Quantum Simulation of Realistic Materials in First Quantization Using Non-local Pseudopotentials

TL;DR

This work advances first-quantized plane-wave quantum simulations by incorporating realistic nonlocal GTH pseudopotentials and generalizing to non-cubic unit cells, enabling accurate treatment of core electrons without exploding the basis size. It develops a scalable block-encoding framework that uses a single exponential evaluation and nested-box state preparation to manage the nonlocal pseudopotential, achieving much lower data-input overhead than prior QROM-heavy methods. The paper provides detailed costing, including λ decompositions and QROM interpolation costs, and demonstrates concrete resource estimates for heterogeneous catalysis (CO on transition metals), comparing first-quantized costs to symmetry-adapted second-quantized simulations. The results show that, for large cells with many particles, first quantization can offer meaningful spacetime savings in memory and qubits, while still demanding substantial Toffoli resources, guiding future improvements in pseudopotential block encoding and non-cubic-cell handling. Overall, the approach delivers a practical pathway to realistic materials simulations on fault-tolerant quantum computers, with explicit benchmarks and a clear space-time trade-off against alternative quantum encoding schemes.

Abstract

This paper improves and demonstrates the usefulness of the first quantized plane-wave algorithms for the quantum simulation of electronic structure, developed by Babbush et al. and Su et al. We describe the first quantum algorithm for first quantized simulation that accurately includes pseudopotentials. We focus on the Goedecker-Tetter-Hutter (GTH) pseudopotential, which is among the most accurate and widely used norm-conserving pseudopotentials enabling the removal of core electrons from the simulation. The resultant screened nuclear potential regularizes cusps in the electronic wavefunction so that orders of magnitude fewer plane waves are required for a chemically accurate basis. Despite the complicated form of the GTH pseudopotential, we are able to block encode the associated operator without significantly increasing the overall cost of quantum simulation. This is surprising since simulating the nuclear potential is much simpler without pseudopotentials, yet is still the bottleneck. We also generalize prior methods to enable the simulation of materials with non-cubic unit cells, which requires nontrivial modifications. Finally, we combine these techniques to estimate the block-encoding costs for commercially relevant instances of heterogeneous catalysis (e.g. carbon monoxide adsorption on transition metals) and compare to the quantum resources needed to simulate materials in second quantization. We conclude that for computational cells with many particles, first quantization often requires meaningfully less spacetime volume.

Figures (6)

• Figure 1: A circuit showing the block encoding of a simplified form of $U_{\rm nonloc}$. For simplicity we are ignoring the sums over nuclei and electrons.
• Figure 2: The method for the interpolation. First the input is divided by $\ln 2$ so we are interpolating $2^{-z}$. QROM outputs coefficients for a polynomial, then those are used for computing the interpolated values on the fractional part of the input. The integer part of the input is used to control a bit shift on the output.
• Figure 3: The convergence of electronic energies (in Ry) versus the plane-wave energy cutoff (in Ry) using the PAW (black lines) and GTH (red lines) pseudopotentials of the three components making up the binding energies: a) isolated CO molecule in vacuum, b) clean Pt slab with no adsorbates, and c) the Pt slab with a CO molecule adsorbed on its surface. Arrows point out the energy cutoff at which convergence of electronic energies has been achieved to within 0.01 Ry. In panels b) and c) the data point for GTH at 30 Ry energy cutoff is omitted because of too large a difference in the corresponding electronic energies. Notice the different scales for the vertical axis in all three panels. The data is generated from a ($4\times 4$) Pt(111) slab, with the Brillouin zone sampled at a $4\times 4\times 1$ Monkhorst-Pack k-point mesh. The insets in each panel depict the atomistic models on which convergence was studied.
• Figure 4: The convergence of the binding energy (in eV) of CO on the fcc hollow site on Pt(111) with respect to the energy cutoff (in Ry) used to calculate each of the three terms of Eq. \ref{['eq:binding_energy_co']}, for both pseudopotential: PAW (blue columns) and GTH (orange columns). We present the binding energies in electronvolts (eV) because it is a more common unit than Ry in applications of computational catalysis. For either pseudopotential, the binding energies converge to within 0.10 eV at 40 Ry energy cutoff.
• Figure 5: A comparison of the convergence of the plane-wave basis towards the MOLOPT-DZVP basis for the primitive cell of the LNO-C2m structure from Ref. PRXQuantum.4.040303 using LDA-DFT. $\Delta$ is the grid resolution in Bohr. The primitive cell of C2m has one formula unit. Thus in the simulation cell we use a supercell of $2\times 2\times 1$ corresponding to $4$ formula units consistent with the $\mathrm{P2_{1}c}$ structure. For the supercell we need a grid of $n=[5, 5, 5]$ qubits to achieve a similar resolution of less than $0.36$ Bohr in each direction. Thus we use a $n=[5, 5, 5]$ for each of the LNO structures. We note that in Ref. PRXQuantum.4.040303 the GTH-HF-REV pseudopotential was used which is a small core pseudopotential. Thus there were more electrons in that simulation (132 electrons for small-core versus 92 electrons for large-core).