Momentum-Space Unitary Couple Cluster and Translational Quantum Subspace Expansion for Periodic Systems on Quantum Computers

One of the leading approximations for simulating solid materials is to consider the solid to be an infinite crystalline array of atoms, in which a small set of the atoms (known as the “unit cell”) is repeated periodically along all directions of space. This approximation is referred to as “Periodic Boundary Conditions” (PBC). We have modified molecular VQE to work with PBC, enabling us to simulate crystalline solids, and have run some tests on simple hydrogen, helium and lithium hydride lattices in one, two and three dimensions. We have done some estimates on the cost of these calculations, and found them to be significantly more expensive than molecular VQE calculations. We have then developed important methods to reduce qubit count and circuit depth that are specific to the PBC approximation, which make these calculations easier to fit into NISQ machines and utilise CQC’s quantum software development tool and optimizer,  t|ket>.

David Zsolt Manrique,  Irfan T. Khan, Kentaro Yamamoto, Vijja Wichitwechkarn, and David Munoz Ramo

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