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The preparation of Hamiltonian eigenstates is essential for many applicationsin quantum computing; the efficiency with which this can be done is of keyinterest. A canonical approach exploits the quantum phase estimation (QPE)algorithm. We adopt ideas from variants of this method to implement aresource-frugal iterative scheme, and provide analytic bounds on the complexity(simulation time cost) for various cases of available information and tools. Wepropose and characterise an extension involving a modification of the targetHamiltonian to increase overall efficiency. The presented methods and boundsare then demonstrated by preparing the ground state of the Hamiltonians of LiHand H$_2$ in second quantisation; we report the performance of both ideal andnoisy implementations using simulated quantum computers. Convergence isgenerally achieved much faster than the bounds suggest, while the qualitativefeatures are validated.

Resource-frugal Hamiltonian eigenstate preparation via repeated quantum phase estimation measurements