Variational quantum circuits to prepare low energy symmetry states

• URL: http://arxiv.org/abs/2112.12857v1
• Date: Thu, 23 Dec 2021 22:04:48 GMT
• Title: Variational quantum circuits to prepare low energy symmetry states
• Authors: Raja Selvarajan, Manas Sajjan, Sabre Kais
• Abstract summary: We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a Symmetry subspace. We create an explicit unitary and a variationally trained unitary that maps any vector output by ansatz A(alpha) from a defined subspace to a vector in the symmetry space.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a Symmetry subspace by explicitly encoding it into the circuit. We create an explicit unitary and a variationally trained unitary that maps any vector output by ansatz A(~{\alpha}) from a defined subspace to a vector in the symmetry space. The parameters are trained varitionally to minimize the energy thus keeping the output within the labelled symmetry value. The method was tested for a spin XXZ hamiltonian using rotation and reflection symmetry and H2 hamiltonian within S_z = 0 subspace using S^2 symmetry. We have found the variationally trained unitary surprisingly giving very good results with very low depth circuits and can thus be used to prepare symmetry states within near term quantum computers.

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