As discussed in Part I of this book, a qubit can in principle be encoded using two energy levels in an atom or ion. These levels are frequently referred to as |g⧽ and |e⧽, suggesting the ground state and some excited state, but the actual choice of levels is made so as to optimize the behavior of the system, and it is common to use two hyperfine sublevels of the ground state. As usual, we will simply call the levels |0⧽ and |1⧽. A quantum computer must, of course, have more than one qubit, and this is achieved by using more than one atom or ion, with one qubit encoded on each physical object. In order to make this approach practical, however, it is essential to trap the atoms or ions so that they can be held in a well-controlled environment where they can easily be manipulated. This can be achieved using electric and magnetic fields.

The use of trapped ions was one of the first proposals for building quantum computers, and is still one of the best developed. Proposals involving trapped atoms are slightly more recent, and have both substantial advantages and disadvantages in comparison with trapped ions. These differences can ultimately be traced back to the fact that ions interact strongly with their environment and have long-range interactions with one another, while atoms interact more weakly and over shorter ranges. Comparing and contrasting the two approaches provides a useful general introduction to the problems underlying many other proposals.

Ion traps

It is relatively easy to trap an ion as it will interact strongly with an electric field through the Coulomb interaction.