Week 9: Physical Implementation of Qubits: Superconducting Transmons

Coursework focused on A Quantum Engineer’s Guide to Superconducting Qubits.

Exercise 1

On the Bloch sphere, show the indicated operation.

a. Start at state $|0\rangle$ with gate $X$ for distance $90\degree$

b. Start at state $|1\rangle$ with gate $Y$ for distance $180\degree$

Exercise 2

Describe how a DC SQUID works.

SQUIDS (or Superconducting Quantum Interference Devices) are extremely sensitive magnetic flux detectors that operate at cryogenic temperatures (approximately 4.2 K or -268.95° C). Versatile, they are able to measure any physical quantity capable of being converted to a flux such as: magnetic fields, magnetic field gradients, current, voltage, displacement and magnetic susceptibility. Applications of SQUIDS include measurement of magnetic fields produced by the human brain, measurement of fluctuating geomagnetic fields of remote areas, detection of gravitational waves and, of course, the observation of spin noise in an arrangement of magnetic nuclei. DC SQUIDS are composed of two Josephson junctions connected in parallel in a superconducting loop where it can be operated with a steady current bias. The junctions are resistively shunted and if biased with a constant current will begin to oscillate the SQUID as Cooper pairs of electrons tunnel through the system. This is observed through the measurement of output voltage of the system. The SQUID is essentially a flux to voltage transducer.

Source:
SQUID Sensors: Fundamentals, Fabrication and Applications
H. Weinstock
Springer Science & Business Media, Dec 6, 2012