A Tale of Colliding Electrons: Boosting the Accuracy of Chemical Simulations on Quantum Computers
By Mario Motta, Tanvi Gujarati, and Julia Rice
Quantum computers are, by their very nature, well-suited to help scientists achieve breakthrough discoveries in chemistry by simulating intrinsically quantum mechanical objects like molecules more efficiently than classical computers can. And as the capabilities of quantum computers and our understanding of how to best use them improve, we shall soon have the potential to predict the properties of molecules with precision on par with actual lab experiments.
Accurately describing molecules requires capturing the delicate balance of many competing effects, which in turn requires large numbers of qubits and quantum operations. To help quantum computers approach the accuracy requirements needed for chemical discovery — or to “punch above their weight,” to use a boxing metaphor — our interdisciplinary team of IBM researchers together with partners from Daimler AG and Virginia Tech has employed the help of classical computers to radically reduce the number of qubits necessary for a quantum computer to simulate molecules. We demonstrate that properties for paradigmatic molecules such as hydrogen fluoride (HF) can be calculated with a higher degree of accuracy on today’s small quantum computers — compared to calculations done with the same basis set functions where the simulation method does not model the electron-electron cusp, explicitly.
We compensated for resource limitations by combining quantum simulation methods with a change in how a molecule’s kinetic and potential energy — a function known as a Hamiltonian — are represented in the computation. The technical details of our work are described in “Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer,”* published in October in the Royal Society of Chemistry’s journal, Physical Chemistry Chemical Physics and chosen as a “hot topic” in 2020.
Better “Hamiltonian”: better simulations
Named after the Irish mathematician Sir William Rowan Hamilton, a Hamiltonian is a mathematical function that determines the properties of the chemical system. Accurately describing the Hamiltonian of a molecule requires a huge number of orbitals, i.e., spatial functions which the electrons can occupy. With a larger set of these orbitals, called an orbital basis set, comes a higher cost in number of qubits and quantum operations. Therefore, we currently can’t represent enough orbitals in our simulations on quantum hardware to correlate the electrons found in complex molecules in the real world. Under such conditions, researchers typically proceed in one of two ways: wait until quantum computers have enough qubits to simulate all of the orbitals needed for a particular study; or continue to do calculations that are useful conceptually but tell little about the real chemistry of the molecules.
We chose a third path, using a Hamiltonian which is “transcorrelated” — i.e. transformed to provide additional information about some of the interactions that need a larger basis set for accurate description and, hence, can’t fit into the quantum computer using a traditional Hamiltonian. The transcorrelated Hamiltonian improves the description of the molecules by accounting for a fundamental fact: since electrons are negatively charged particles, they repel each other!
This important and complicated phenomenon, known by the name of electron-electron cusp, requires a large number of orbitals to be accurately described. Our method, building on the work at Virginia Tech for classical simulations, enables quantum simulations based on a transcorrelated Hamiltonian that approximately incorporates the electron-electron cusp. The result is a more accurate simulation of the molecule, without the need for hundreds more qubits or deeper quantum circuit, where a quantum circuit represents the number of qubits together with the operations applied to them. Deeper circuits can perform more operations but also present increased opportunities for errors during quantum computation.
Better simulation: a tool for materials design
Although today’s high-performance classical computers can render detailed chemical simulations, quantum computers have the potential to deliver simulations that are orders of magnitude more accurate for many complex and large molecular systems that the classical computers cannot tackle. Daimler was particularly interested in this collaboration given the car company’s research into novel quantum algorithms for quantum chemistry and materials science to support its goal of designing better batteries.
New materials may lead to the development of higher performing, longer lasting and less expensive batteries. Daimler has long recognized the role electric vehicles will play in reducing automobile emissions and fossil fuel consumption, and its quantum computing collaboration with IBM aligns with that electrification initiative. Our method is a step along the way to calculating materials’ properties with experimental accuracy on a quantum computer. The more orbitals you can simulate, the closer you can get to reproducing the results of an actual experiment. Better modelling and simulations will ultimately result in the prediction of new materials with specific properties of interest.
Others who contributed to this article include: Ashutosh Kumar, Conner Masteran, and Edward Valeev of Virginia Tech; Eunseok Lee, and Tyler Takeshita from Mercedes-Benz Research and Development North America, a part of Daimler AG; and Joe Latone from IBM.
Mario Motta, Tanvi P. Gujarati, Julia E. Rice, Ashutosh Kumar, Conner Masteran, Joseph A. Latone, Eunseok Lee, Edward F. Valeev and Tyler Y. Takeshita, Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer, Phys. Chem. Chem. Phys., “The Royal Society of Chemistry”, 2020,22, 24270–24281, http://dx.doi.org/10.1039/D0CP04106H
To facilitate certain required tasks for this project, some of this research was done through custom designs of Qiskit software modules, such as the Qiskit Chemistry module. These modules “represent an important step toward frictionless quantum computing, where developers can write applications reaping the benefits of quantum computers without concerning themselves with the intricacies of the hardware.” For more about how domain experts without a deep quantum computing background, as well as quantum algorithms researchers who want to develop and test new algorithms, read “Continuing the journey to frictionless quantum software: Qiskit Chemistry module & Gradients framework”.
