Fault-tolerant simulation of the electronic structure using Projector Augmented-Waves and Bloch orbitals

TL;DR

This paper introduces the Bloch-UPAW framework for fault-tolerant quantum simulation of electronic structures in strongly correlated materials, improving efficiency and control over convergence.

Contribution

It develops a novel Bloch--UPAW approach combining Bloch orbitals with UPAW augmentation, enabling efficient quantum simulation of bulk materials.

Findings

Resource estimates for diamond show ~10x reduction in Toffoli count.

The framework handles supercells and Brillouin-zone sampling efficiently.

The method is applicable to both plane-wave and localized bases.

Abstract

Strongly correlated materials are a natural target for fault-tolerant quantum computers, but they require tools beyond those developed for molecules. Electronic wavefunctions vary rapidly near nuclei yet remain delocalized across many unit cells, and bulk properties must be converged systematically with respect to finite-size errors. To resolve such issues, we present the Bloch--UPAW framework that combines Bloch-orbital $k$-space structure with unitary projector-augmented-wave (UPAW) augmentation. The UPAW Hamiltonian, expressed directly in the Bloch basis, retains explicit control of Brillouin-zone sampling, and incorporates near-nuclear physics through strictly local on-site corrections. The construction is independent of the underlying one-particle representation, so it applies to both plane-wave and localized bases, and it handles supercells for symmetry-breaking phenomena more efficiently. We derive a linear-combination-of-unitaries decomposition and a block-encoding circuit suitable for qubitization; UPAW augmentation adds one ancilla qubit and no Toffoli gates at leading order relative to a Bloch-only block encoding. Asymptotically, the Toffoli cost scales as $\mathcal{O}(N_k^3)$ when refining the $k$-mesh and as $\mathcal{O}(N_a^{3.5})$ when enlarging the supercell, enabling convergence to be steered by the most favorable route for a given material. Resource estimates for bulk diamond show approximately an order-of-magnitude reduction in Toffoli count relative to prior work on periodic solids.