Quantum computing and its applications in chemistry and physics

Quantum computing is emerging as a new paradigm for the solution of a wide class of problems that are not accessible by conventional high performance classical computers. Quantum computers can in principle efficiently solve problems that require exponential resources on classical hardware, even when using the best known classical algorithms. In the last few years, several interesting solutions with potential quantum speedup have been brought forward in the domain of quantum physics, like the quantum phase estimation and the hybrid variational quantum eigensolver [1] for the solution of optimization problems. The original idea that a quantum computer can potentially solve many-body quantum mechanical problems more efficiently than classical computers is due to
R. Feynman who proposed the use of quantum algorithms to investigate the fundamental properties of nature at the quantum scale. In particular, the solution of the electronic structure and statistical mechanics problems is a challenging computational task as the number of resources increases exponentially with the number of degrees of freedom. Thanks to the development of new quantum technologies witnessed over the last decades, we have now the possibility to address this class of problems with the help quantum computers. To achieve this goal, new quantum algorithms able to best exploit the potential quantum speedup of state-of-the-art noisy quantum hardware have also been developed [2,3]. In this talk, I will first introduce the basics of quantum computing using superconducting qubits, focusing on those aspects that are crucial for the implementation of quantum chemistry and physics algorithms. In the second part, I will highlight the potential advantages of the new generation of quantum algorithms for applications in electronic structure calculations for ground [4] and excited states [5], molecular dynamics [6], and statistical physics [7].

[1] A. Peruzzo et al., Nature Communications 5, 4213 (2014).
[2] N. Moll, et al., Quantum Sci. Technol. 3, 030503 (2018).
[3] A. Kandala et al., Nature, 549, 242 (2017).
[4] P. Baroutsos, et al., Phys. Rev. A, 98 022322 (2018).
[5] M. Ganzhorn,, et al., Phys. Rev. Appl., 11 044092 (2019); P. Ollitrault et al.
arXiv:1910.12890 (2019).
[6] I. O. Sokolov, P. Kl Barkoutsos, L. Moeller, et al., arXiv:2008.08144 (2020).
[7] A. Robert et al., arXiv:1908.02163 (2019).