CNOT-Efficient Circuits for Arbitrary Rank Many-Body Fermionic and Qubit Excitations

Efficient
quantum circuits are necessary for realizing quantum
algorithms on noisy intermediate-scale quantum devices. Fermionic
excitations entering unitary coupled-cluster (UCC) ansätze
give rise to quantum circuits containing CNOT “staircases”
whose number scales exponentially with the excitation rank. Recently,
Yordanov et al. [Phys. Rev. A102, 062612
(2020); Commun. Phys.4, 228 (2021)]
constructed CNOT-efficient quantum circuits for both Fermionic- (FEB)
and qubit-excitation-based (QEB) singles and doubles and illustrated
their usefulness in adaptive derivative-assembled pseudo-Trotterized
variational quantum eigensolver (ADAPT-VQE) simulations. In this work,
we extend these CNOT-efficient quantum circuits to arbitrary excitation
ranks. To illustrate the benefits of these compact FEB and QEB quantum
circuits, we perform numerical simulations using the recently developed
selected projective quantum eigensolver (SPQE) approach, which relies
on an adaptive UCC ansatz built from arbitrary-order particle–hole
excitation operators. We show that both FEB- and QEB-SPQE decrease
the number of CNOT gates compared to traditional SPQE by factors as
large as 15. At the same time, QEB-SPQE requires, in general, more
ansatz parameters than FEB-SPQE, in particular those corresponding
to higher-than-double excitations, resulting in quantum circuits with
larger CNOT counts. Although ADAPT-VQE generates quantum circuits
with fewer CNOTs than SPQE, SPQE requires orders of magnitude less
residual element evaluations than gradient element evaluations in
ADAPT-VQE.