Bibliographic Details
| Title: |
Fast quantum simulation of electronic structure by spectrum amplification |
| Authors: |
Low, Guang Hao, King, Robbie, Berry, Dominic W., Han, Qiushi, DePrince III, A. Eugene, White, Alec, Babbush, Ryan, Somma, Rolando D., Rubin, Nicholas C. |
| Publication Year: |
2025 |
| Collection: |
Physics (Other)
Quantum Physics |
| Subject Terms: |
Quantum Physics, Physics - Chemical Physics |
| More Details: |
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. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2502.15882 |
| Accession Number: |
edsarx.2502.15882 |
| Database: |
arXiv |
