Top 20 molecules for quantum computing

One of the obstacles we face in developing quantum computing as a commercial technology is finding concrete examples where quantum computers could outperform classical methods for industrially interesting use cases. Quantum chemistry applications are no exception. With the goal of helping the community address this challenge, we introduce a curated list of molecules for quantum computing.

This is an endeavor that we have begun and will continue to pursue at Xanadu, and we invite you to join our efforts.

The full list is shown below. Continue to read to learn more about our methodology and what makes each molecule interesting for quantum computing.

Contents

• Top 20 molecules for quantum computing
  • 1. Hydrogen (H₂)
  • 2. Methylene (CH₂)
  • 3. Ammonia (NH₃)
  • 4. Water (H₂O)
  • 5. Dicarbon (C₂)
  • 6. Nitrogen (N₂)
  • 7. Ethylene (C₂H₄)
  • 8. Ozone (O₃)
  • 9. Thioformaldehyde (CH₂S)
  • 10. Benzene (C₆H₆)
  • 11. Pyrazine (C₄H₄N₂)
  • 12. Manganese carbide (MnC)
  • 13. Titanium oxides (Ti_nO_m)
  • 14. Chromium dimer (Cr₂)
  • 15. Iron–sulfur clusters (Fe_nS_m)
  • 16. Pentacene (C₂₂H₁₄)
  • 17. oxo-Mn(salen)
  • 18. Iridium complexes
  • 19. Iron porphyrin complexes
  • 20. FeMoco
• Final thoughts

Top 20 molecules for quantum computing

This Top 20 list is ordered by increasing complexity: it begins with simple molecules with few electrons and ends with some of the most difficult molecules to simulate, with properties are not yet fully understood.

The list is not exhaustive or definitive; some of you may protest about omissions or disagree with our inclusions, but what’s more important to us is that we begin a discussion. One of our goals in writing this post is to encourage the community to do two things:

1. Focus on standard and widely-adopted systems for benchmarking quantum algorithms.
2. Identify clear challenge tasks, motivated both by their relevance and potential for quantum advantage.

Quantum properties of many of the molecules listed here can be found, downloaded and easily implemented into various calculations using PennyLane Datasets. ⚛️

1. Hydrogen (H₂)

With only two electrons and two protons, H₂ is the smallest neutral molecule. In many ways, hydrogen is the "hello world" of quantum algorithms for chemistry (for example, for the application of the variational quantum eigensolver — VQE). But this is far from the whole story. Many conventional quantum chemistry methods fail to accurately describe the energy profile of hydrogen stretching, and hydrogen atoms can also form more complex systems like chains, squares, or rings. Hydrogen chains have many interesting physical properties that make them great candidates for quantum computing experiments.

Hydrogen is the right molecule to begin your journey in quantum algorithms for chemistry.

2. Methylene (CH₂)

The small hydrocarbon methylene is a diradical molecule with two unpaired electrons. Despite its apparent simplicity, answering the question of whether the spins of these electrons are the same or opposite requires the singlet–triplet gap to be computed. This is not an easy task for conventional quantum chemistry methods, making it a prototypical system for the application of advanced electronic structure methods.

Methylene is a simple molecule relevant to excited-state energy calculations.

3. Ammonia (NH₃)

Ammonia has one nitrogen and three hydrogen atoms arranged in a pyramidal shape. At sufficiently high temperatures, this molecule experiences pyramidal inversion, a process similar to that which turns an umbrella inside out in strong wind. Pyramidal inversion of ammonia is a famous example of a reaction with a relatively small barrier, and even small errors in predicting this barrier lead to large errors in predicting the rate of inversion.

Ammonia is a good candidate for simulating reactions and testing the accuracy of quantum algorithms.

4. Water (H₂O)

A considerable fraction of Earth’s water was synthesized around 4.5 billion years ago, and the importance of water cannot be overstated, so it should be no surprise that the water molecule has been extensively studied, making it a very good benchmark for quantum algorithms. For example, the calculation of the double dissociation of water — computing ground-state energies when stretching both OH bonds simultaneously — is a difficult problem that has commonly been used to benchmark advanced quantum chemistry methods, and water chains can be used as a model for correlated periodic systems.

Water is an intermediate-size molecule that is ideal for benchmarking more sophisticated quantum algorithms.

5. Dicarbon (C₂)

Did you know that diatomic carbon is the reason that a comet’s head is green but its tail is not? It is also one of the most abundant molecules in interstellar medium, and a typical example of a system with strong static correlation, which is challenging for conventional quantum chemistry methods. The nature of the chemical bond between the carbon atoms has also been the subject of several theoretical investigations.

Dicarbon is an example of a deceivingly complicated molecule of intermediate size.

