We have developed state-of-the-art parallel codes for simulating the behavior of quantum systems described by large Hilbert spaces. The associated static and time-dependent behavior is obtained by numerical simulations of large matrices representing Hamiltonians, rate matrices and time-evolution operators. In particular, zero- and finite-temperature Lanczos codes are used to simulate the behavior of molecular nanomagnets with large number of magnetic ions (see, e.g., E. Garlatti, S. Carretta, J. Schnack, G. Amoretti, P. Santini, Theoretical design of molecular nanomagnets for magnetic refrigeration,i Applied Physics Letters 103, 202410 (2013). The relaxation of such systems in the phonon bath and the associated effects in NMR are obtained by solving large systems of master-equations (see, e.g., P. Santini, S. Carretta, E. Liviotti, G. Amoretti, P. Carretta, M. Filibian, A. Lascialfari, E. Micotti, NMR as a Probe of the Relaxation of the Magnetization in Magnetic Molecules, Phys. Rev. Lett. 94, 077203 (2005)..High-performance codes have also been developed for simulating the time-evolution of qubit systems in quantum.computation setups based on molecular nanomagnets (see. e,g, P. Santini, S. Carretta, F. Troiani, and G. Amoretti, Molecular Nanomagnets as Quantum Simulators, Phys. Rev. Lett. 107, 230502 (2011)) or photons in circuits of superconducting resonators (see, e.g., S. Carretta, A. Chiesa, F. Troiani, D. Gerace, G. Amoretti, and P. Santini, Quantum Information Processing with Hybrid Spin-Photon Qubit Encoding, Phys. Rev. Lett. 111, 110501 (2013)).
