Classical computer memories

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Table of contents

1 Introduction 
1.1 Quantum information
1.2 Quantum error correction
1.2.1 Classical error correction
1.2.2 Bit-flip Correction
1.3 Classical computer memories
1.3.1 Dynamic RAM
1.3.2 Static RAM
1.3.3 Conclusions
1.4 Bistable systems in classical mechanics
1.4.1 Driven oscillator
1.4.2 Parametric oscillator
1.5 Superconducting circuits
1.6 Outline
2 Hamiltonian and dissipation engineering with superconducting circuits
2.1 Circuit quantization
2.1.1 Circuit description
2.1.2 Equations of motion
2.1.3 Quantization
2.1.4 AC Biases
2.2 Engineering dynamics
2.2.1 Hamiltonian engineering
2.2.2 Dissipation engineering
3 Parametric pumping with a transmon 
3.1 The Transmon qubit
3.1.1 Low energy behaviour
3.1.2 Full description
3.2 Quantum dynamics of a driven transmon
3.2.1 Description of the experiment
3.2.2 Observing the transmon escape into unconfined states
3.2.3 Effect of pump-induced quasiparticles
3.3 Additional Material
3.3.1 Sample fabrication
3.3.2 Photon number calibration
3.3.3 Multi-photon qubit drive
3.3.4 Charge noise
3.3.5 Numerical simulation
3.3.6 Quasiparticle generation
4 Exponential bit-flip suppression in a cat-qubit 
4.1 Protecting quantum information in a resonator
4.1.1 General considerations
4.1.2 The bosonic codes
4.2 Exponential bit-flip suppression in a cat-qubit
4.2.1 The dissipative cat-qubits
4.2.2 Engineering two-photon coupling to a bath
4.2.3 Coherence time measurements
4.3 Additional Material
4.3.1 Full device and wiring
4.3.2 Hamiltonian derivation
4.3.3 Circuit parameters
4.3.4 Semi-classical analysis
4.3.5 Bit-flip time simulation
4.3.6 Tuning the cat-qubit
5 Itinerant microwave photon detection 
5.1 Dissipation engineering for photo-detection
5.1.1 Engineering the Qubit-Cavity dissipator
5.1.2 Efficiency
5.1.3 Dark Counts
5.1.4 Detector Reset
5.1.5 QNDness
5.2 Additional Material
5.2.1 Circuit parameters
5.2.2 Purcell Filter
5.2.3 System Hamiltonian derivation
5.2.4 Adiabatic elimination of the waste mode
5.2.5 Qubit dynamics and detection efficiency
5.2.6 Reset protocol
5.2.7 Spectroscopic characterization of the detector
5.2.8 Tomography of the itinerant transmitted photon
Conclusion and perspectives 
A Circuit quantization
A.1 LC-oscillator
A.2 General Circuit quantization
B Native couplings in superconducting circuits
B.1 Capacitively coupled resonators
B.2 Mutual inductances in superconducting loops
B.3 Inductively coupled resonators
C Useful Formulae
C.1 Miscellaneous
C.2 Standard changes of frame
D Classical mechanical analogy to the stabilisation of cat-qubits
E Fabrication Recipes
E.1 Wafer preparation
E.2 Circuit patterning
E.3 Junction fabrication
Bibliography