6. Nitrogen (N₂)

Nitrogen is the most abundant molecule in the Earth's atmosphere. Its triple bond is among the strongest bonds in chemistry, and the dissociation of the nitrogen molecule is also a famous example of a process that showcases strong electron correlation. Nitrogen is a molecule of intermediate size that has already undergone heavy benchmarking for ground-state energy calculations. It would be an impressive result if quantum computers could be used to reproduce the accuracy of classical methods for this problem.

Nitrogen is a good molecule with few electrons to study the effects of strong correlation.

7. Ethylene (C₂H₄)

Ethylene is one of the smallest planar hydrocarbons and the most widely produced organic compound in the chemical industry. The calculation of the excitation energy of ethylene is a famously arduous problem that has been the subject of extensive investigations. More interestingly, the rotation of ethylene around the axis of the carbon double bond, which requires systematically breaking one of the bonds in the double bond, has historically been very demanding to simulate.

Ethylene is an industrially relevant molecule that is ideal to study excitation energies and correlation at rotated geometries.

8. Ozone (O₃)

Ozone is another molecule with a strong static correlation, as seen in dicarbon. With 24 electrons, it is a relatively large molecule and a difficult case to address with advanced electronic structure methods. Ozone is a very important compound of the Earth's atmosphere (we’ve all heard of the ozone layer) and its chemistry has been extensively studied. In particular, its dissociation energy path is known to be problematic for electronic structure theory applications.

Ozone is an intermediate-size molecule that is not easy to simulate accurately.

9. Thioformaldehyde (CH₂S)

Simulating the dynamics of a molecule during a transition between two electronic states with different spin multiplicities is a demanding problem in quantum chemistry. It requires an accurate prediction of excited-state potential energy surfaces, which is very difficult to achieve using conventional quantum chemistry methods. Because of its small size and existing accurate benchmark studies, thioformaldehyde is a great candidate for investigating the dynamics of transition between two electronic states, also known as intersystem crossing. These studies show that conventional quantum chemistry methods can fail to correctly predict potential energy curves for excited states.

Thioformaldehyde is a great benchmark molecule for computing excited-state energy curves.

10. Benzene (C₆H₆)

Benzene is one of the most important molecules in organic chemistry, found everywhere from gasoline (called benzin in some countries) to deep space. Because of its importance in chemistry, biochemistry, and industry, benzene has been the subject of extensive investigations. It has also been selected as the target of a blind challenge in an international endeavor for determining its exact ground-state energy.

The accurate calculation of the ground-state energy of benzene would be a milestone achievement for quantum computing.

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We are now entering the second half of the list, which presents molecules that are too large to be treated with existing quantum hardware or simulators. In our view, these molecules are representative of some of the most demanding simulation problems in quantum chemistry. If quantum computing is to become a disruptive new approach for chemistry, it will have to demonstrate its ability to handle systems of this size and importance.

11. Pyrazine (C₄H₄N₂)

The photoexcitation of pyrazine is a complex problem and requires a sophisticated electronic structure treatment. Pyrazine is particularly relevant for the simulation of quantum molecular dynamics and effects related to conical intersections, where the potential energy surfaces of two electronic states cross and the Born–Oppenheimer approximation breaks down.

Pyrazine is an ideal molecule to study quantum algorithms for quantum molecular dynamics.

12. Manganese carbide (MnC)

The first transition metal in the list! This is worth highlighting because transition metals are infamous for the problems they introduce for accurate simulations, usually attributed to correlation effects arising from the half-filling of d-orbitals. Transition metal carbides are molecules difficult to research even using advanced electronic structure methods. Manganese carbide has been included in our Top 20 list because it has been identified among the most challenging molecules for calculating accurate bond dissociation energies using coupled cluster methods.

Manganese carbide is one of the smallest transition metal compounds with very strong correlation.

13. Titanium oxides (Ti_nO_m)

Titanium oxides form families of clusters that can be scaled up to increase system size while maintaining chemical consistency, and they have undergone heavy benchmarking because of their wide range of applications in solar cells, sensors, and catalysis (in solid form). Computing accurate excitation energies of titanium oxide clusters requires sophisticated electronic structure methods.

Titanium oxides are great candidates for exploring the application of quantum algorithms to simple transition-metal molecules.

14. Chromium dimer (Cr₂)

Computing the potential energy curve of the chromium dimer is a famous problem in quantum chemistry due to its complicated bonding at dissociation. It has served as a benchmark molecule to evaluate a variety of electronic structure methods, including density functional theory and advanced wave function methods. The electronic structure of the chromium dimer has arguably been solved in a recent investigation, which makes it great for benchmarking.

Reconstructing the accurate potential energy surface of the chromium dimer would be a milestone achievement for quantum computing.

