QUANTUM COMPUTING - Bio-Inspired and Nanoscale Integrated Computing - page 87

per operation, at up to about 50 giga-ops per second, with memory of about 10 to
100 giga-bytes, and in a volume of about 10 cm 2 . The volume scales as the number
of bits of storage.

Energy Bounds for QC. The conventional linear model of QC allows only
unitary state transformations and so by definition is reversible (with the
possible exception of the observation operation that does quantum state
reduction). Benioff [48] noted that as a consequence of the reversibility of
the unitary state transformations of QC, these transformations dissipate no
energy. But this does not consider (i) the precision of the amplitudes to be
preserved nor (ii) the expected time duration required to drive the
operation to completion. Gea-Banacloche [276] and Ozawa [277] indepen-
dently derived lower bounds on the energy needed to execute within a given
precision of the amplitudes and in a given time, an elementary qubit logical
operation on a quantum computer. They derived energy lower bounds
depending inversely on the time duration for the operation and on the
precision of the amplitudes to be preserved. Hence, for polynomial time
quantum computations requiring polynomial relative precision, the lower
bounds on energy are polynomial, though the constant factors could be a
limitation for practical implementations. (Recall that Bernstein, Vazirani
[50] proved that BQP computations can be done with unitary operations
specified by only logarithmic bits of precision, which corresponds to
relative precision e where e4 1 n O ð 1 Þ :

) These energy lower bound results
were stated to be independent of the nature of the physical system encoding
the qubits and under what the authors claimed normal circumstances in a
wide variety of conditions for implementations of quantum computers.
Nevertheless, the matter still appears to not be completely resolved, since
there may be physical implementations of quantum computers that do not
abide by their assumptions. Energy bounds for the quantum qubit logical
operations require better understanding and study, particularly with
respect to their dependence on the technology used.
Processing Rate of QC. In QC, the rate of execution unitary operations
largely depends on the implementation technology (see Section 3.9); certain
techniques can execute unitary operations in microseconds (e.g., bulk
NMR) and some might execute at microsecond or even picosecond rates
(e.g., photonic techniques for NMR). The time duration to do observation
can also be very short, but it may be highly dependent on the size of the
measuring apparatus and the required precision. (See the following
discussion on the observation operation and its volume).
Volume Bounds for QC. We now consider (perhaps more closely than usual
in the quantum literature) the volume bounds of QC. Potentially, the
modest volume bounds of QC may be the one significant advantage over
classical methods for computation. Due to the quantum parallelism (i.e., the
superposition of the basis states allows each basis state to exist in parallel),

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