Momentum-Space Unitary Coupled Cluster and Translational Quantum
Subspace Expansion for Periodic Systems on Quantum Computers
- URL: http://arxiv.org/abs/2008.08694v2
- Date: Mon, 4 Jan 2021 17:54:44 GMT
- Title: Momentum-Space Unitary Coupled Cluster and Translational Quantum
Subspace Expansion for Periodic Systems on Quantum Computers
- Authors: David Zsolt Manrique, Irfan T. Khan, Kentaro Yamamoto, Vijja
Wichitwechkarn, David Mu\~noz Ramo
- Abstract summary: We demonstrate the use of the Variational Quantum Eigensolver (VQE) to simulate solid state crystalline materials.
We map complex cluster operators to a quantum circuit ansatz to take advantage of the reduced number of excitation operators and Hamiltonian terms.
We also demonstrate an extension of the point group symmetry based qubit tapering method to periodic systems.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We demonstrate the use of the Variational Quantum Eigensolver (VQE) to
simulate solid state crystalline materials. We adapt the Unitary Coupled
Cluster ansatz to periodic boundary conditions in real space and momentum space
representations and directly map complex cluster operators to a quantum circuit
ansatz to take advantage of the reduced number of excitation operators and
Hamiltonian terms due to momentum conservation. To further reduce required
quantum resources, such as the number of UCCSD amplitudes, circuit depth,
required number of qubits and number of measurement circuits, we investigate a
translational Quantum Subspace Expansion method (TransQSE) for the localized
representation of the periodic Hamiltonian. Additionally, we also demonstrate
an extension of the point group symmetry based qubit tapering method to
periodic systems. We compare accuracy and computational costs for a range of
geometries for 1D chains of dimerized hydrogen, helium and lithium hydride with
increasing number of momentum space grid points and also demonstrate VQE
calculations for 2D and 3D hydrogen and helium lattices. Our presented
strategies enable the use of near-term quantum hardware to perform solid state
simulation with variational quantum algorithms.
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