Superconductor qubits hamiltonian approximations effect on quantum state evolution and control

Microwave IQ-mixer controllers are designed for the three approximated Hamiltonians of charge, phase and flux qubits and the controllers are exerted both on approximate and precise quantum system models. The controlled qubits are for the implementation of the two quantum-gates with these three fundamental types of qubits, Quantum NOT-gate and Hadamard-gate. In the charge-qubit, for implementation of both gates, in the approximated and precise model, we observed different controlled trajectories. But fortunately, applying the controller designed for the approximated system over the precise system leads to the passing of the quantum state from the desired state sooner that the expected time. Phase-qubit and flux qubit have similar behaviour under the control system action. In both of them, the implementation of NOT-gate operation led to same trajectories which arrive at final goal state at different times. But in both of those two qubits for implementation of Hadamard-gate, desired trajectory and precise trajectory have some angle of deviation, then by exerting the approximated design controller to precise system, it caused the quantum state to approach the goal state for Hadamard gate implementation, and since the quantum state does not completely reach the goal state, we can not obtain very high gate fidelity.

Superconductor Qubits Hamiltonian Approximations Effect on Quantum State Evolution and Control

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 µV voltage control and nA current control is designed for general qubit which completely stabilizes quantum state toward a desired state.

Entanglement Research for the Coupled Superconducting Phase Qubit and a Two-Level System

Entanglement can exist not only in the microscopic system (e.g., atom, photon, and ion trap) but also in macroscopic systems. According to recent research, entanglement can be achieved and controlled in superconducting devices. The quantum dynamics and entanglement mechanism of the coupled superconducting phase qubit and a two-level system (TLS) were demonstrated when the bipartite system was under microwave driving. Besides, the results reveal that when the system was experiencing decoherence, entanglement (concurrence) of the coupled superconducting phase qubit and TLS would oscillate damply with microwave driving time, even exhibiting concurrence sudden death and revival. The coupling effect of the superconducting qubit and TLS system and the resonant microwave together help to achieve entanglement, while concurrence death and concurrence revival are dependent on the decoherence source and mechanism, for example, the resonant microwave driving time acting on the bipartite coupling system. Furthermore, the simulation results show the entanglement of the coupled qubit and TLS system also depends on the purity of the initial states of the system. The article carried out a numerical simulation on the entanglement of different initial states, and the results showed that the entanglement of the coupled system changes with different initial states. For different initial states, entanglement, sudden death, and rejuvenation are still visible.

Coupling Superconducting Qubits to Electromagnetic and Piezomechanical Resonators

Quantum bits have been under intense development since the late 1990s, due to the discovery of a number of potential applications for engineered quantum systems to problems in computation or communication. As superconducting circuits provide a straightforward path to scaling up to large numbers of qubits and are exible in terms of their application to a range of different problems, This chapter focuses on the problem of coupling superconducting qubits to other systems, in particular to microwave frequency electromagnetic resonators as well as mechanical resonators. It begins by introducing the topics of piezoelectricity and its role in solid mechanics, then turns to a description of one flavour of superconducting qubit, the phase qubit. It then describes how the phase qubit can be used to control and measure a superconducting electromagnetic resonator, and concludes by describing how a phase qubit can also be used to control and measure a piezomechanical resonator.

Dispersive reservoir influence on the superconducting phase qubit

An analytical description of a superconducting (SC) phase qubit coupled to a torsional resonator, which is damped by a dispersive reservoir, is presented based on the master equation. Therefore, the effect of the qubit phase damping on the dynamical behavior of the entanglement, purity loss and qubit inversion are investigated. It is found that the collapse and revival phenomena of qubit inversion are very sensitive not only to the damping parameter but also to the frequency detuning and the qubit distribution angle of the initial state. It is interesting to note that the purity of the state of the SC-qubit, which is measured by von Neumann entropy, can be completely lost due to the dispersive reservoir parameter. Because of the existence of dispersive reservoir, the von Neumann entropy cannot be a measure for the entanglement in open system. So, the negative eigenvalue of the partially transposed density matrix of qubit-resonator system is used to quantify the entanglement. For certain parameter sets, it is possible to control the degree and the dynamics of entanglement between the qubit and the torsional resonator.