  We propose an efficient ${\cal O}(N^2)$-parameter ansatz that consists of a
sequence of exponential operators, each of which is a unitary variant of
Neuscamman's cluster Jastrow operator. The ansatz can also be derived as a
decomposition of T$_2$ amplitudes of the unitary coupled cluster with
generalized singles and doubles, which gives a near full-CI energy, and
reproduces it by extending the exponential operator sequence. Because the
cluster Jastrow operators are expressed by a product of number operators and
the derived Pauli operator products, namely the Jordan-Wigner strings, are all
commutative, it does not require the Trotter approximation to implement to a
quantum circuit and should be a good candidate for the variational quantum
eigensolver algorithm by a near-term quantum computer. The accuracy of the
ansatz was examined for dissociation of a nitrogen dimer, and compared with
other existing ${\cal O}(N^2)$-parameter ansatzs. Not only the original ansatzs
defined in the second-quantization form but also their Trotterized variants, in
which the cluster amplitudes are optimized to minimize the energy obtained with
a few, typically single, Trotter steps, were examined by quantum circuit
simulators.
