Zero and Finite Temperature Quantum Simulations Powered by Quantum Magic

Andi Gu; Hong-Ye Hu; Di Luo; Taylor L. Patti; Nicholas C. Rubin; Susanne F. Yelin

doi:10.22331/q-2024-07-23-1422

Zero and Finite Temperature Quantum Simulations Powered by Quantum Magic

Andi Gu¹, Hong-Ye Hu¹, Di Luo^1,2,3, Taylor L. Patti⁴, Nicholas C. Rubin⁵, and Susanne F. Yelin^1,3

¹Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA
²Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
³The NSF AI Institute for Artificial Intelligence and Fundamental Interactions
⁴NVIDIA, Santa Clara, CA 95051, USA
⁵Google Quantum AI, Venice, CA 90291, United States

Published:	2024-07-23, volume 8, page 1422
Eprint:	arXiv:2308.11616v2
Doi:	https://doi.org/10.22331/q-2024-07-23-1422
Citation:	Quantum 8, 1422 (2024).

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Abstract

We introduce a quantum information theory-inspired method to improve the characterization of many-body Hamiltonians on near-term quantum devices. We design a new class of similarity transformations that, when applied as a preprocessing step, can substantially simplify a Hamiltonian for subsequent analysis on quantum hardware. By design, these transformations can be identified and applied efficiently using purely classical resources. In practice, these transformations allow us to shorten requisite physical circuit-depths, overcoming constraints imposed by imperfect near-term hardware. Importantly, the quality of our transformations is $tunable$: we define a 'ladder' of transformations that yields increasingly simple Hamiltonians at the cost of more classical computation. Using quantum chemistry as a benchmark application, we demonstrate that our protocol leads to significant performance improvements for zero and finite temperature free energy calculations on both digital and analog quantum hardware. Specifically, our energy estimates not only outperform traditional Hartree-Fock solutions, but this performance gap also consistently widens as we tune up the quality of our transformations. In short, our quantum information-based approach opens promising new pathways to realizing useful and feasible quantum chemistry algorithms on near-term hardware.

Popular summary

Quantum computers hold great promise for solving complex problems in chemistry and materials science, but current devices are limited by noise and errors. This work introduces a new method to make quantum simulations more practical on today’s imperfect quantum hardware. We’ve developed a technique called the "quantum magic ladder" that uses carefully designed mathematical transformations to simplify quantum chemistry problems before they’re run on a quantum computer.

Our approach is inspired by concepts from quantum information theory, particularly the ideas of entanglement and "quantum magic" – both measures of how difficult a quantum state is to simulate classically. By applying our transformations, we can reduce the amount of entanglement and quantum magic needed to solve a problem, making it easier for near-term quantum devices to handle. We've demonstrated that our method outperforms traditional techniques for calculating molecular energies, both at zero temperature and finite temperatures. As we climb higher on our "quantum magic ladder" by fine-tuning our approach, we see consistent improvements in accuracy. This work suggests new pathways for enhancing the capabilities of quantum chemistry simulations on current quantum computers, potentially contributing to progress towards practical quantum advantage in this important field.

► BibTeX data

@article{Gu2024zerofinite,
  doi = {10.22331/q-2024-07-23-1422},
  url = {https://doi.org/10.22331/q-2024-07-23-1422},
  title = {Zero and {F}inite {T}emperature {Q}uantum {S}imulations {P}owered by {Q}uantum {M}agic},
  author = {Gu, Andi and Hu, Hong-Ye and Luo, Di and Patti, Taylor L. and Rubin, Nicholas C. and Yelin, Susanne F.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1422},
  month = jul,
  year = {2024}
}

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