References
- A. Surana and A. Gnanasekaran (2024). “Variational quantum framework for partial differential equation constrained optimization”. arXiv preprint arXiv:2405.16651.
- H. Antil, D.P. Kouri, M.-D. Lacasse and D. Ridzal (2018). Frontiers in PDE-constrained Optimization, volume 163. Springer.
- L.T. Biegler, O. Ghattas, M. Heinkenschloss, and B. van BloemenWaanders (2003) “Large-scale pde-constrained optimization: an introduction”, in Large-scale PDE-Constrained Optimization. Springer, pp. 3–13.
- M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich (2008). Optimization with PDE Constraints, volume 23. Springer Science & Business Media.
- K. Kowalski and W.-H. Steeb (1991). Nonlinear Dynamical Systems and Carleman Linearization. Singapore: World Scientific.
- A. Amini, C. Zheng, Q. Sun, and N. Motee (2025). “Carleman linearization of nonlinear systems and its finite-section approximations”. Discrete and Continuous Dynamical Systems-B, 30: 2. 577–603.
- M. Forets and A. Pouly (2017). “Explicit error bounds for Carleman linearization.” arXiv preprint arXiv:1711.02552.
- J.-P. Liu, H. Ø. Kolden, H.K. Krovi, N.F. Loureiro, K. Trivisa, and A.M. Childs. (2021). “Efficient quantum algorithm for dissipative nonlinear differential equations”. Proceedings of the National Academy of Sciences, 118: 35, e2026805118.
- A. Surana, A. Gnanasekaran, and T. Sahai (2024). “An efficient quantum algorithm for simulating polynomial dynamical systems”. Quantum Information Processing, 23: 3, 1–22.
- X. Li, X. Yin, N. Wiebe, J. Chun, G. K. Schenter, M. S. Cheung, and J. M”ulmenst”adt (2025). “Potential quantum advantage for simulation of fluid dynamics”. Physical Review Research 7, 013036.
- J. Penuel, A. Katabarwa, P.D Johnson, C. Farquhar, Y. Cao, and M.C. Garrett (2024). “Feasibility of accelerating incompressible computational fluid dynamics simulations with fault-tolerant quantum computers”. arXiv preprint arXiv:2406.06323.
- R. Demirdjian, D. Gunlycke, C.A. Reynolds, J.D. Doyle, and S. Tafur. (2022). “Variational quantum solutions to the advection–diffusion equation for applications in fluid dynamics”. Quantum Information Processing, 21: 9, 322.
- C. B.-Prieto, R. LaRose, M. Cerezo, Y. Subasi, L. Cincio, and P. J. Coles. (2023). “Variational quantum linear solver.” Quantum, 7, 1188.
- A. Gnanasekaran and A. Surana. (2024). “Efficient variational quantum linear solver for structured sparse matrices.” In 2024 IEEE International Conference on Quantum Computing and Engineering (QCE), volume 1. IEEE, pp. 199–210.
- M. A. Nielsen and I. L. Chuang (2010). Quantum Computation and Quantum Information. Cambridge University Press.
- J.C. D. Reyes (2015). Numerical PDE-Constrained Optimization. Springer.
- L. Hantzko, L. Binkowski, and S. Gupta. (2024). “Tensorized pauli decomposition algorithm.” Physica Scripta, 99: 8, 085128.
- H.-L. Liu, Y.-S. Wu, L.-C. Wan, S.-J. Pan, Su-Juan Qin, Fei Gao, and Qiao-Yan Wen (2021). “Variational quantum algorithm for the poisson equation.” Physical Review A, 104: 2, 022418.
- P. Costa, P. Schleich, M.ES Morales, and D.W Berry (2023). “Further improving quantum algorithms for nonlinear differential equations via higher-order methods and rescaling.” arXiv preprint arXiv:2312.09518.
- S. Sim, P.D. Johnson, and A. Aspuru-Guzik (2019). “Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms.” Advanced Quantum Technologies, 2: 12, 1900070.
- A. Pellow-Jarman, I. Sinayskiy, A. Pillay, and F. Petruccione (2021). “A comparison of various classical optimizers for a variational quantum linear solver.” Quantum Information Processing, 20: 6, 202.
- P.C.S. Costa, D. An, Y.l.R. Sanders, Y. Su, R. Babbush, and D.W. Berry (2022). “Optimal scaling quantum linear-systems solver via discrete adiabatic theorem.” PRX quantum, 3: 4, 040303.
- D. Dervovic, M. Herbster, P. Mountney, S. Severini, N. Usher, and L. Wossnig (2018). “Quantum linear systems algorithms: a primer.” arXiv preprint arXiv:1802.08227.
- A.W. Harrow, A. Hassidim, and S. Lloyd (2009). “Quantum algorithm for linear systems of equations.” Physical Review Letters, 103: 15, 150502.