Efficient quantum algorithm for dissipative nonlinear differential equations

Journal Article · 25 August 2021 · Proceedings of the National Academy of Sciences of the United States of America

DOI: https://doi.org/10.1073/pnas.2026805118 · OSTI ID:1817263

Liu, Jin-Peng  ^[1]; Kolden, Herman Øie  ^[2]; Krovi, Hari K. ^[3]; Loureiro, Nuno F. ^[4]; Trivisa, Konstantina ^[5]; Childs, Andrew M.  ^[6]

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1. Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742,, Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742,, Department of Mathematics, University of Maryland, College Park, MD 20742,
2. Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway,, Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139,
3. Quantum Engineering and Computing, Raytheon BBN Technologies, Cambridge, MA 02138,
4. Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139,
5. Department of Mathematics, University of Maryland, College Park, MD 20742,, Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742,
6. Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742,, Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742,, Department of Computer Science, University of Maryland, College Park, MD 20742

Significance Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution time, we give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to nonlinear and forcing terms and the solution does not decay too rapidly. We also establish a lower bound showing that differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics. Furthermore, numerical results for the Burgers equation suggest that our algorithm may potentially address complex nonlinear phenomena even in regimes with weaker dissipation.

• Research Organization: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: SC0020264; SC0020312
• OSTI ID: 1817263
• Journal Information: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 35 Vol. 118; ISSN 0027-8424
• Publisher: Proceedings of the National Academy of SciencesCopyright Statement
• Country of Publication: United States
• Language: English