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Transcorrelated methods provide an efficient way of partially transferringthe description of electronic correlations from the ground state wavefunctiondirectly into the underlying Hamiltonian. In particular, Dobrautz et al. [Phys.Rev. B, 99(7), 075119, (2019)] have demonstrated that the use of momentum-spacerepresentation, combined with a non-unitary similarity transformation, resultsin a Hubbard Hamiltonian that possesses a significantly more compact groundstate wavefunction, dominated by a single Slater determinant. Thiscompactness/single-reference character greatly facilitates electronic structurecalculations. As a consequence, however, the Hamiltonian becomes non-Hermitian,posing problems for quantum algorithms based on the variational principle. Weovercome these limitations with the ansatz-based quantum imaginary timeevolution algorithm and apply the transcorrelated method in the context ofdigital quantum computing. We demonstrate that this approach enables up to 4orders of magnitude more accurate and compact solutions in various instances ofthe Hubbard model at intermediate interaction strength ($U/t=4$), enabling theuse of shallower quantum circuits for wavefunction ansatzes. In addition, wepropose a more efficient implementation of the quantum imaginary time evolutionalgorithm in quantum circuits that is tailored to non-Hermitian problems. Tovalidate our approach, we perform hardware experiments on the ibmq_lima quantumcomputer. Our work paves the way for the use of exact transcorrelated methodsfor the simulations of ab initio systems on quantum computers.

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