Filtering refers to the process of using algorithms to enhance desired or mask undesired states in quantum computing and is essential for preparing or isolating quantum many-body states. One class of filters is based on quantum phase estimation (QPE). Such QPE-based filters have a simple circuit implementation, but their performance remains unclear, particularly when compared to other filtering methods such as those with quantum signal processing. In this work we investigate the performance of QPE-based filters with three commonly used window functions: a rectangular window, a sine window, and a Kaiser window. We analyze how the choice of window affects results; one noticeable observation is that the oscillation of the filter (the Gibbs phenomenon) seen in the conventional rectangular-window result can be mitigated when the sine and Kaiser windows are applied. Furthermore, we compare the performance of QPE-based methods to quantum eigenvalue transformation of unitary matrices with real polynomials (QETU) and find that the Kaiser-window-based filter and QETU result in a similar number of queries to the Hamiltonian time-evolution operation. QPE-based filtering methods may therefore be an alternative to signal-processing-based methods. Finally, as an application of the QPE-based filter, we propose a two-step QPE algorithm for low-energy spectral simulations, composed of a coarse grid for filtering and a fine grid for obtaining final high-resolution spectra. As a benchmark of the proposed scheme for realistic continuous spectra, we present the calculation of the density of states of antiferromagnetic type-II MnO in a one-particle approximation.

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• Density of states
• Electronic structure of atoms & molecules
• First-principles calculations
• Quantum algorithms
• Quantum algorithms & computation
• Quantum simulation