Orders of magnitude reduction in the computational overhead for quantum many-body problems on quantum computers via an exact transcorrelated method

• URL: http://arxiv.org/abs/2201.03049v1
• Date: Sun, 9 Jan 2022 16:37:32 GMT
• Title: Orders of magnitude reduction in the computational overhead for quantum many-body problems on quantum computers via an exact transcorrelated method
• Authors: Igor O. Sokolov, Werner Dobrautz, Hongjun Luo, Ali Alavi and Ivano Tavernelli
• Abstract summary: We show that the Hamiltonian becomes non-Hermitian, posing problems for quantum algorithms based on the variational principle. We overcome these limitations with the ansatz-based quantum imaginary time evolution algorithm. Our work paves the way for the use of exact transcorrelated methods for the simulations of ab initio systems on quantum computers.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Transcorrelated methods provide an efficient way of partially transferring the description of electronic correlations from the ground state wavefunction directly into the underlying Hamiltonian. In particular, Dobrautz et al. [Phys. Rev. B, 99(7), 075119, (2019)] have demonstrated that the use of momentum-space representation, combined with a non-unitary similarity transformation, results in a Hubbard Hamiltonian that possesses a significantly more compact ground state wavefunction, dominated by a single Slater determinant. This compactness/single-reference character greatly facilitates electronic structure calculations. As a consequence, however, the Hamiltonian becomes non-Hermitian, posing problems for quantum algorithms based on the variational principle. We overcome these limitations with the ansatz-based quantum imaginary time evolution algorithm and apply the transcorrelated method in the context of digital quantum computing. We demonstrate that this approach enables up to 4 orders of magnitude more accurate and compact solutions in various instances of the Hubbard model at intermediate interaction strength ($U/t=4$), enabling the use of shallower quantum circuits for wavefunction ansatzes. In addition, we propose a more efficient implementation of the quantum imaginary time evolution algorithm in quantum circuits that is tailored to non-Hermitian problems. To validate our approach, we perform hardware experiments on the ibmq_lima quantum computer. Our work paves the way for the use of exact transcorrelated methods for the simulations of ab initio systems on quantum computers.

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