Quantum splines

TL;DR

Quantum splines are smooth, time-parameterized curves in the space of unitary transformations that optimize the control of quantum states by minimizing the Hamiltonian's rate of change, with applications demonstrated in quantum control.

Contribution

The paper introduces the concept of quantum splines, providing a solution method and numerical scheme for optimal quantum control of pure states.

Findings

Successfully derived the quantum spline solution.

Implemented an efficient numerical scheme.

Demonstrated application in quantum control examples.

Abstract

A quantum spline is a smooth curve parameterised by time in the space of unitary transformations, whose associated orbit on the space of pure states traverses a designated set of quantum states at designated times, such that the trace norm of the time rate of change of the associated Hamiltonian is minimised. The solution to the quantum spline problem is obtained, and is applied in an example that illustrates quantum control of coherent states. An efficient numerical scheme for computing quantum splines is discussed and implemented in the examples.