# Computing with quantum dots

The enormous success of the semiconductor fabrication industry has involved building devices that have structure in the nanometre range, and the ability to control such properties of the system as the conductivity, the electric potential and the semiconductor bandgap (the energy gap between the lower valence band and the upper conduction band which determines much of the behaviour of the semiconductor). It is not surprising that such structures have been the basis of a very large number of different proposals for implementation of quantum computation.

Many of these have utilized the idea of *quantum dots,* a quantum dot being a three-dimensional structure in which electrons may be confined, so that the energy of the electron in the dot has discrete levels. Typical sizes of quantum dots may be between 5 and 50 nm (or between 5 x 10^{-9 }and 5 x 1o^{-8} m).

Quantum dots may form spontaneously when one semiconductor material is deposited or absorbed onto a substrate of a different semiconductor. There are two factors involved in this process. First, the different macroscopic electrical properties of the two materials may lead to the flow of electric charge perpendicular to the surface, and this can cause a so-called *inversion layer,* or a potential minimum in a region parallel to and in the vicinity of the boundary between the two semiconductor species. Then the mismatch in the lattice constants (the interatomic spacings) of the two materials leads to movement of the atoms parallel to the surface in the vicinity of this boundary, and this can cause localized potential differences to develop within the inversion layer itself. The net result is the creation of potential minima in all three dimensions, or just the required quantum dots.

Two of the most promising suggestions for use of quantum dots in quantum computation have been the *charge qubit* and the *spin qubit. *The first uses the double quantum dot, which consists of two neighbouring quantum dots. The two states of the qubit, | 0) and |1), correspond to which of the two quantum dots is occupied; we can alternatively write them as | *L)* and | R), for whether the left- or right-hand quantum dot contains an extra electron. The qubit also includes five control gate electrodes to control the overall charge of the qubit, and the current into and out of the qubit.

On the DiVincenzo criteria, the charge quantum dot scheme can provide well-characterized qubits, and a rather more complicated scheme involving a GaAs/Al/GaAs heterostructure is potentially scalable using currently available semiconductor lithography technology. (Here GaAs is gallium arsenide, a much-used semiconductor, while Al is aluminium.) Already a two-qubit system has been fabricated and coupling has been demonstrated between the qubits.

Also initialization is easy, as one can merely inject electrons, but decoherence times are unfortunately short because charges fluctuate and phonons may be emitted. On the question of gates, one-qubit gates have been constructed, but no two-qubit gates have been produced so far. For the last criterion, measurement is relatively straightforward through investigation of the current tunneling from the qubit. Overall implementation of quantum computation by charge qubits is a promising scheme, but clearly substantial advances are still required for several of these criteria.

We now consider use of the spin qubit, which involves using the electron spin to encode the qubits. The technology to take advantage of this idea is given the rather nice name of *spintronics,* It is natural to compare the technique with that using NMR, which also uses spins, though, of course, nuclear ones. Spin-^{1}^ systems are always excellent candidates for qubits, as there are, of course, always exactly the two states. In atomic systems, for example, though our qubit may be formed from the two lowest energy levels, there are always many more actually in existence, and there will be some leakage of electrons to and from these levels.

Another advantage of spin qubits, particularly as compared with charge qubits, is that decoherence times can be as high as a few millionths of a second, because the spins are coupled only rather weakly to the environment. Also electron spins are coupled to magnetic fields much more strongly than nuclear spins, because although the charges of nuclei and electrons are of the same magnitude, the mass of the electron is only about 1000 that of the nucleus, and coupling to magnetic field is inversely proportional to mass. This means that gate operations can be much faster than for NMR.

Actually it is possible to combine the advantages of fast gates for electron spins and long decoherence times for nuclear spins by storing the information with nuclear spins, but changing it to electronic spins for processing.

Let us now turn to the DiVincenzo criteria for spin qubits. The technique is expected to be scalable with current semiconductor lithographic technology, and initialization may also be achieved by electron injection. Unfortunately addressing of individual spins has not been demonstrated yet. As we have just said, a great advantage of the scheme is that decoherence times may be much greater than gate operation times. The last criterion of measurement can also be achieved by measurement of tunnelling current.

However, the provision of a universal set of quantum gates as yet presents serious difficulties, mainly because of the difficulty of addressing individual qubits. So, as with charge qubits, though some of the DiVincenzo criteria are met extremely well, others still prevent difficulties yet to be resolved. In fact that same comment might be extended to the whole field of quantum computation using solids, where there have been far more approaches than have been described here. With all the promise of the field, it is disappointing that, as yet, no clear way has been found to making at least substantial progress towards quantum computation.