Principle of least action for quasi-adiabatic state transfers with dissipation

TL;DR

This paper introduces a formalism based on the least action principle to optimize quasi-adiabatic state transfers in dissipative quantum systems, achieving high fidelity by controlling system dynamics within a protected dark subspace.

Contribution

It develops a novel formalism linking fidelity loss to a classical action, enabling the determination of optimal transfer protocols in dissipative quantum systems.

Findings

Derived a fidelity upper bound using least action principle.

Applied the formalism to a two-qubit system with dissipation.

Characterized the optimal state-transfer fidelity in the example.

Abstract

We discuss a general formalism to optimize quasi-adiabatic state-transfer protocols, where high fidelity is achieved by maintaining the system in a dark subspace protected from the dominant dissipative channels. We cast the residual fidelity loss, induced by a combination of dissipation and non-adiabatic transitions, in the form of a classical action where the time-dependent control parameters act as coordinates. This allows us to apply the least action principle, yielding the fidelity upper-bound and the corresponding optimal transfer time. As an application, we analyze a system of two qubits subject to weak relaxation and dephasing, interacting through a strongly dissipative quantum bus. In this case, our formalism, we obtain a full characterization of the optimal state-transfer fidelity.