Vibrational ADAPT-VQE: Critical points leads to problematic convergence
arxiv(2024)
摘要
Quantum chemistry is one of the most promising applications for which quantum
computing is expected to have significant impact. Despite considerable research
in the field of electronic structure, calculating the vibrational properties of
molecules on quantum computers remain a relatively unexplored field. In this
work, we develop a vibrational ADAPT-VQE (vADAPT-VQE) formalism based on an
infinite product representation (IPR) of anti-Hermitian excitation operators of
the Full Vibrational Configuration Interaction (FVCI) wavefunction which allows
for preparing eigenstates of vibrational Hamiltonians on quantum computers. In
order to establish the vADAPT- VQE algorithm using the IPR, we study the
exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory
and show that dUVCC can formally represent the FVCI wavefunction in an infinite
expansion. To investigate the performance of the vADAPT-VQE algorithm, we
numerically study whether the vADAPT-VQE algorithm generates a sequence of
operators which may represent the FVCI wavefunction. Our numerical results
indicate frequent appearance of critical points in the wavefunction preparation
using vADAPT-VQE. These results imply that one may encounter diminishing
usefulness when preparing vibrational wavefunctions on quantum computers using
vADAPT-VQE and that additional studies are required to find methods that can
circumvent this behavior.
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