A Jastrow-type decomposition in quantum chemistry for low-depth quantum circuits

Abstract

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.