Principles of Superconducting Quantum Computers

1 Qubits, Gates, and Circuits

1.1 Bits and Qubits

Digital systems that are most familiar are based on binary digits, or “bits.” Each bit can take on either the value “1” or “0,” and any arbitrary data can be represented by such a binary representation. In addition, any arbitrary logical operation can be implemented using bits. We will refer to these familiar systems as “classical” systems, since they are governed by the everyday laws of classical physics.

Quantum computing is different from classical computing in a number of significant ways. The fundamental unit of information in quantum computing is the qubit (pronounced “KEW-bit”), short for quantum bit. The capabilities and behavior of qubits are quite different than bits, and we begin by pointing out and discussing the key differences as a launching point for our study of quantum computing.

1.1.1 Circuits in Space vs. Circuits in Time

A simple classical logic circuit is represented by the NOT gate shown in Figure 1.1(a). The NOT gate turns a “0” into “1” and vice versa. In this circuit diagram the horizontal direction represents space, i.e., the input and output of the circuit are physically accessible from different points in the circuit, and they can be measured simultaneously.

Figure 1.1 Interpretation of classical versus ...