Fig. 5: Application to the OEC.
From: Programmable simulations of molecules and materials with reconfigurable quantum processors
Our programmable quantum simulation framework can be used to compute detailed model spin Hamiltonian properties. a, Here, we illustrate the procedure on the OEC, an organometallic catalyst with strong spin correlations. In particular, we simulate model spin Hamiltonians for two structures S2H-1b and S2H-2b, which have three spin-3/2 and one spin-2 Mn (purple) active sites (reproduced from ref. 28 with permission from the Royal Society of Chemistry). Model Heisenberg coefficients for both hypothetical structures have been computed from broken-symmetry DFT28. b, A density of states \({D}^{{\mathbb{1}}}(\omega )\) calculation is simulated for the S2H-1b model spin Hamiltonian. Here, we use a polarized reference state \(\left\vert S\right\rangle ={\left\vert 0\right\rangle }^{\otimes 13}\) a probe states \(\left\vert R\right\rangle\) generated by random single-site rotations and an evolution time t. We select 50,000 circuits with independently chosen \(\left\vert R\right\rangle ,t\) pairs and draw ten snapshots from each circuit. c, Focusing on the lowest-lying states, we see three distinct peaks in \({D}^{{\mathbb{1}}}(\omega )\). However, by evaluating spin-resolved quantities \({D}^{{P}_{s}}(\omega )\) on the same set of measurements, we identify three additional peaks, whose energies and total-spin match exact diagonalization results (vertical dotted lines). d, This information is known as the spin ladder and can be computed using many-body spectroscopy for both the 1b and 2b states. Importantly, the spin ladder can also be measured experimentally (Exp.) and, therefore, can be used to help determine which structure appears in nature. In this example, experimental measurements indicate a spin-5/2 ground state and spin-7/2 first excited state. However, the ordering of low-energy states is flipped in the 2b configuration, indicating that the S2H-1b hypothesis is more likely28. We note that quantities beyond total spin can also be readily evaluated in low-lying eigenstates by inserting different operators A (Methods).
