue their present small investments (typically < 0.5% of R&D budgets) in exploration of potential quantum computing opportunities in chemistry, to be ready for any potential breakthroughs and to have appropriate talent onboard to respond to nonchemistry opportunities, e.g., use of quantum computing for logistics optimization.
Financial investors should think very carefully before investing in quantum computing startups that have a strong chemistry focus. The potential returns could be very far in the future, or never.
Author: Alan Martin, amartin@psiontic.com
References

P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford at the Clarendon Press

Richard P. Feynman, “Simulating Physics with Computers”, Journal of Theoretical Physics, Vol. 21, 1982

See, for example, Steven Weinberg “Foundations of Modern Physics”, Chapter 7, Cambridge University Press, 2021

McArdle et al. “Quantum Computational Chemistry”, 2020 https://arxiv.org/abs/1808.10402

Gil Kalai, “The argument against quantum computers”, 2020, https://arxiv.org/abs/2008.05188v1

Lee et al., “Is there evidence for exponential quantum advantage in quantum chemistry?”, 2022, https://arxiv.org/abs/2208.02199v3

Blunt et al., “A perspective on the current stateoftheart of quantum computing for drug discovery applications, 2023, https://arxiv.org/abs/2206.00551