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Table of contents
1 Introduction and summary
1.1 Microelectronic industry scaling down to mesoscopic physics
1.2 Quantum computing
1.2.1 Evaluating the complexity of a problem
1.2.2 Quantum resources
1.2.3 The problem of decoherence
1.3 Physical implementations of qubits
1.3.1 Microscopic qubits
1.3.2 Macroscopic qubits based on electronic circuits
1.4 The Quantronium
1.4.1 Description of the circuit
1.4.2 Readout of the quantum state
1.5 NMR-like manipulation of the qubit
1.5.1 Rabi oscillations
1.5.2 Combined rotations
1.5.3 Implementation of robust operations
1.6 Analysis of decoherence during free evolution
1.6.1 Noise sources in the quantronium
1.6.2 Relaxation measurement
1.6.3 Dephasing measurement
1.6.4 Summary and analysis of decoherence during free evolution
1.7 Decoherence during driven evolution
1.8 Towards Quantum Non Demolition measurement of a qubit
1.8.1 Principle of the ac dispersive readout of the quantronium: the JBA
1.8.2 Characterization of the microwave readout circuit
1.8.3 Measurement of the quantronium qubit with a JBA
1.8.4 Partially non-demolition behavior of the readout
1.9 Conclusion
2 A superconducting qubit: the Quantronium
2.1 The Cooper pair box
2.2 The Quantronium
2.2.1 Quantronium circuit
2.2.2 Energy spectrum
2.2.3 The optimal working point strategy
2.2.4 Loop current
2.3 Measuring the quantum state of the quantronium
2.3.1 Principle of the switching readout
2.3.2 Dynamics of a current biased Josephson junction
2.3.3 Escape dynamics of the readout junction coupled to the split Cooper pair box
2.4 Experimental setup and characterization of the readout
2.4.1 Current biasing line
2.4.2 Measuring line
2.4.3 Experimental characterization of the readout junction
2.4.4 Experimental characterization of the quantronium sample A
2.4.5 Spectroscopy of the qubit
2.4.6 Back-action of the readout on the qubit
2.4.7 Conclusion
3 Manipulation of the quantum state of the Quantronium
3.0.8 Bloch sphere representation
3.1 Manipulation of the qubit state with non-adiabatic pulses
3.1.1 Non-adiabatic DC pulses
3.1.2 Non-adiabatic AC resonant pulses
3.2 Combination of rotations: Ramsey experiments
3.2.1 Principle
3.2.2 Experimental results
3.3 Manipulation of the quantum state with adiabatic pulses: Z rotations
3.3.1 Principle
3.3.2 Experimental setup and results
3.4 Implementation of more robust operations
3.4.1 Composite rotations
3.4.2 Fidelity of unitary operations
3.4.3 The CORPSE sequence
3.4.4 Implementation of a robust NOT operation
3.5 Conclusion
4 Analysis of decoherence in the quantronium
4.1 Introduction
4.1.1 Decoherence
4.1.2 Decoherence in superconducting quantum bits
4.1.3 Decoherence sources in the Quantronium circuit
4.2 Theoretical description of decoherence
4.2.1 Expansion of the Hamiltonian
4.2.2 Depolarization (T1)
4.2.3 Pure dephasing
4.2.4 1=f noise: a few strongly coupled °uctuators versus many weakly coupled ones
4.2.5 Decoherence during driven evolution
4.3 Experimental characterization of decoherence during free evolution
4.3.1 Longitudinal relaxation: time T1
4.3.2 Transverse relaxation: coherence time T2
4.3.3 Echo time TE
4.3.4 Discussion of coherence times
4.4 Decoherence during driven evolution
4.4.1 Coherence time ~ T2 determined from Rabi oscillations
4.4.2 Relaxation time ~ T1 determined from spin-locking experiments
4.5 Decoherence mechanisms in the quantronium: perspectives, and conclusions
4.5.1 Summary of decoherence mechanisms in the quantronium
4.5.2 Does driving the qubit enhance coherence?
4.5.3 Coherence and quantum computing
5 Towards a Non Demolition measurement of the quantronium
5.1 Readout strategies
5.1.1 Drawbacks of the switching readout
5.1.2 New dispersive strategies
5.2 The Josephson bifurcation ampli¯er
5.2.1 Principle of the qubit state discrimination
5.2.2 Dynamics of the JBA at zero temperature
5.2.3 Solution stability and dynamics in the quadrature phase-space
5.2.4 Theory at ¯nite temperature
5.2.5 Dykman’s approach of the bifurcation
5.3 Experimental characterization of the JBA
5.4 Measurement of the qubit with a JBA
5.4.1 Characterization of the QND behavior of the readout
5.5 Conclusion
6 Conclusions and perspectives
