6 Introduction
At the present time there exist several approaches to the problem of
realizing a quantum computer.
1. Individual atoms or ions. This first-proposed and best-developed idea
exists in several variants. For representing a quantum bit one can employ
both the usual electron levels and the levels of fine and superfine structures.
There is an experimental technique for keeping an individual ion or atom in
the trap of a steady magnetic or alternating electric field for a reasonably
long time (of the order of 1 hour). The ion can be “cooled down” (i.e.,
its vibrational motion eliminated) with the aid of a laser beam. Selecting
the duration and frequency of the laser pulses, it is possible to prepare an
arbitrary superposition of the ground and excited states. In this way it
is rather easy to control individual ions. Within the trap, one can also
place two or more ions at distances of several microns one from another,
and control each of them individually. However, it is rather difficult to
choreograph the interactions between the ions. To this end it has been
proposed that collective vibrational modes (ordinary mechanical vibrations
with a frequency of several MHz) be used. Dipole-dipole interactions could
also be used, with the advantage of being a lot faster. A second method
(for neutral atoms) is as follows: place atoms into separate electromagnetic
resonators that are coupled to one another (at the moment it is unclear how
to achieve this technically). Finally, a third method: using several laser
beams, one can create a periodic potential (“optical lattice”) which traps
unexcited atoms. However, an atom in an excited state can move freely.
Thus, by exciting one of the atoms for a certain time, one lets it move
around and interact with its neighbors. This field of experimental physics
is now developing rapidly and seems to be very promising.
2. Nuclear magnetic resonance. In a molecule with several different
nuclear spins, an arbitrary unitary transformation can be realized by a suc-
cession of magnetic field pulses. This has been tested experimentally at
room temperature. However, for the preparation of a suitable initial state,
a temperature
10−3
K is required. Apart from difficulties with the cooling,
undesirable interactions between the molecules increase dramatically as the
liquid freezes. In addition, it is nearly impossible to address a given spin
selectively if the molecule has several spins of the same kind.
3. Superconducting granules and “quantum dots”. Under super-
cool temperatures, the unique degree of freedom of a small (submicron size)
superconducting granule is its charge. It can change in magnitude by a
multiple of two electron charges (since electrons in a superconductor are
bound in pairs). Changing the external electric potential, one can achieve
a situation where two charge states have almost the same energy. These
two states can be used as basis states of a quantum bit. The granules in-
teract with each other by means of Josephson junctions and mutual electric
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