Quantum computers must overcome major technical hurdles before tackling quantum chemistry problems

Krystal Kasal

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Although the potential applications of quantum computing are widespread, a new feasibility study suggests quantum computers still face major hurdles in solving quantum chemistry problems. The study, published in Physical Review B, evaluates what criteria are needed for a quantum advantage in searching for the ground state energy of molecules. The researchers attempt this feat using two different algorithms with differing strengths and weaknesses.

The variational quantum eigensolver algorithm

The team first determined the criteria for the variational quantum eigensolver (VQE) algorithm, which is used for noisy, near-term devices and sets an upper bound to the level of imprecision or decoherence in quantum hardware. The researchers derived quantitative criteria for VQE and QPE based on error rates, energy scales, and overlap with the ground state.

Results showed that VQE is extremely sensitive to hardware errors and decoherence. The team says that achieving chemical accuracy would require error rates far below current hardware capabilities. Available error mitigation techniques offer only limited improvement and scale poorly with system size.

"We find that decoherence is highly detrimental to the accuracy of VQE and performing relevant chemistry calculations would require performances that are expected for fault-tolerant quantum computers, not mere noisy hardware, even with advanced error mitigation techniques," the study authors explained.

The authors do say that some approaches work well for many molecules, but typically fail for strongly correlated molecules, like those containing transition metals. These correlated molecules are identified as an early target for quantum algorithms, particularly useful in the application of nitrogen fixation for fertilizers.

When scaling is attempted, exceptionally long runtimes are a frequent result. The study authors note an example with the Cr₂ molecule, in which the total runtime for one iteration of VQE is estimated at 25 days. But when the total number of iterations are taken into account, the required time is estimated at 24 years.

The quantum phase estimation algorithm

The team also determined criteria for the quantum phase estimation (QPE) algorithm, which may be used with fault-tolerant quantum computers that could be available in the near future. Previous studies found that QPE is theoretically more precise, but depends on preparing a good initial state, which may be exponentially hard.

The new study found that QPE's success hits a wall due to the orthogonality catastrophe, which makes it impractical for large molecules. With the orthogonality catastrophe, the probability that QPE can calculate a molecule's lowest energy level drops exponentially as the size of the molecule increases.

"QPE requires an input state with a large enough overlap with the sought-after ground state. We provide a criterion to estimate quantitatively this overlap based on the energy and the energy variance of said input state. Using input states from a variety of state-of-the-art classical methods, we show that the scaling of this overlap with system size does display the standard orthogonality catastrophe, namely an exponential suppression with system size. This, in turn, leads to an exponentially reduced QPE success probability," the study authors explain.

Classical still has the advantage

At this time, classical algorithms, like the variational Monte Carlo (VMC) algorithm, remain superior to VQE even with perfect quantum hardware, and QPE still needs to overcome the orthogonality catastrophe.

The study authors write, "These observations may also suggest that ground state estimation in chemistry may not be the most appropriate target for quantum computers. Besides the issues of quantum processors we outlined in this paper, this statement is also due to the comparatively good quality of classical state preparation methods."

However, hybrid quantum-classical algorithms and novel error correction methods may offer incremental improvements in the future. Further research is still needed to find practical quantum advantage in chemistry.

Written for you by our author Krystal Kasal, edited by Gaby Clark, and fact-checked and reviewed by Robert Egan—this article is the result of careful human work. We rely on readers like you to keep independent science journalism alive. If this reporting matters to you, please consider a donation (especially monthly). You'll get an ad-free account as a thank-you.

Publication details

Thibaud Louvet et al, Feasibility of performing quantum chemistry calculations on quantum computers, Physical Review B (2026). DOI: 10.1103/hpt6-9tnk. On arXiv: DOI: 10.48550/arxiv.2306.02620

Journal information: Physical Review B , arXiv

Key concepts

Electronic structureQuantum algorithms & computationStrongly correlated systemsMonte Carlo methods

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