2025/02/21 by Guang Hao Low, Robbie King, Low, Guang Hao +15 · 19 citations
Physics and Astronomy · #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Laser-Matter Interactions and Applications #Quantum Physics (quant-ph) #Quantum optics and atomic interactions #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2502.15882
openalex publication_date 2025/02/21 · openalex created_date 2025/10/05 · openalex updated_date 2026/07/29
The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings of the Hamiltonian. A natural challenge of these methods is the degree to which block-encoding costs can be reduced. We address this challenge through the technique of spectrum amplification, which magnifies the spectrum of the low-energy states of Hamiltonians that can be expressed as sums of squares. Spectrum amplification enables estimating ground-state energies with significantly improved cost scaling in the block encoding normalization factor Λ to just √2ΛEgap, where Egap ≪ Λ is the lowest energy of the sum-of-squares Hamiltonian. To achieve this, we show that sum-of-squares representations of the electronic structure Hamiltonian are efficiently computable by a family of classical simulation techniques that approximate the ground-state energy from below. In order to further optimize, we also develop a novel factorization that provides a trade-off between the two leading Coulomb integral factorization schemes -- namely, double factorization and tensor hypercontraction -- that when combined with spectrum amplification yields a factor of 4 to 195 speedup over the state of the art in ground-state energy estimation for models of Iron-Sulfur complexes and a CO2-fixation catalyst.