Chapter 2 - Qubits and Collections of Qubits

Qubits and Collections of Qubits

There are several parts to any quantum information processing task. Some of these were written down and discussed by David DiVincenzo in the early days of quantum computing research and are therefore called DiVincenzo’s requirements for quantum computing. These include, but are not limited to, the following, which will be discussed in this chapter. Other requirements will be discussed later.

Five requirements [3]:

1. Be a scalable physical system with well-defined qubits
2. Be initializable to a simple fiducial state such as |000...i
3. Have much longer decoherence times than gating times
4. Have a universal set of quantum gates
5. Permit qubit-specific measurements

The first requirement is a set of two-state quantum systems which can serve as qubits. The second is to be able to initialize the set of qubits to some reference state. In this chapter, these will be taken for granted. The third concerns noise and noise has become known by the term decoherence. The term decoherence has had a more precise definition in the past, but here it will usually be synomous with noise. Noise and decoherence will be the topics of later sections. The fourth and fifth will be discussed in this chapter.

Backwards is it? Not from a computer science perspective or from a motivational perspective. Besides, to a large extent, the first two rely very heavily on experimental physics and engineering. These topics are primarily beyond the scope of this introductory material, but will be treated superficially in Chapter 6.

Qubit States

As mentioned in the introduction, a qubit, or quantum bit, is represented by a two-state quantum system. It is referred to as a two-state quantum system, although there are many physical examples of qubits which are represented by two different states of a quantum system which has many available states. These two states are represented by the vectors $\left\vert {0}\right\rangle$ and $\left\vert {1}\right\rangle$ and qubit could be in the state $\left\vert {0}\right\rangle$, or the state $\left\vert {1}\right\rangle$, or a complex superposition of these two. A qubit state which is an arbitrary superposition is written as