Quantum processor prosimulirovali isomerization and calculated energy of the hydrogen chains

Experts from Google AI implemented on 54 Kubina quantum processor Sycamore variational quantum algorithm VQE 12 qubits, which made it possible to implement the method of Hartree-Fock and calculate the energy of the ground state of the hydrogen chain from 6,8,10 and 12 atoms. The algorithm allowed for the first time to describe a chemical reaction, namely highlighted various options of isomerization of molecules diazene (NH)2. Preprint available at arxiv.org.

Quantum chemistry describes a set of nuclei and electrons in the atom or molecule as the total quantum system and uses quantum mechanics to locate the main parameters of the molecule, for example, the electron ground state energy or the ionization energy. It is known that the electrons in atoms are in certain configurations, atomic orbitals. There are s-, p-, d-, f-orbitals, and there are severe restrictions on possible number and location of electrons in each orbitals. The structure and the occupancy of these orbitals and determine the rules of quantum chemistry. Method Hartree-Fock is one of the simple but effective tools used to calculate energy States and configurations of the wave functions in the molecule. It defines a way of finding the wave function of the ground state of an atom or molecule as a special antisymmetric combination (Katerousha determinant) of the basis wave functions.

As basis functions can be used the same atomic orbital, but as a rule, set the change to use the method and for more complex tasks, for example, to calculate the polarization of the molecules. In the mean-field approximation, using a variational search are a linear combination of basis orbitals, which minimize the average energy of the whole molecule. They are accepted as inferior energy States that are further used to embed individual electrons of the molecule.

Quantum chemistry is considered to be one of the most promising applications of quantum processors. Great success in this direction has achieved team from IBM and Google with the most powerful quantum processor with superconducting qubits. In September 2017, we wrote about how professionals from IBM have calculated the structure of the hydride of beryllium on semicubical processor. For this purpose we used a hybrid algorithm VQE, which includes quite a small calculation on a quantum processor and then optimizing it by using ordinary classical computer. Recently, 53-Cubana processor Sycamore researchers from Google have demonstrated the superiority of quantum over 200 seconds was followed by a special calculation, which have the most powerful classical supercomputer would take a thousand years of computing time. Now a team of scientists from Google have adapted the VQE algorithm to calculate the spectra of the hydrogen chains, as well as to simulate molecular dynamics.

The essence of the variational algorithm VQE is to find the minimum of this magnitude, which can be easily measured on a quantum processor. This is usually the total energy of the system. Initially made of different unitary rotations cubital system that parametrize the sought wave function, then the system is measured. Using variations of rotation angles with the classical optimization algorithm is the search of minimum energy. In the end, in addition to spectrum, get ready to “recipe” for cooking the desired state directly on the processor used. Recently, this algorithm was used to calculate the energy of the hydrogen molecule H2 with chemical accuracy, i.e. with error no more than 10-3 from energy Hartree. It was enough to use only 2 of the qubit. The next logical step, implemented in this work is to test such calculations for more complex systems, requiring a greater number of fully controllable qubits.

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