On Lagrangian Formalism of Quantum Computation

TL;DR

This paper introduces a Lagrangian (sum-over-path) approach to quantum computation, offering a new perspective that complements the traditional Hamiltonian formalism and provides insights into complexity and simulation.

Contribution

It reformulates quantum computation using Lagrangian formalism, applying it to models like quantum circuits, optimization, and random walks, and proposes an analog quantum simulation scheme.

Findings

Lagrangian formalism offers a new perspective on quantum computation.

Application to standard models demonstrates the formalism's versatility.

Proposes an analog quantum simulation scheme based on the Lagrangian approach.

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.