Superconductor Qubits Hamiltonian Approximations Effect on Quantum State Evolution and Control

TL;DR

This paper investigates how approximations of Hamiltonians in superconducting qubits affect quantum state evolution and control, revealing significant deviations and proposing nonlinear control methods to stabilize desired states.

Contribution

It analyzes the impact of Hamiltonian approximations on qubit dynamics and introduces a nonlinear control scheme to stabilize quantum states in superconducting qubits.

Findings

Approximate Hamiltonians cause different quantum state trajectories compared to exact Hamiltonians.

Microwave drive control based on approximations leads to trajectories deviating from the desired.

Nonlinear control stabilizes the quantum state towards a target state despite Hamiltonian approximations.

Abstract

Quantum state on Bloch sphere for superconducting charge qubit, phase qubit and flux qubit for all time in absence of external drive is stable to initial state. By driving the qubits, approximation of charge and flux Hamiltonian lead to quantum state rotation in Bloch sphere around an axis completely differ from rotation vector of exact Hamiltonian. The trajectory of quantum state for phase qubit for approximated and exact Hamiltonian is the same but the expectation of quantum observable has considerable errors as two other qubits. microwave drive control is designed for approximated Hamiltonian and exerted on actual systems and shows completely different trajectory with respect to desired trajectory. Finally a nonlinear control with external $\mu$V voltage control and nA current control is designed for general qubit which completely stabilizes quantum state toward a desired state.