  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.
