Qubits of higher dimension

Question

In Quantum Computing, one usually looks at two-state-systems named qubits to perform a computation. One problem arises when the number of qubits is increased, because the whole system becomes in such a case very sensitive to noise. Some time ago, I stumbled across and article saying that the problem could be mitigated by using three-state-systems instead of the usual two-state-system-based qubits. This would allow for the whole system to have $3^n$ states instead of $2^n$ (if $n$ is the number of qubits), therefore reducing the amount of qubits needed for a quantum computer.

I would like to know, why this approach seems to get largely ignored and what are the specific problems regarding a quantum computing device consisting of three-state-systems compared to the traditional ones made of two-state-systems.

Answer 1

Qubits are the standard 'currency' in quantum information theory for the same reason that bits are in classical information theory. It is because they suffice for the treatment of many of the main ideas.

When it comes to practical considerations, then in the lab one uses whatever systems one can control most easily. In ion trap work, for example, it is very common to use more than two of the internal states of each ion to do some of the work of storing and processing information, but nonetheless it usually happens that just two per ion are best able to be protected against magnetic field noise and things like that. The move from 2 to $k$ states per entity makes a saving in the number of entities (e.g. atoms or flux loops or whatever) required to store a given body of information, but this is accompanied by an increase in the complexity of the operations required to manipulate those entities. For this reason the move from qubits to qutrits is not employed much (believe me, if it were a useful move then experimentalists would have made it immediately!)

One might also suggest using a very large number of internal states of a given entity, but then the control problem becomes insuperable. It is a very important property of quantum states that if one has a collection of $n$ qubits stored in $n$ separate systems then the sensitivity to noise scales only in proportion to $n$ or possibly $n^2$, whereas if one tries to use $2^n$ states of a single thing (e.g. internal energy levels) then the sensitivity to noise scales as $2^n$. This is one of the wonderful features of entanglement and lies close to the heart of why quantum computing is powerful.

Answer 2

As mentioned in comments, it is hard to prepare a qutrit system.

However, even with qubits you can reduce the noise as low as possible thanks to the threshold theorem which states that with sufficient number of ancilla qubits you can get rid of the noise. But the theorem does not state what is the sufficient number. In practice you have more qubits for removing the noise than for the implementation itself.

Another way how to reduce the noise is topological quantum computer which should be less sensitive to it than current designs. Unfortunately there is a lot engineering obstacles to construct such a computer, although Microsoft has made some progress. See this discussion for more information on the topological quantum computer construction.