State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

Abstract

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.

Modular Cluster Circuits for the Variational Quantum Eigensolver

“…The minimal design of the circuit allows for a chemical interpretation in terms of valence bond (VB) structures. , The textbook picture of a VB structure is a resonance between different electron pair configurations and provides a chemically inspired means of constructing compact wave functions. Paired electron wave function ansätz has been considered, both in the context of unitary pair coupled cluster doubles (UpCCD) wave functions and antisymmetrized geminal powers (AGP), , however with a circuit complexity that is comparable to UCC methods or with the circuit designs that explicitly target certain electron pairing and VB resonance schemes such as in the separable pair approximations (SPA) and graph-based approach . We will make a connection with the resonating VB (RVB) method, applied to the finite-size transverse-field Ising model, known from condensed matter physics and statistical physics …”

Physical Chemistry of Quantum Information Science

“…We investigate the topic of quantum algorithms tailored for quantum chemistry, molecular dynamics, and statistical mechanics. This includes a quest to enhance the accuracy of classical computations for difficult chemistry problems involving strongly correlated systems in the works by A. Tammaro et al., A. Khamoshi et al, and N. T. Le and L. N. Tran., and calculations of excited states in articles by Y. Kim and A. I. Krylov and by T. Yoshikura et al Outstanding problems of quantum state preparation were discussed by I. Magoulas and F. A. Evangelista, S. G. Mehendale et al, S. E. Ghasempouri et al, J. H. Zhang et al., and L. M. Sager-Smith et al, for near-term quantum algorithms. An equally important topic of quantum measurement is touched upon by Z. P. Bansingh et al and T. Kurita et al In addition, Hamiltonian learning from quantum dynamics is presented by R. Gupta et al, and an interesting and accessible approach to visualization of quantum algorithms is described by I. Ganti and S. S. Iyengar …”