Manipulating quantum information on the controllable systems or subspaces

TL;DR

This paper presents methods for manipulating qubits on the Bloch sphere using various Hamiltonian controls, optimizing time-energy trade-offs, and extending these techniques to controllable subspaces for quantum information processing.

Contribution

It introduces new control schemes for qubit manipulation with optimized time-energy performance and generalizes the approach to controllable subspaces.

Findings

Constructed three-rotation and one-rotation Hamiltonian controls for qubit steering.

Demonstrated local-wave function controls like Bang-Bang, triangle, and quadratic functions.

Proposed a new time-energy performance index for resource optimization.

Abstract

In this paper, we explore how to constructively manipulate qubits by rotating Bloch spheres. It is revealed that three-rotation and one-rotation Hamiltonian controls can be constructed to steer qubits when two tunable Hamiltonian controls are available. It is demonstrated in this research that local-wave function controls such as Bang-Bang, triangle-function and quadratic function controls can be utilized to manipulate quantum states on the Bloch sphere. A new kind of time-energy performance index is proposed to trade-off time and energy resource cost, in which control magnitudes are optimized in terms of this kind of performance. It is further exemplified that this idea can be generalized to manipulate encoded qubits on the controllable subspace.