2025/04/22 by Szymon Pliś, Pliś, Szymon, E. J. Zak +1 · 1 citation
Physics and Astronomy · #68Q12 #68Q17 #81-08 #81-10 #81P68 #81V55 #81V74 #Chemical Physics (physics.chem-ph) #Computational Physics (physics.comp-ph) #FOS: Physical sciences #G.1.2 #G.1.3 #G.1.6 #I.6.1 #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2504.15841
openalex publication_date 2025/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a fault-tolerant quantum algorithm for implementing the Discrete Variable Representation (DVR) transformation, a technique widely used in simulations of quantum-mechanical Hamiltonians. DVR provides a diagonal representation of local operators and enables sparse Hamiltonian structures, making it a powerful alternative to the finite basis representation (FBR), particularly in high-dimensional problems. While DVR has been extensively used in classical simulations, its quantum implementation, particularly using Gaussian quadrature grids, remains underexplored. We develop a quantum circuit that efficiently transforms FBR into DVR by following a recursive construction based on quantum arithmetic operations, and we compare this approach with methods that directly load DVR matrix elements using quantum read-only memory (QROM). We analyze the quantum resources, including T-gate and qubit counts, required for implementing the DVR unitary and discuss preferable choices of QROM-based and recursive-based methods for a given matrix size and precision. This study lays the groundwork for utilizing DVR Hamiltonians in quantum algorithms such as quantum phase estimation with block encoding.