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

Abstract

We propose an efficient 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 T2 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 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.

Orbital optimized unitary coupled cluster theory for quantum computer

“…VQE calculations using actual quantum computers have already been performed for small molecules [16,[18][19][20][21][22][23]. Recently, researchers have proposed electron-correlation methods based on UCC for quantum computers [24][25][26][27][28][29][30][31][32][33].…”

Gutzwiller wave function on a digital quantum computer

“…Once the repetition overhead is overcome, further simulations of the Hubbard model with the GWF should be carried out, particularly for two-dimensional lattices, where a quantum advantage is likely to be attained first. It must be ensured that, for lattice sizes beyond the capacity of conventional numerical methods, the GWF suffices to achieve a high enough overlap with the exact ground state, otherwise more sophisticated methods that capture nonlocal correlations, such as Jastrow operators [43,50,51], may be required. Similar considerations hold for the application of the GWF to molecular systems, where the need to consider the full Coulomb interaction likely leads to a lower overlap with the exact ground state relative to what is observed for the Hubbard model.…”

Qulacs: a fast and versatile quantum circuit simulator for research purpose

“…To date, Qulacs has been used in a few tens of research papers. For example, Qulacs is used by papers related to noisy intermediatescale quantum (NISQ) applications [37,[37][38][39][40][41][42] and fault-tolerant quantum computing [43]. Although Qulacs does not support gate decomposition, which is supported by high-layer libraries, Qulacs can be used as a faster backend library.…”