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Cited by 163Quantum Computing Algorithms and ArchitectureQuantum many-body systemsQuantum Information and Cryptography

Resource-efficient digital quantum simulation of d-level systems for photonic, vibrational, and spin-s Hamiltonians

Open access
Sawaya, Nicolas P. D., Menke, Tim, Kyaw, Thi Ha, Johri, Sonika, Aspuru-Guzik, Alán, Guerreschi, Gian Giacomo·2020·npj Quantum Information
DOI 10.1038/s41534-020-0278-0
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Abstract

Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin- $$\frac{1}{2}$$ 1 2 systems. Here, we instead consider encodings of d -level (i.e., qudit) quantum operators into multi-qubit operators, studying resource requirements for approximating operator exponentials by Trotterization. We primarily focus on spin- s and truncated bosonic operators in second quantization, observing desirable properties for approaches based on the Gray code, which to our knowledge has not been used in this context previously. After outlining a methodology for implementing an arbitrary encoding, we investigate the interplay between Hamming distances, sparsity patterns, bosonic truncation, and other properties of local operators. Finally, we obtain resource counts for five common Hamiltonian classes used in physics and chemistry, while modeling the possibility of converting between encodings within a Trotter step. The most efficient encoding choice is heavily dependent on the application and highly sensitive to d , although clear trends are present. These operation count reductions are relevant for running algorithms on near-term quantum hardware because the savings effectively decrease the required circuit depth. Results and procedures outlined in this work may be useful for simulating a broad class of Hamiltonians on qubit-based digital quantum computers.

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  • Gray code is resource efficient in simulating some specific bosonic and spin Hamiltonians.

    “Gray code in particular is found to be resource efficient (in terms of number of qubits and two-qubit entangling gates) in simulating some specific bosonic and spin Hamiltonians (Sawaya et al. , 2020).”

    From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Sawaya et al. , 2020

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Research works printed but not linked: 8

  1. McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S. & Yuan, X. Quantum com- putational chemistry. Rev. Mod. Phys. 92, 015003 (2020).
  2. Levitt, M. H. Spin Dynamics: Basics of Nuclear Magnetic Resonance, 2nd edn. (Wiley, 2008).
  3. Paolo, A. D., Barkoutsos, P. K., Tavernelli, I. & Blais, A. Variational quantum simu- lation of ultrastrong light-matter coupling. arXiv: http://arxiv.org/abs/ arXiv:1909.08640 (2019). · arXiv
  4. Somma, R. D. Quantum computation, complexity, and many-body physics. arXiv: http://arxiv.org/abs/arXiv:quant-ph/0512209 (2005). · arXiv
  5. Childs, A. M., Maslov, D., Nam, Y., Ross, N. J. & Su, Y. Toward the first quantum simulation with quantum speedup. Proc. Natl Acad. Sci. USA 115, 9456-9461 (2018b).
  6. Childs, A. M., Su, Y., Tran, M. C., Wiebe, N. & Zhu, S. A theory of trotter error. arXiv: http://arxiv.org/abs/arXiv:1912.08854 (2019).
  7. Merzbacher, E. Quantum Mechanics, 3rd ed. (John Wiley and Sons, 2004).
  8. Gosset, D., Kliuchnikov, V., Mosca, M. & Russo, V. An algorithm for the T-count. arXiv: http://arxiv.org/abs/arXiv:1308.4134 (2013).

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Authors
Sawaya, N. P. D., Menke, T., Kyaw, T. H., Johri, S., Aspuru-Guzik, A., & Guerreschi, G. G.
Affiliations
  • Intel (United States) (US)
  • Harvard University (US)
  • University of Toronto (CA)
Corresponding author
  • Sawaya, Nicolas P. D.
  • Guerreschi, Gian Giacomo
ORCID
Venue
npj Quantum Information
Publisher
Springer Science and Business Media LLC
Published
2020-06-02
Volume
6
Issue
1
ISSN
2056-6387 (ISSN-L)
DOI
10.1038/s41534-020-0278-0
OpenAlex
W2976208308
Cited by
163
References
42
Citations by year
2026: 18 · 2025: 41 · 2024: 29 · 2023: 19 · 2022: 27 · 2021: 25 · 2020: 4
FWCI
7.37
Type
journal article
Language
en
Open access
Licence
Locations
  • npj Quantum Information (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Intel Research
  • Vannevar Bush Faculty Fellowship and the Canada 150 Research Chairs Program.
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
digital quantum simulation, qudits, d-level systems, Trotterization, Gray code, second quantization, Hamming distance, sparsity pattern, circuit depth, vibrational Hamiltonian, spin Hamiltonian

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