Solving the electronic structure of correlated lattice models and molecular systems will probably be one of the firsts problems in which quantum computers might show advantage over classical computers [1,2]. In the near future, the near-term gate-model quantum computers (as implemented by IBM, Google, Microsoft, Rigetti, IonQ and other companies) will still have limitations due to reduced number of qubits, high level of noise or short coherence time. New theoretical techniques and algorithms to tackle the electronic structure must be designed by theoretical and computational physicists and chemists to take advantage of such imperfect devices.

The present contribution will review in an introductive manner the basic concepts of quantum computation and the main algorithms that are currently used on currently available quantum computers to solve prototypical examples of electronic structure problems. To alleviate the hardware limitations, we have recently proposed a non-unitary version of the Variational Quantum Eigensolver algorithm that can be used to effectively improve the variational space of wavefunction ansatzes. [3-4] Using the proposed strategies it is possible to recover a large amount of electron correlation energy using shallow-depth quantum circuits. A further improvement has been achieved by optimizing the Hamiltonian itself with respect a circuit (wavefunction) ansatz of a given topology, exploiting the invariance of the molecular Hamiltonian by orbital rotations. [5]

[1] S. McArdle, S. Endo, A. Aspuru-Guzik, S. Benjamin, X. Yuan: Quantum computational chemistry Rev. Mod. Phys. 2020, 92, 015003.

[2] A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, J. M. Gambetta: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 2017, 549, 242-246.

[3] F. Benfenati, L. Guidoni, G. Mazzola, P. Barkoutsos, P. Ollitrault, I. Tavernelli: Extended wavefunctions for the Variational Quantum Eigensolver, Quantum Information and Measurement 2019,  F5A 36.

[4] F. Benfenati, G. Mazzola, C. Capecci, P. Barkoutsos, P. Ollitrault, I. Tavernelli and L. Guidoni: Improved accuracy on noisy devices by non-unitary Variational Quantum Eigensolver for chemistry applications, J. Chem. Theo. Comp. 2021, accepted for publication.

[5] L. Ratini, C. Capecci, F. Benfenati, L. Guidoni, Wavefunctio-Adapted Hamiltonian for Quantum Computing, J. Chem. Theo. Comp. 2022, 18, 2, 899-909.

Professor Guidoni was awarded his PhD in the Theory of Condensed Matter at the International School for Advanced Studies of Trieste. He was then a PostDoctoral researcher at the Swiss Federal Institute of Technology in Lausanne and between 2004-2008 he held a Professorship in Computational Biophysics and Biochemistry at the department of Physics of the University of Rome “La Sapienza”. Since 2008 he has been at the University of L’Aquila where he is now a full Professor of Physical Chemistry.

Between 2009-2015 he was Principal Investigator of the ERC Project entitled “Electronic Structure of Chemical, Biochemical, and Biophysical Systems: Multiscale Approach with Electron Correlation” and is currently Partner Coordinator of the Marie Skłodowska-Curie Innovative Training Network : MOQS MOlecular Quantum Simulations.

Over the past 11 years he has been awarded 7 PRACE grants for computational resources in the field of Computational Biochemistry.