Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers

I-Chi Chen; Klée Pollock; Yong-Xin Yao; Peter P. Orth; Thomas Iadecola

doi:10.22331/q-2024-12-03-1545

Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers

I-Chi Chen^1,2, Klée Pollock¹, Yong-Xin Yao^1,2, Peter P. Orth^1,2,3, and Thomas Iadecola^1,2

¹Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
²Ames National Laboratory, Ames, Iowa 50011, USA
³Department of Physics, Saarland University, 66123 Saarbrücken, Germany

Published:	2024-12-03, volume 8, page 1545
Eprint:	arXiv:2310.03924v4
Doi:	https://doi.org/10.22331/q-2024-12-03-1545
Citation:	Quantum 8, 1545 (2024).

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Abstract

The transport of conserved quantities like spin and charge is fundamental to characterizing the behavior of quantum many-body systems. Numerically simulating such dynamics is generically challenging, which motivates the consideration of quantum computing strategies. However, the relatively high gate errors and limited coherence times of today's quantum computers pose their own challenge, highlighting the need to be frugal with quantum resources. In this work we report simulations on quantum hardware of infinite-temperature energy transport in the mixed-field Ising chain, a paradigmatic many-body system that can exhibit a range of transport behaviors at intermediate times. We consider a chain with $L=12$ sites and find results broadly consistent with those from ideal circuit simulators over 90 Trotter steps, containing up to 990 entangling gates. To obtain these results, we use two key problem-tailored insights. First, we identify a convenient basis$\unicode{x2013}$the Pauli $Y$ basis$\unicode{x2013}$in which to sample the infinite-temperature trace and provide theoretical and numerical justifications for its efficiency relative to, e.g., the computational basis. Second, in addition to a variety of problem-agnostic error mitigation strategies, we employ a renormalization strategy that compensates for global nonconservation of energy due to device noise. We discuss the applicability of the proposed sampling approach beyond the mixed-field Ising chain and formulate a variational method to search for a sampling basis with small sample-to-sample fluctuations for an arbitrary Hamiltonian. This opens the door to applying these techniques in more general models.

► BibTeX data

@article{Chen2024problemtailored,
  doi = {10.22331/q-2024-12-03-1545},
  url = {https://doi.org/10.22331/q-2024-12-03-1545},
  title = {Problem-tailored {S}imulation of {E}nergy {T}ransport on {N}oisy {Q}uantum {C}omputers},
  author = {Chen, I-Chi and Pollock, Kl{\'{e}}e and Yao, Yong-Xin and Orth, Peter P. and Iadecola, Thomas},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1545},
  month = dec,
  year = {2024}
}

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