Principles of Superconducting Quantum Computers

4 Superconducting Quantum Computer Systems

With the high-level description in Section 1.10 as motivation, in this chapter we consider the components of the superconducting quantum computer system and their operation in more detail. At RF and microwave frequencies, care must be taken about how components are connected. In particular, when the wavelength of the signal is comparable to circuit/system dimensions, familiar low-frequency circuit concepts such as Kirchoff’s voltage law no longer hold. Instead, we must look at the connections between all of the components as transmission lines and ensure that we are treating the signals conveyed by these transmission lines correctly. Consequently we begin our in-depth consideration of the system components with transmission lines.

4.1 Transmission Lines

4.1.1 General Transmission Line Equations

One type of transmission line that can be used at radio frequencies is the “ladder line” shown in Figure 4.1. In this type of line, the conductor distance is maintained by insulating spacers placed at regular intervals. As suggested in the diagram, currents flow in the conductors when signals are traveling along the line. These currents create magnetic fields encircling the wires resulting in a small amount of inductance per unit length. Since real, normal metals also have some small electrical resistance, the currents also see a small resistance per unit length. Similarly, the two conductors may have different potentials at a given location ...