The antisymmetrized geminal power (AGP) wave function has a long history and is known by different names in various chemical and physical problems. There has been recent interest in using AGP as a starting point for strongly correlated electrons. Here, we show that in a seniority-conserving regime, different AGP-based correlator representations based on generators of the algebra, killing operators, and geminal replacement operators are all equivalent. We implement one representation that uses number operators as correlators and has linearly independent curvilinear metrics to distinguish the regions of Hilbert space. This correlation method called J-CI provides excellent accuracy in energies when applied to the pairing Hamiltonian.
We show how to construct a linearly independent set of antisymmetrized geminal power (AGP) states, which allows us to rewrite our recently introduced geminal replacement models as linear combinations of non-orthogonal AGPs. This greatly simplifies the evaluation of matrix elements and permits us to introduce an AGP-based selective configuration interaction method, which can reach arbitrary excitation levels relative to a reference AGP, balancing accuracy and cost as we see fit.
The antisymmetrized geminal power (AGP) is equivalent
to the number
projected Bardeen–Cooper–Schrieffer (PBCS) wave function.
It is also an elementary symmetric polynomial (ESP) state. We generalize
previous research on deterministically implementing the Dicke state
to a state preparation algorithm for an ESP state, or equivalently
AGP, on a quantum computer. Our method is deterministic and has polynomial
cost, and it does not rely on number symmetry breaking and restoration.
We also show that our circuit is equivalent to a disentangled unitary
paired coupled cluster operator and a layer of unitary Jastrow operator
acting on a single Slater determinant. The method presented herein
highlights the ability of disentangled unitary coupled cluster to
capture nontrivial entanglement properties that are hardly accessible
with traditional Hartree–Fock based electronic structure methods.
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