continuous variable quantum simulation of nonlinear partial differential equations

  • Gan, Yu (University of Pittsburgh)
  • Alipanah, Hirad (University of Pittsburgh)
  • Cheng, Jinglei (University of Pittsburgh)
  • Wu, Zeguan (University of Pittsburgh)
  • Li, Guangyi (University of Michigan)
  • Mendoza-Arenas, Juan JosĂ© (University of Pittsburgh)
  • Givi, Peyman (University of Pittsburgh)
  • R. Malik, Mujeeb (NASA Langley Research Center)
  • J. McDermott, Brian (Naval Nuclear Laboratory)
  • Liu, Junyu (University of Pittsburgh)

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A framework is presented of continuous variable quantum computing for the numerical simulation of partial differential equations. Based on the Koopman-von Neumann formalism, this framework deals with nonlinearities by encoding the transport differential equation variables as coherent states of photonic degrees of freedom of an optical system. By leveraging the infinite-dimensional Hilbert space associated to the photons, very large nonlinearities can be effectively considered. Using photonic creation and annihilation operators, the finite-difference algorithms are expressed as a Hamiltonian that describes the dynamics of the coherent state. The resulting analog computing model is employed for solving Burgers’ equation, closely matching the classical numerical simulations. The effects of photon loss as the most significant source of noise are explored, showing the ability to perform error correction for the flow variables. The results demonstrate that the analog quantum computer is a handy tool for computational fluid dynamics, opening new possibilities for outperforming classical numerical simulations.