Demonstration of logical quantum phase estimation for X-ray absorption spectra

TL;DR

This work demonstrates Fourier-based quantum phase estimation as a viable route to computing X-ray absorption spectra, focusing on Fe L-edge XANES in FeO6-based clusters with an eight-orbital active space. It compares input-state strategies and analyzes resolution and measurement errors, showing that Lorentzian broadening and entangled-phase estimation improve spectral fidelity. The authors implement QPE on a trapped-ion quantum computer using dynamic circuits and the Iceberg error-detection code, achieving spectra that closely resemble noiseless references after processing. Collectively, the results establish a path toward larger active spaces and more complex XAS simulations on quantum hardware, with data and spectra openly accessible to the community.

Abstract

In this study, we employed Fourier-based quantum phase estimation (QPE) to calculate X-ray absorption spectroscopy (XAS) spectra. The primary focus of this study is the calculation of the XAS spectra of transition metal $L_{2,3}$-edges, which are dominated by strong correlation effects. First, the Fe $L_{2,3}$-edge X-ray absorption near-edge structure of FePO$_4$ is calculated using a noiseless simulator. The present computation involves a comparison of three types of input states: a uniform superposition state, optimal entangled input state, and Slater function state. Subsequently, we investigated the resolution error of the QPE and statistical error attributed to the measurements. It was revealed that post-processing to introduce Lorentzian broadening reduces the statistical error, which becomes a significant problem for a large number of qubits. Subsequently, we implemented QPE on a trapped-ion quantum computer, encompassing three orbitals within the active space. To this end, we implemented QPE using dynamic circuits to reduce ancilla qubits and [[k+2, k, 2]] quantum error detection code to mitigate the quantum noise inherent in current quantum computers. As a result, it was demonstrated that hardware noise was reduced, and spectra close to the noiseless ones were obtained.

Figures (12)

• Figure 1: The quantum circuit for the XAS spectra in Eq. (\ref{['eq:spectral_function']}) based on the QPE sampling when $n_q=3$. $U=e^{2\pi i t_0 \mathcal{H}/ N_q}$ was used in this figure.
• Figure 2: The quantum circuit for QPE sampling using dynamic circuits corresponding to those for $n_q=3$ and $U_{\mathrm{in}}=H^{\otimes n_q}$ in Fig. \ref{['circuit:qpe_sampling']}. The gray double lines indicate the classical registers. Classically controlled phase gates are denoted by $P$ with a rotation angle.
• Figure 3: The quantum circuit for QPE sampling using dynamic circuits illustrated in Fig. \ref{['fig:qc_dynamic_qpe']}, which is encoded using iceberg code. Four logical qubits and $n_q=4$ are used in this study.
• Figure 4: Calculated Fe-$L_{2,3}$ XANES of FePO$_4$ using CASCI and QPE calculations. We use $\eta=0.3$ eV and $n_q=7$ in this figure. The upper panel shows the experimental spectrum Augustsson2005JCP.
• Figure 5: The $\ell^2$-errors of the three QPE sampling methods with respect to (a) resolution, (b) statistical, and (c) total error according to the number of ancilla qubits. In Figs. (b) and (c), the number of measurements was set to $N_{\mathrm{meas}}=1,000$ and the average of 10 trials was represented as a marker. The standard deviation is indicated by an error bar.