QUANTUM COMPUTING - Bio-Inspired and Nanoscale Integrated Computing - page 86

classical parallelism, where the quantum superposition of basis states is encoded
using multiple molecules where each molecule is in a distinct basis state. If the
latter is true (each molecule is in a distinct basis state) then the volume may grow
grow exponentially with the number n of qubits, since each basis state may need to
be stored by at least one molecule, and the number of basis states can be 2 n . (See
Williams, Clearwater [23]) Also, even if each molecule is in some partially mixed
quantum state (see Zyczkowski et al. [275]), the volume may still need to grow very
large.)
In summary, some possible disadvantages of bulk QC that may make it
difficult to scale are (i) the inability to do observation (strong measurement with
quantum state reduction); (ii) the difficulty to do even a weak measurement
without the use of exponential volume; (iii) difficulty (possibly now resolved) to
obtain pure initial states without the use of exponential volume; and (iv) the
possibility that bulk QC is not a quantum phenomena at all (an unresolved
controversy within physics), and so may require use of exponential volume.
It is interesting to consider whether NNR can be scaled down from the
macroscopic to molecular level. DiVincenzo [255] and Wei et al. [256, 257] propose
doing QC using the nuclear spins of atoms or electrons in a single molecule.
The main advantages are (i) small volume and (ii) the long time duration
until decoherence (an advantage shared with NMR). The key difficulty of this
approach is the measurement of the state of each spin, which does not appear to be
feasible by the mechanical techniques for detection of magnetic resonance usually
used in NMR (which can only do detection of the spin for large ensembles of
atoms).
3.10. RESOURCE BOUNDS
In this chapter, we have discussed many applications of quantum computation
that provide advantages over classical methods of computation. Certain applica-
tions of QC (e.g., quantum cryptography) require only a small or constant number
of qubits, whereas other applications (e.g., factoring and database search) require
a large number of qubits and moreover require an observation operation at least
as the final step of the QC. For these advantages to be practical, we need to
determine that there are no unfeasible, large resources required by QC. Hence we
complete the chapter with a review of the resource bounds of quantum computing
compared to the resources required by classical methods for computation. In
particular, we will conclude that for the advantages of QC (with a large number of
qubits) to be practical for applications requiring a large number of qubits, there
needs to be determined (theoretical and practically) bounds on the volume
required of observation operations. This seems to us a major missing element in
the field of QC.
The energy consumption, processing rate, and volume are all important
resources to consider in computing devices. Conventional (classical) electronic
supercomputers of the size of a work station operate in the range of 10 9 Joules