![]() Quantum computing and quantum communication are research areas that have seen significant developments and progress in recent years, as is apparent from the work covered in this book. Further development steps required to embed the introduced algorithms into larger-scale algorithms are discussed. The importance of including sub-normal numbers in the floating-point quantum arithmetic is demonstrated for a representative example problem. A complexity analysis shows that even with the limited number of qubits available on current and near-term quantum computers (<100), nonlinear product terms can be computed with good accuracy. Furthermore, a floating-point type data representation is used instead of the fixed-point representation typically employed in quantum algorithms. The quantum algorithms introduced use encoding in the computational basis, and employ arithmetic based on the Quantum Fourier Transform. Then, as the main contribution of this work, quantum circuits are presented that represent the nonlinear convection terms in the Navier–Stokes equations. First, the key challenges related to nonlinear equations in the context of quantum computing are discussed. In the present work, the focus is on nonlinear partial differential equations arising as governing equations in fluid mechanics. ![]() There has not been similar progress in the development of quantum algorithms for nonlinear differential equations. In recent years, significant progress has been made in the development of quantum algorithms for linear ordinary differential equations as well as linear partial differential equations. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |