292 Quantum computing
a few qubits to demonstrate the principle of some elementary opera-
tions. These experiments all use state-of-the-art techniques, but for
large systems the external perturbations blur the entangled states so
that they cannot be distinguished from each other, e.g. for ions in the
Paul trap the electrical noise on the radio-frequency electrodes causes
random changes of the phase of the states within a superposition. In the(^10) At that time NMR experiments used year 2000 the best ion trap experiment was limited to four qubits. (^10) De-
up to seven qubits. coherence quickly causes a system of many qubits to become so muddled
up that it is impossible to pick out the required output. In contrast, in a
classical computer errors which change 0 into 1, or the other way round,
occur extremely rarely, and present-day computers have procedures for
correcting errors so that they have a negligible effect.
Decoherence was thought to be an incurable disease in real quan-
tum systems that would prevent quantum information processing from
ever being carried out with enough qubits to make it really useful. How-
ever, a new cunning way of encoding information has been invented that
cures the symptoms of decoherence. So-called quantum error correction
(QEC) exploits the subtle features of the theory of quantum mechanics
to get rid of the small amounts of the unwanted states that gradually
get mixed into the states containing the quantum information by per-
turbations on the system. Broadly speaking, making a certain type of
quantum measurement causes the wavefunction of the system of qubits
to ‘collapse’, in a way that destroys any additional phase or amplitude in-
troduced by decoherence. This measurement must be made with respect
to a very carefully chosen basis of eigenstates to preserve the entangle-
ment of the wavefunction. Clearly, it is not adequate to make a simple
measurement that causes quantum superpositions to collapse into just
one of the states within the superposition, since this would completely
(^11) QEC manages to make measure- destroy the coherence between the states that we want to preserve. 11
ments on eigenstates that are in some
sense orthogonal to those in the origi-
nal superposition. These special quan-
tum measurements cause the small ad-
mixture of other states introduced into
the wavefunction by the noise to col-
lapse to zero. The QEC measurements
are performed on extra qubits entan-
gled with the qubits in the quantum
register; measurements made on these
ancillaryqubits do not reduce the size
of the superposition state that stores
quantum information (in the register),
i.e. the number of qubits in the su-
perposition is preserved in QEC. The
technical details of this process are ex-
plained in Steane (1998). Some elemen-
tary aspects of QEC can be appreciated
by analogy with the quantum Zeno ef-
fect described in Exercise 13.5.
In the context of ion traps, the recent advances in quantum com-
puting and QEC can be regarded as the latest steps in the evolution
of spectroscopy and laser cooling, as illustrated by the following rough
history.
(1) The first spectroscopists observed light from discharge lamps, e.g.
the Balmer lines in atomic hydrogen. They used spectrographs and
́etalons and the resolution was limited by Doppler broadening, to-
gether with collisions and other broadening mechanisms in the dis-
charge.
(2) Atomic beams allowed experimenters to change the population be-
tween the various energy levels of the atoms, using radio-frequency
or microwave radiation to manipulate hyperfine and Zeeman levels
in the ground state. (Optical pumping was applied to the ground
states of certain atoms.) Atoms were deflected slightly in the Stern–
Gerlach experiment but without a significant change in speed. The
laser extended these techniques to the higher levels using optical
transitions, so that, in principle, atomic physics experiments can
manipulate the internal states of the atoms and put atoms into any