*Crossposted on the Google Research Blog*

*“The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.”*

-Paul Dirac, Quantum Mechanics of Many-Electron Systems (1929)

In this passage, physicist Paul Dirac laments that while quantum mechanics accurately models all of chemistry, exactly simulating the associated equations appears intractably complicated. Not until 1982 would Richard Feynman suggest that instead of surrendering to the complexity of quantum mechanics, we might harness it as a computational resource. Hence, the original motivation for quantum computing: by operating a computer according to the laws of quantum mechanics, one could efficiently unravel exact simulations of nature. Such simulations could lead to breakthroughs in areas such as photovoltaics, batteries, new materials, pharmaceuticals and superconductivity. And while we do not yet have a quantum computer large enough to solve classically intractable problems in these areas, rapid progress is being made. Last year, Google published this paper detailing the first quantum computation of a molecule using a superconducting qubit quantum computer. Building on that work, the quantum computing group at IBM scaled the experiment to larger molecules, which made the cover of Nature last month.

Today, we announce the release of OpenFermion, the first open source platform for translating problems in chemistry and materials science into quantum circuits that can be executed on existing platforms. OpenFermion is a library for simulating the systems of interacting electrons (fermions) which give rise to the properties of matter. Prior to OpenFermion, quantum algorithm developers would need to learn a significant amount of chemistry and write a large amount of code hacking apart other codes to put together even the most basic quantum simulations. While the project began at Google, collaborators at ETH Zurich, Lawrence Berkeley National Labs, University of Michigan, Harvard University, Oxford University, Dartmouth College, Rigetti Computing and NASA all contributed to alpha releases. You can learn more details about this release in our paper, OpenFermion: The Electronic Structure Package for Quantum Computers.

One way to think of OpenFermion is as a tool for generating and compiling physics equations which describe chemical and material systems into representations which can be interpreted by a quantum computer

^{1}. The most effective quantum algorithms for these problems build upon and extend the power of classical quantum chemistry packages used and developed by research chemists across government, industry and academia. Accordingly, we are also releasing OpenFermion-Psi4 and OpenFermion-PySCF which are plugins for using OpenFermion in conjunction with the classical electronic structure packages Psi4 and PySCF.

The core OpenFermion library is designed in a quantum programming framework agnostic way to ensure compatibility with various platforms being developed by the community. This allows OpenFermion to support external packages which compile quantum assembly language specifications for diverse hardware platforms. We hope this decision will help establish OpenFermion as a community standard for putting quantum chemistry on quantum computers. To see how OpenFermion is used with diverse quantum programming frameworks, take a look at OpenFermion-ProjectQ and Forest-OpenFermion - plugins which link OpenFermion to the externally developed circuit simulation and compilation platforms known as ProjectQ and Forest.

The following workflow describes how a quantum chemist might use OpenFermion in order to simulate the energy surface of a molecule (for instance, by preparing the sort of quantum computation we described in our past blog post):

- The researcher initializes an OpenFermion calculation with specification of:

- An input file specifying the coordinates of the nuclei in the molecule.
- The basis set (e.g. cc-pVTZ) that should be used to discretize the molecule.
- The charge and spin multiplicity (if known) of the system.

- The researcher uses the OpenFermion-Psi4 plugin or the OpenFermion-PySCF plugin to perform scalable classical computations which are used to optimally stage the quantum computation. For instance, one might perform a classical Hartree-Fock calculation to choose a good initial state for the quantum simulation.
- The researcher then specifies which electrons are most interesting to study on a quantum computer (known as an active space) and asks OpenFermion to map the equations for those electrons to a representation suitable for quantum bits, using one of the available procedures in OpenFermion, e.g. the Bravyi-Kitaev transformation.
- The researcher selects a quantum algorithm to solve for the properties of interest and uses a quantum compilation framework such as OpenFermion-ProjectQ to output the quantum circuit in assembly language which can be run on a quantum computer. If the researcher has access to a quantum computer, they then execute the experiment.

*By Ryan Babbush and Jarrod McClean, Quantum Software Engineers, Quantum AI Team*

**1 **If we may be allowed one sentence for the experts: the primary function of OpenFermion is to encode the electronic structure problem in second quantization defined by various basis sets and active spaces and then to transform those operators into spin Hamiltonians using various isomorphisms between qubit and fermion algebras.^{↩}