Fast quantum simulation of electronic structure by spectrum amplification

• URL: http://arxiv.org/abs/2502.15882v1
• Date: Fri, 21 Feb 2025 19:01:12 GMT
• Title: Fast quantum simulation of electronic structure by spectrum amplification
• Authors: Guang Hao Low, Robbie King, Dominic W. Berry, Qiushi Han, A. Eugene DePrince III, Alec White, Ryan Babbush, Rolando D. Somma, Nicholas C. Rubin,
• Abstract summary: We develop a novel factorization that provides a trade-off between the two leading Coulomb integral factorization schemes.<n>We show that sum-of-squares representations of the electronic structure Hamiltonian are efficiently computable.
• Score: 0.020255670159345252
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\Lambda$ to just $\sqrt{2\Lambda E_{\text{gap}}}$, where $E_{\text{gap}} \ll \Lambda$ 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 CO$_{2}$-fixation catalyst.

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