Quantum Embedding of Non-local Quantum Many-body Interactions in Prototypal Anti-tumor Vaccine Metalloprotein on Near Term Quantum Computing Hardware

The real world obeys quantum physics and quantum computing presents an alternative way to map physical problems to systems that follow the same laws. Such computation fundamentally constitutes a better way to understand the most challenging quantum problems. One such problem is the accurate simulation of highly correlated quantum systems. Due to the high dimensionality of the problem classical computers require considerable computer power to accurately predict material properties, especially when strong electron interactions are present. Still, modern day quantum hardware has many limitations and only allows for modeling of very simple systems. Here we present for the first time a quantum computer model simulation of a complex hemocyanin molecule, which is an important respiratory protein involved in various physiological processes such as oxygen transport and immune defence, and is also used as a key component in therapeutic vaccines for cancer. To better characterise the mechanism by which hemocyanin transports oxygen, variational quantum eigensolver (VQE) based on fermionic excitations and quantum embedding methods is used in the context of dynamic mean field theory to solve Anderson impurity model (AIM). Finally, it is concluded that the magnetic structure of hemocyanin is largely influenced by the many-body correction and that the computational effort for solving correlated electron systems could be substantially reduced with the introduction of quantum computing algorithms. We encourage the use of the Hamiltonian systems presented in this paper as a benchmark for testing quantum computing algorithms efficiency for chemistry applications.