Quantum phase estimation based filtering: performance analysis and application to low-energy spectral calculation

TL;DR

This paper analyzes the performance of quantum phase estimation-based filters, compares their efficiency with other algorithms, and demonstrates their application in low-energy spectral calculations, including a case study on MnO.

Contribution

It introduces a detailed performance analysis of QPE-based filters with different window functions and applies this to low-energy spectral simulations in quantum systems.

Findings

Kaiser window suppresses Gibbs phenomenon in QPE filters.

Query complexity of Kaiser window filtering is comparable to QETU.

Demonstrated application in calculating the density of states for MnO.

Abstract

Filtering is an important technique in quantum computing used for isolating or enhancing some specific states of quantum many-body systems. In this paper, we analyze the performance of filters based on the quantum phase estimation (QPE) algorithm, in which filtering removes states associated with bitstrings in the ancilla register above a given threshold. We show that when the conventional rectangular window function is used for the QPE input state, the resulting filter function exhibits an oscillating behavior known as the Gibbs phenomenon. We also show that in the case of the sine and Kaiser windows, this phenomenon is suppressed. Furthermore, we perform numerical simulations to compare the number of necessary queries to the Hamiltonian time evolution operation of for the QPE-based filtering algorithm and the quantum eigenvalue transformation of unitary matrices with real polynomials (QETU). We find that the number of queries required for Kaiser window-based filtering is comparable to that for QETU with optimized phase angles. As an application of the QPE-based filter, we also study a two-step 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 density-of-states (DOS) calculation of antiferromagnetic type-II MnO in a one-particle approximation.