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Quantum Simulation
On Lagrangian Formalism of Quantum Computation
arXiv
Authors: Jue Xu
Year
2021
Paper ID
40908
Status
Preprint
Abstract Read
~2 min
Abstract Words
80
Citations
N/A
Abstract
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.
Why This Paper Matters
- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- We reformulate quantum computation in terms of Lagrangian (sum-over-path) formalism, in contrast to the widely used Hamiltonian (unitary gate) formulation.
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