In the first part of this internship I did a study on superconducting qubits that can be seen on my final report using as bibliography Gross [1] for the first part which is a study on the superconducting effect. Then, a study of circuit Quantum Electrodynamics (QED) using Girvin [2] where I went through the josephson junction, the quantum harmonic oscillator, the inharmony that using a Josephson junction in place of of an inductor causes creating an "artificial atom" qubit and the Jaynes-Cumming approximation of the Hamiltonian of the qubit coupled to a microwave cavity.
The second part I did several simulations. The first notebook simulates a using Qutip a cavity plus two qubits system that is controlled to do a series of one gate and two gates operations. With this we obtain the equivalent of applying a CNOT gate plus some one qubit gate operations described with better details on the notebook. References quoted in this notebook are Krantz’s [3] and Wolfowicz’s [4]. (In this notebook I basically do the same but play with a cavity using Jaynes-Cumming).
In the second notebook we simulate two qubits and vary the frequency of one of them to measure the amount of interaction it has with one another. In this case with a iSWAP gate like used before. Then we vary the time they interact and conduct a measurement from whose period of variation of the state transfer we can find the g interaction factor. This is supposed to emulate a common process of calibration of this factor in a real quantum computer.
In the third notebook of the simulations we emulate the process of conducing a measurement through a cavity. For that we drive the cavity with a cosine wave and read the reflected/transmitted back wave with the expected value for the a operator of the cavity. Different states of the qubit will result in waves with different frequency as explained further in the notebook.
Finally, using the tool from IBM, qiskit metal. I studied and modified two notebooks available from IBM tutorials:
Creating with these two tutorials a notebook for two transmon qubits coupled by a cavity and another notebook for the transmons coupled by a coupler qubit.
[1] R. Gross, A. Marx, F. Deppe, Applied Superconductivity: Josephson Effect and Superconducting Electronics, Walter De Gruyter Incorporated, 2016.
[2] S. M. Girvin, R. J. Schoelkopf in, 2015.
[3] P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, W. D. Oliver, Applied Physics Reviews 2019, 6, 021318.
[4] G. Wolfowicz, J. J. Morton in eMagRes, Vol. 5, 4, John Wiley & Sons, Ltd, Chichester, UK, 2016, pp. 1515–1528.