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Up to this point, the ground-state energy of all molecules we have covered has arguably been solved using the most advanced classical methods — and only very recently for the chromium dimer. From here onwards, the electronic structure of the systems we will present is still not fully understood. They are representatives of hopeful candidates for quantum advantage demonstrations.

15. Iron–sulfur clusters (Fe_nS_m)

Iron–sulfur clusters are components of iron–sulfur proteins, which are found in a variety of biological systems. They typically contain 2–4 iron and sulfur atoms, and they are important in electron transfer, catalysis, and oxygen sensing. This multifunctional character is a manifestation of their low-lying electronic states, which are hard to describe theoretically. Predicting the correct electronic structure of these compounds helps give a better understanding of their chemistry, which has mainly been described based on phenomenological models. These clusters have already been used as model systems to benchmark quantum computing for quantum chemistry, including in Xanadu's work on initial state preparation on quantum computers. The sizes of the iron–sulfur clusters can also be scaled up to increase system size while maintaining chemical consistency.

Iron–sulfur clusters are scientifically and industrially relevant transition-metal complexes that are very difficult to simulate accurately using classical methods.

16. Pentacene (C₂₂H₁₄)

Pentacene is a polycyclic aromatic hydrocarbon that is used in organic electronic devices. Understanding the lowest-lying electronic excited states of pentacene requires a multireference treatment to unravel its complex electronic structure. So far, the ground-state energy of pentacene has been calculated using exact diagonalization methods in an active space of 22 orbitals and 22 electrons. To the best of our knowledge, this is the largest active space used in a calculation of a full configuration interaction to date. This offers an ideal candidate for benchmarking advanced quantum algorithms.

Pentacene is the largest system studied using exact diagonalization methods on classical supercomputers.

17. oxo-Mn(salen)

The oxo-Mn(salen) complex is a coordination compound that belongs to the family of metal salen complexes. It has been used as a model system for the application of wavefunction methods in quantum chemistry and the investigation of Jacobsen’s catalyst to understand the relation between the catalyst’s low spin states and the relevant reaction paths. Accurate computation of the energies of these spin states is a crucial prerequisite for the mechanistic studies of Jacobsen's catalyst, which is difficult because of their strong multireference character.

Oxo-Mn(salen) is a potential candidate for demonstrating quantum advantage in electronic structure calculations.

18. Iridium complexes

Iridium complexes are used both in electronic devices such as organic light-emitting diodes and also as catalysts. If you own an OLED TV, know that there are some fascinating phenomena happening inside of it. The phosphorescent properties of these complexes depend on triplet-to-singlet transitions. Computing these transitions requires simulations of the molecules’ ground and excited states, which are notoriously difficult for conventional quantum chemistry methods. Iridium complexes have been extensively investigated experimentally and computationally.

Iridium complexes are candidates for industrially relevant systems with potential for quantum advantage for excited-state calculations.

19. Iron porphyrin complexes

Fe(II)–porphyrin complexes are intriguing examples of metal porphyrins that play a crucial role in many chemical reactions relevant to biological processes. They are found in biological systems, for example in hemoglobin, which is responsible for delivering oxygen in human blood, and they also form the active sites of cytochrome P450 enzymes, which are important in the metabolism of drugs. The spin fluctuations that emerge from the closely lying spin states of these complexes are at the heart of their biological behavior. Accurate simulation of the spin states of iron porphyrin complexes is extremely hard and requires a sophisticated treatment of the molecules’ electronic structure. This makes them good candidates for quantum advantage.

Iron porphyrins are among the most difficult and important biologically relevant molecules.

20. FeMoco

The iron–molybdenum cofactor (FeMoco) is arguably the most famous molecule in quantum computing. It is found in the active sites of nitrogenase enzymes and plays a crucial role in the catalytic process of nitrogen fixation. However, the presence of transition-metal ions with multiple spin couplings and charge states poses a significant challenge to understanding the electronic structure of this remarkable biological complex. It has been argued that a better understanding of the catalytic behavior of FeMoco may pave the way for future advancements in producing fertilizers and improving the Haber–Bosch process.

FeMoco is the holy grail of quantum algorithms for quantum chemistry.

Final thoughts

We hope that our Top 20 list will serve as a useful guide for anyone working at the intersection of quantum computing and quantum chemistry. We have also included links to many references that can help you dive deeper into technical details. At Xanadu, we continue to expand quantum datasets for chemistry and to develop more powerful quantum algorithms, targeted at the most promising applications. The future of quantum computing will likely be closely tied to quantum chemistry and quantum simulation; as a community, we should be ready to meet it.

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To let your work go as smoothly as possible, our team has prepared numerous quantum chemistry datasets that you can set up and download, plug-and-play directly into your PennyLane workflow. Learn more in our blog post about quantum datasets or jump right in with PennyLane Datasets!