QUANTUM COMPUTING - Bio-Inspired and Nanoscale Integrated Computing - page 84

Of these, ion trap QC, cavity QED QC, and photonics have been experimen-
tally demonstrated up to a very small number of qubits (about three bits). The
apparent intention of such micromolecular methods for QC is to have an
apparatus for storing qubits and executing unitary operations (but not necessarily
executing observation operations) which requires only volume linear in the
number of qubits. One difficulty (addressed by Kak [259], and Murao et al.
[260]) is purification of the initial state: If the state of a QC is initially in an
entangled state, and each of the quantum gate transformations introduces phase
uncertainty during the QC, then the effect of these perturbations may accumulate
to make the output to the QC incorrect. A more basic difficulty for these
micromolecular methods is that they all use experimental technology that is not
well established; in particular, their approaches each involve containment of
atomic size objects (such as individual atoms, ions, or photons) and manipulations
of their states. A further difficulty of the micromolecular methods for QC is that
apparatus for the observation operation—even if observation is approximated—
seems to require volume growing exponential with the number of qubits, as
described earlier in this paper.
(B) Bulk (or NMR) QC. Nuclear magnetic resonance (NMR) spectroscopy is
an imaging technology using the spin of the nuclei of a large collection of atoms.
Bulk QC is executed on a macroscopic volume containing a large number of
identical molecules in solution, each of which encodes all the qubits. The
molecule can be chosen so that it has n distinct quantized spins modes (e.g.,
each of the n nuclei may have a distinct quantized spins). Each of the n qubits is
encoded by one of these spin modes of the molecule. The coupling of qubits is via
spin-spin coupling between pairs of distinct nuclei. Unitary operations such as
XOR can be executed by radio frequency (RF) pulses at resonance frequencies
determined in part by this spin-spin coupling between pairs of nuclei (and also by
the chemical structure of the molecule). Bulk QC was independently proposed by
Cory, Fahmy, Havel [261] and Gershenfeld, Chuang [22, 262]. Also see Berman
et al. [266] and the proposal of Wei et al. [257] for doing NMR QC on doped
crystals rather than in solutions, and see Kane [264] for another solid state NMR
architecture for quantum computing using silicon.
Bulk QC. was experimentally tested (Jones et al. [265, 266]) and applied to
demonstrate the following tasks: quantum search (Jones [267]), approx-
imate quantum counting (Jones, Mosca [268]), Deutsch's problem (Jones,
Mosca [269]), and the Deutsch-Jozsa algorithm on 3 qubits (Linden,
Barjat, Freeman [270]).
Advantages of Bulk QC. (i) it can use well established NMR technology
and in particular macroscopic devices, The main advantages are (ii) the
long time duration until decoherence (due to a low coupling with the
environment) and (iii) scaling to more qubits than other proposed
technologies for QC.