Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model
on a quantum computer
- URL: http://arxiv.org/abs/2112.14077v2
- Date: Thu, 10 Mar 2022 09:48:45 GMT
- Title: Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model
on a quantum computer
- Authors: Kazuhiro Seki, Seiji Yunoki
- Abstract summary: We apply the symmetry-adapted variational-quantum-eigensolver (VQE) to a two-component Fermi-Hubbard model on a bipartite lattice.
In the extended VQE method, the Rayleigh quotient for the Hamiltonian and a parametrized quantum state in a properly chosen subspace is minimized.
We show that spatial symmetry operations for fermions in an occupation basis can be expressed as a product of the nearest-neighbor fermionic swap operations on a quantum circuit.
- Score: 0.9137554315375919
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose an extended version of the symmetry-adapted
variational-quantum-eigensolver (VQE) and apply it to a two-component
Fermi-Hubbard model on a bipartite lattice. In the extended symmetry-adapted
VQE method, the Rayleigh quotient for the Hamiltonian and a parametrized
quantum state in a properly chosen subspace is minimized within the subspace
and is optimized among the variational parameters implemented on a quantum
circuit to obtain variationally the ground state and the ground-state energy.
The corresponding energy derivative with respect to a variational parameter is
expressed as a Hellmann-Feynman-type formula of a generalized eigenvalue
problem in the subspace, which thus allows us to use the parameter-shift rules
for its evaluation. The natural-gradient-descent method is also generalized to
optimize variational parameters in a quantum-subspace-expansion approach. As a
subspace for approximating the ground state of the Hamiltonian, we consider a
Krylov subspace generated by the Hamiltonian and a symmetry-projected
variational state, and therefore the approximated ground state can restore the
Hamiltonian symmetry that is broken in the parametrized variational state
prepared on a quantum circuit. We show that spatial symmetry operations for
fermions in an occupation basis can be expressed as a product of the
nearest-neighbor fermionic swap operations on a quantum circuit. We also
describe how the spin and charge symmetry operations, i.e., rotations, can be
implemented on a quantum circuit. By numerical simulations, we demonstrate that
the spatial, spin, and charge symmetry projections can improve the accuracy of
the parametrized variational state, which can be further improved
systematically by expanding the Krylov subspace without increasing the number
of variational parameters.
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