Lagrangian Formalism

Jue Xu

We reformulate quantum computation in terms of Lagrangian (sum-over-path) formalism, in contrast to the widely used Hamiltonian (unitary gate) formulation. We exemplify this formalism with some widely-studied models, including the standard quantum circuit model, quantum optimization heuristics, and quantum random walks. The meanings of Lagrangian (action) are interpreted in various contexts of quantum computation, such as complexity analysis. Furthermore, an analog quantum simulation scheme is suggested where the Lagrangian serves as the starting point and the sum-over-path method is applied.

K. Nishijima

The differences between Lagrangian and Hamiltonian formalisms are discussed through the concept of chronological ordering operators thereby keeping close correspondence to Feynman's path integral. Next a method to derive commutation relations without referring to Hamiltonian formalism is presented.

Ingvar Lindgren

Peter Woit

Shahram Khosravi

Direct quantization of classical systems using the equation of motion and removing the degeneracy of Lagrangian formalism