Quantum computing

13

13.1 Qubits and their
properties 283
13.2 A quantum logic gate 287
13.3 Parallelism in quantum
computing 289
13.4 Summary of quantum
computers 291
13.5 Decoherence and
quantum error
correction 291
13.6 Conclusion 293

Further reading 294

Exercises 294

Quantum computing will be a revolutionary new form of computation in

the twenty-first century, able to solve problems inaccessible to classical

computers. However, building a quantum computer is very difficult, and

so far only simple logic gates have been demonstrated in experiments on

ions in a linear Paul trap. The ideas of quantum computing have also

been tested in experiments using nuclear magnetic resonance (NMR).

In the Paul trap, the ions sit in an ultra-high vacuum (pressure∼

10 −^11 mbar) so that collisions rarely happen, and the ions are well iso-

lated from the environment. We have seen that these conditions enable

extremely high-resolution spectroscopy of single ions because of the very

small perturbations to the energy levels. Quantum computing requires

more than one ion in the trap, and all of these ions must be cooled to the

lowest vibrational level to give a well-defined initial quantum state for

the system.^1 This presents a much greater experimental challenge than

(^1) Quantum computing requires precise
control of the motion of the ions, i.e.
their external degrees of freedom, as
well as their internal state|F, MF〉.
the laser cooling of a single ion to reduce Doppler broadening, but it has
been achieved in some experiments. The previous chapter describes the
physics of the linear Paul trap but for the purposes of this chapter we
simply assume that the trap produces a harmonic potential with strong
confinement in the radial direction, so that the ions lie in a line along its
z-axis, as shown in Fig. 13.1; their mutual electrostatic repulsion keeps
the ions far enough apart for them to be seen separately.
Fig. 13.1Astringoffourions in a linear Paul trap. Coulomb repulsion keeps the
ions apart and the gap corresponds to an ion in the dark state. In this experiment
two laser beams simultaneously excite strong and weak transitions to give quantum
jumps, as described in Section 12.6, so that each ion flashes on and off randomly. This
snapshot of the system at a particular time could be taken to represent the binary
number 1101. A quantum logic gate requires much more sophisticated techniques in
which laser pulses determine precisely the initial state of each individual ion in the
chain, as described in this chapter. Courtesy of Professors A. M. Steane and D. N.
Stacey, D. M. Lucas and co-workers, Physics department, University of Oxford.