A method and system are provided for estimating ground state and excited state energies of fermionic Hamiltonians using a classically-boosted Variational Quantum Eigensolver (VQE). The disclosed technology overcomes the drawbacks of prior VQE methods, which require large numbers of circuit repetitions and excessive runtimes to achieve precision, especially when implemented using Noisy Intermediate-Scale Quantum NISQ) devices. The disclosed classically-boosted VQE provides an estimation of expectation values using classical methods. The quantum computer is not used to prepare the trial state, but instead uses the difference between the trial state and a classical tractable approximation to the target state. Ground-state energy estimations are provided at an accelerated rate. Also, the measurement reduction of single basis state boosting of conventional VQE, may be estimated using only the overlap between the ground state and the computational basis state used for boosting.
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