Jastrow-type Decomposition in Quantum Chemistry for Low-Depth Quantum Circuits

Abstract

We propose an efficient O(<i>N</i>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 <i>T</i>₂ amplitudes of the unitary coupled cluster with generalized singles and doubles, which gives a near full-CI energy. The proposed ansatz therefore can reproduce the uCCGSD energy, or rather will reach the exact full-CI energy because of the exponential operator product form. 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 of a near-term quantum computer. The accuracy of the ansatz was examined for dissociation of a nitrogen dimer, and compared with other existing O(<i>N</i>²)-parameter ansatzs. Not only the original ansatzs defined in the second-quantization form but also their Trotter-splitting 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.