User:Gblair13/Flux qubit

Flux Qubit Plan
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 * Edits to Existing Article:
 * Additions to Article:
 * Dr. Shcherbakova's group reported using niobium as the contacts for their flux qubits. Niobium is often used as the contact and is deposited by employing a sputtering technique and using optical lithography to pattern the contacts. An argon beam can then be used to reduce the oxide layer that forms on top of the contacts. The sample must be cooled during the etching process in order to keep the niobium contacts from melting. At this point, the aluminum layers can be deposited on top of the clean niobium surfaces. The aluminum is then deposited in two steps from alternating angles on the niobium contacts. An oxide layer forms between the two aluminum layers in order to create the Al/AlOx/Al Josephson junction. In standard flux qubits, 3 or 4 Josephson junctions will be patterned around the loop.
 * Resonators can be fabricated to measure the readout of the flux qubit through a similar techniques. The resonator can be fabricated by e-beam lithography and CF4 reactive ion etching of thin films of niobium or a similar metal. The resonator could then be coupled to the flux qubit by fabricating the flux qubit at the end of the resonator.
 * Dr. Jerger's group uses resonators that are coupled with the flux qubit. Each resonator is dedicated to just one qubit, and all resonators can be measured with a single transmission line. The state of the flux qubit alters the resonant frequency of the resonator due to a dispersive shift that is picked up by the resonator from the coupling with the flux qubit. The resonant frequency is then measured by the transmission line for each resonator in the circuit. The state of the flux qubit is then determined by the measured shift in the resonant frequency.
 * Josephson Junctions
 * In order for a superconducting circuit to function as a qubit, there needs to be a non-linear element. This is because if the circuit has a harmonic oscillator, such as in an LC-circuit, the energy levels are degenerate. This prohibits the formation of a two qubit computational space because any microwave radiation that is applied to manipulate the ground state and the first excited state to perform qubit operations would also excite the higher energy states. Josephson junctions are the only electronic element that are non-linear as well as non-dissipative at low temperatures. These are requirements for quantum integrated circuit, making the Josephson junction essential in the construction of flux qubits. Understanding the physics of the Josephson junction will improve comprehension of how flux qubits operate.
 * Josephson junctions consist of two pieces of superconducting thin film that are separated by a layer of insulator. The wave functions of the superconducting components overlap, and this construction allows for the tunneling of electrons, which creates a phase difference between the wave functions on either side of the insulating barrier. This phase difference is equivalent to:
 * $$\phi = \phi_2 - \phi_1
 * $$\phi = \phi_2 - \phi_1
 * Where Φ2 and Φ1 correspond to the wave functions on either side of the tunneling barrier. For this phase difference, the following Josephson relations have been established:
 * $$I_J = I_osin\phi $$   and  $$V = (\phi_0/2\pi)*(d\phi/dt) $$
 * Where $$I_J$$ is the Josephson current and $$\phi_O$$ is the flux quantum. By differentiating the current equation and using substitution, one obtains the inductance term, which is:
 * $$L_J = (\phi_0)/2\pi I_0 cos\phi_0 $$
 * From these equations, one can observe that the Josephson Inductance term is non-linear; because of this, the energy level spacings are no longer degenerate, restricting the dynamics of the system to the two qubit states.