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The possibility of using the generator coordinate method (GCM) using hybridquantum-classical algorithms with reduced quantum resources is discussed. Thetask of preparing the basis states and calculating the various kernels involvedin the GCM is assigned to the quantum computer, while the remaining tasks, suchas finding the eigenvalues of a many-body problem, are delegated to classicalcomputers for post-processing the generated kernels. This strategy reduces thequantum resources required to treat a quantum many-body problem. We apply themethod to the Lipkin model. Using the permutation symmetry of the Hamiltonian,we show that, ultimately, only two qubits is enough to solve the problemregardless of the particle number. The classical computing post-processingleading to the full energy spectrum can be made using standard generalizedeigenvalues techniques by diagonalizing the so-called Hill-Wheeler equation. Asan alternative to this technique, we also explored how the quantum statedeflation method can be adapted to the GCM problem. In this method, variationalprinciples are iteratively designed to access the different excited states withincreasing energies. The methodology proposed here is successfully applied tothe Lipkin model with a minimal size of two qubits for the quantum register.The performances of the two classical post-processing approaches with respectto the statistical noise induced by the finite number of measurements andquantum devices noise are analyzed. Very satisfactory results for the fullenergy spectra are obtained once noise correction techniques are employed.

Solving the Lipkin model using quantum computers with two qubits only  with a hybrid quantum-classical technique based on the Generator Coordinate  Method