Type YES into the blank below after reading the following: I…

Type YES into the blank below after reading the following: I understand I have to upload my work in the last question of the test.  Work submitted through email will have a deduction of points.  ONLY if there are extenuating circumstances and I have technical difficulties when uploading work, I am to screenshot the technical issue when submitting my work to my teacher through email. You can email Mr. Brown at wbrown@dwight.global or Mrs. Thul at lthul@dwight.global. Not leaving enough time at the end of the test is not a technical difficulty, you are to plan for the last 10 minutes to upload your work. There is only one attempt on the Week 21 Polygons & Quadrilaterals Exam B. I understand I am to enter my answer for each individual question inside the blank provided. 

To measure the state of a transmon qubit, we make use of the…

To measure the state of a transmon qubit, we make use of the capacitive coupling between the qubit and a resonator captured by the Hamiltonian H=g[σ+a+σ−a†]{“version”:”1.1″,”math”:”\(H = g [\sigma_+ a + \sigma_- a^\dagger]\)”}. Given that the qubit frequency ωq=(2π)5{“version”:”1.1″,”math”:”\(\omega_q = (2\pi)\, 5 \)”} GHz, the resonator frequency ωr=(2π)4{“version”:”1.1″,”math”:”\(\omega_r = (2\pi)\,4 \)”} GHz, and the capacitive coupling g=(2π)10{“version”:”1.1″,”math”:”\(g = (2\pi)\, 10\)”} MHz: Considering the qubit to be in the state |0⟩{“version”:”1.1″,”math”:”\(\vert 0 \rangle\)”}, what is the magnitude of the shift in the resonator’s frequency (assuming ℏ=1{“version”:”1.1″,”math”:”\(\hbar = 1\)”})?

What is the average flux carried by the first excited state…

What is the average flux carried by the first excited state of the quantum LC oscillator with resonant frequency ω0=(2π)×2GHz{“version”:”1.1″,”math”:”\(\omega_0 = (2\pi) \times 2 \, \text{GHz}\)”} ? Note that Φ0{“version”:”1.1″,”math”:”\(\Phi_0\) “} denotes the flux quantum.

Consider a quantum LC oscillator with capacitor energy EC/h=…

Consider a quantum LC oscillator with capacitor energy EC/h=100{“version”:”1.1″,”math”:”\(E_C/h = 100\)”} MHz and inductor energy EL/h=5{“version”:”1.1″,”math”:” \(E_L/h = 5\)”} GHz in its ground state. What is the fluctuation in flux Φzpf{“version”:”1.1″,”math”:”\(\Phi_\text{zpf}\)”} (expressed in terms of the magnetic flux quantum Φ0{“version”:”1.1″,”math”:”\(\Phi_0\)”})?

We have seen that to design a two-qubit gate, two transmon q…

We have seen that to design a two-qubit gate, two transmon qubits are capacitively coupled giving rise to a transverse coupling between the two transmon qubits. When on-resonance, the Hamiltonian of this interaction in the rotating wave approximation is given by H=g[σ−σ++σ+σ−]{“version”:”1.1″,”math”:”\(H = g [\sigma_- \sigma_+ + \sigma_+ \sigma_-]\)”}. What is the final state of the two qubits [up to an overall phase] starting from the initial state is |10⟩{“version”:”1.1″,”math”:”\(\vert 1 0 \rangle\)”} when the time duration for which the transmons are in-resonance is t=π/(4g){“version”:”1.1″,”math”:”\(t=\pi/(4g)\)”}?