Circuit implementation of oracles used in a quantum algorithm for solving nonlinear partial differential equations
Frank Gaitan
Abstract
In 2020 and 2021, the author introduced quantum algorithms for solving the Navier-Stokes equations and systems of nonlinear partial differential equations (PDEs), respectively. These algorithms make use of three quantum oracles. In this paper, we show how all three oracles can be implemented as quantum circuits. We cost the circuit implementations, determining their depth, width, and number of non-Clifford gates used as a function of user-specified (i) error tolerances, and (ii) algorithm success probability. With these quantum oracle circuits in hand, the quantum Navier-Stokes and PDE algorithms are now completely specified as quantum circuits.
Topics & Concepts
Nonlinear systemPartial differential equationComputer scienceAlgorithmQuantumDifferential equationPhysicsApplied mathematicsQuantum mechanicsMathematicsQuantum Computing Algorithms and ArchitectureQuantum Information and CryptographyNumerical Methods and Algorithms