Quantum computing & quantum information

Abstract

This report is an introduction to quantum computation and quantum information. We present a two-part theory section followed by data analysis of a transmon qubit. The ¯rst theory part, needed for the analysis, introduces fundamental properties of qubit states and the Bloch sphere description. The qubit manipulation, interaction with a electromagnetic ¯eld, is then studied in the Rabi model (semi-classical) and the Jaynes-Cummings model (fully quantized). The second theory part is a qualitative presentation of the density matrix representation, decoherence (e®ects of noise) and read-out, which are useful topics in more advanced analysis. We also present a summary of qubit realizations, with focus on the superconduct- ing qubits: charge, phase and transmon. In the last part of the report, we analyze spectroscopic measurements on a trans- mon qubit in a cavity resonator, performed atMC2 Chalmers. The data was compared to the expected behavior from the Jaynes-Cummings Hamiltonian and then the full Hamiltonian for the transmon. The comparison enabled us to extract the parame- ters of the transmon. The ratio of the Josephson energy and the charge energy was determined to be EJ=EC = 34:5644 § 0:9456 GHz, which is in the transmon regime. Furthermore, the coupling strength between the cavity resonator and the qubit was determined to be 2¯eV 0 rms = 0:1301 § 0:00095 GHz, with a 68% con¯dence interval.