# Quantum Information and Quantum Optics with Superconducting Circuits - Exercise Solutions (Chapter 8)

8.1 By expanding the tensor product, we have the all possible binary numbers.As discussed in 6.1.4, for a single qubit, Hadamard gate can be implemented as: using the coherent drive: that's on resonance and .To apply it to identical flux q…

# Derivation of Input-Output relations for waveguide-QED

Target system The system is similar to the following one.enakai00.hatenablog.comHere we restrict the states with only one excitation (either qubit or a propagating photon). --- (7.13)The Heisenberg equations are: --- (7.14)Using the same a…

# Detailed derivation of the Input-Output theory

Basic definitions Think of a system consisted of: A long waveguide with length accommodating a photon field . A small resonator at accommodating an electric oscillation . that has the RWA Hamiltonian (5.60): --- (5.60)where we use the unit…

# Quantum Information and Quantum Optics with Superconducting Circuits - Exercise Solutions (Chapter 7)

7.1 Using the unit system and adding constant to the total energy, the Hamiltonian is: The anzatz is: where Then, Hence, from the Schroedinger equation , we have: 7.2 From (5.61), we have a Langevin equation for the qubit's amplitude. We i…

# Quantum Information and Quantum Optics with Superconducting Circuits - Exercise Solutions (Chapter 6) : Part2

6.10 (1) Define as: Then, So, the interaction Hamiltonian is: Since: We have: By dropping the non-RWA terms such as , we have: (2) By dropping the third state, we have: For Hence, from the Schroedinger equation: , we have: --- (1) --- (2)B…

# Quantum Information and Quantum Optics with Superconducting Circuits - Exercise Solutions (Chapter 6) : Part1

6.1 Unitary operation for a rotation around axis is: An operator to swap x and y is: An operator to swap x and z is: 6.2 The general solution to the linear interaction case is given by (5.10) as: Note that this is valid not only for , but …

# Quantum Information and Quantum Optics with Superconducting Circuits - Exercise Solutions (Chapter 5)

5.1 You can redefine with the same commutation relation .So you can set without losing the generality of the discussion.Now, and, Hence, By scaling back with , For and , use the relationship 5.2 gist.github.com 5.3 Hence, the coherent stat…