How to measure a molecule’s energy using a quantum computer

While BeH2 is the largest molecule ever simulated by a quantum computer to date, the considered model of the molecule itself is still simple enough for classical computers to simulate exactly. This made it a test case to push the limits of what our seven qubit processor could achieve, further our understanding of the requirements to enhance the accuracy of our quantum simulations, and lay the foundational elements necessary for exploring such molecular energy studies.

The best simulations of molecules today are run on classical computers that use complex approximate methods to estimate the lowest energy of a molecular Hamiltonian. A “Hamiltonian” is a quantum mechanical energy operator that describes the interactions between all the electron orbitals and nuclei of the constituent atoms. The “lowest energy” state of the molecular Hamiltonian dictates the structure of the molecule and how it will interact with other molecules. Such information is critical for chemists to design new molecules, reactions, and chemical processes for industrial applications.


Although our seven qubit quantum processor is not fully error-corrected and fault-tolerant, the coherence times of the individual qubits last about 50 µs. It is thus really important to use a very efficient quantum algorithm to make the most out of our precious quantum coherence and try to understand molecular structures. The algorithm has to be efficient in terms of number of qubits used and number of quantum operations performed.

How to measure a molecule’s energy using a quantum computer

Our scheme contrasts from previously studied quantum simulation algorithms, which focus on adapting classical molecular simulation schemes to quantum hardware – and in so doing not effectively taking into account the limited overheads of current realistic quantum devices.

So instead of forcing classical computing methods onto quantum hardware, we have reversed the approach and asked: how can we extract the maximal quantum computational power out of our seven qubit processor?

Our answer to this combines a number of hardware-efficient techniques to attack the problem:

With future quantum processors, that will have more quantum volume, we will be able to explore the power of this approach to quantum simulation for increasingly complex molecules that are beyond classical computing capabilities. The ability to simulate chemical reactions accurately, is conductive to the efforts of discovering new drugs, fertilizers, even new sustainable energy sources.

The experiments we detail in our paper were not run on our currently publically available five qubit and 16 qubit processors on the cloud. But developers and users of the IBM Q experience can now access quantum chemistry Jupyter notebooks on the QISKit github repo. On the five qubit system, users can explore ground state energy simulation for the small molecules hydrogen and LiH. Notebooks for larger molecules are available for those with beta access to the upgraded 16-qubit processor.

More information:
Abhinav Kandala et al. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets, Nature (2017). DOI: 10.1038/nature23879

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