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Running quantum algorithms on real hardware is essential for understandingtheir strengths and limitations, especially in the noisy intermediate scalequantum (NISQ) era. Herein we focus on the practical aspect of quantumcomputational calculations of solid-state crystalline materials based on theorydeveloped in our group by using real quantum hardware with a novel noisemitigation technique referred to as partition-measurement symmetryverification, which performs post-selection of shot counts based on $Z_{2}$ and$U_{1}$ symmetry verification. We select two periodic systems with differentlevel of complexity for these calculations. One of them is the distortedhydrogen chain as an example of very simple systems, and the other one is ironcrystal in the BCC and FCC phases as it is considered to be inaccessible byusing classical computational wavefunction methods. The ground state energiesare evaluated based on the translational quantum subspace expansion (TransQSE)method for the hydrogen chain, and periodic boundary condition adapted VQE forour iron models. By applying these techniques for the simplest 2 qubit ironmodel systems, the correlation energies obtained by the hardware calculationsagree with those of the state-vector simulations within $\sim$5 kJ/mol.Although the quantum computational resources used for those experiments arestill limited, the techniques applied to obtain our simplified models will beapplicable in essentially the same manner to more complicated cases as quantumhardware matures.

physical review research

Quantum hardware calculations of periodic systems with  partition-measurement symmetry verification: simplified models of hydrogen  chain and iron crystals