Accelerating the computation of quantum brachistochrone

TL;DR

This paper introduces a new differential equation framework for faster quantum control computations, reducing complexity and enabling efficient detection of entangled optimal paths, with insights into system symmetries.

Contribution

It presents an alternative set of equations for quantum control that simplifies calculations and incorporates a relaxation technique for entanglement, revealing symmetries in the control paths.

Findings

Reduced computational load in quantum control calculations.

Effective detection of entangled optimal paths.

Identification of continuous symmetries in the control problem.

Abstract

Efficient control of qubits plays a key role in quantum information processing. In the current work, an alternative set of differential equations are derived for an optimal quantum control of single or multiple qubits with or without interaction. The new formulation enables a great reduction of the computation load by eliminating redundant complexity involved in previous formulations. A relaxation technique is designed for numerically detecting optimal paths involving entanglement. Interesting continuous symmetries are identified in the Lagrangian, which indicates the existence of physically equivalent classes of paths and may be utilized to remove neutral directions in the Jacobian of the evolution. In the 'ground state' solution among the set of optimal paths, the time-reversal symmetry of the system shows up, which is expected to be universal for the symmetry-related initial and final state.