71,484 research outputs found
ROM-based computation: quantum versus classical
We introduce a model of computation based on read only memory (ROM), which
allows us to compare the space-efficiency of reversible, error-free classical
computation with reversible, error-free quantum computation. We show that a
ROM-based quantum computer with one writable qubit is universal, whilst two
writable bits are required for a universal classical ROM-based computer. We
also comment on the time-efficiency advantages of quantum computation within
this model.Comment: 12 pages, 3 figures, minor corrections + section 5 substantially
change
Reversible Simulation of Irreversible Computation by Pebble Games
Reversible simulation of irreversible algorithms is analyzed in the stylized
form of a `reversible' pebble game. While such simulations incur little
overhead in additional computation time, they use a large amount of additional
memory space during the computation. The reacheable reversible simulation
instantaneous descriptions (pebble configurations) are characterized
completely. As a corollary we obtain the reversible simulation by Bennett and
that among all simulations that can be modelled by the pebble game, Bennett's
simulation is optimal in that it uses the least auxiliary space for the
greatest number of simulated steps. One can reduce the auxiliary storage
overhead incurred by the reversible simulation at the cost of allowing limited
erasing leading to an irreversibility-space tradeoff. We show that in this
resource-bounded setting the limited erasing needs to be performed at precise
instants during the simulation. We show that the reversible simulation can be
modified so that it is applicable also when the simulated computation time is
unknown.Comment: 11 pages, Latex, Submitted to Physica
Reversible Computation in Term Rewriting
Essentially, in a reversible programming language, for each forward
computation from state to state , there exists a constructive method to
go backwards from state to state . Besides its theoretical interest,
reversible computation is a fundamental concept which is relevant in many
different areas like cellular automata, bidirectional program transformation,
or quantum computing, to name a few.
In this work, we focus on term rewriting, a computation model that underlies
most rule-based programming languages. In general, term rewriting is not
reversible, even for injective functions; namely, given a rewrite step , we do not always have a decidable method to get from
. Here, we introduce a conservative extension of term rewriting that
becomes reversible. Furthermore, we also define two transformations,
injectivization and inversion, to make a rewrite system reversible using
standard term rewriting. We illustrate the usefulness of our transformations in
the context of bidirectional program transformation.Comment: To appear in the Journal of Logical and Algebraic Methods in
Programmin
Reversibility and Adiabatic Computation: Trading Time and Space for Energy
Future miniaturization and mobilization of computing devices requires energy
parsimonious `adiabatic' computation. This is contingent on logical
reversibility of computation. An example is the idea of quantum computations
which are reversible except for the irreversible observation steps. We propose
to study quantitatively the exchange of computational resources like time and
space for irreversibility in computations. Reversible simulations of
irreversible computations are memory intensive. Such (polynomial time)
simulations are analysed here in terms of `reversible' pebble games. We show
that Bennett's pebbling strategy uses least additional space for the greatest
number of simulated steps. We derive a trade-off for storage space versus
irreversible erasure. Next we consider reversible computation itself. An
alternative proof is provided for the precise expression of the ultimate
irreversibility cost of an otherwise reversible computation without
restrictions on time and space use. A time-irreversibility trade-off hierarchy
in the exponential time region is exhibited. Finally, extreme
time-irreversibility trade-offs for reversible computations in the thoroughly
unrealistic range of computable versus noncomputable time-bounds are given.Comment: 30 pages, Latex. Lemma 2.3 should be replaced by the slightly better
``There is a winning strategy with pebbles and erasures for
pebble games with , for all '' with appropriate
further changes (as pointed out by Wim van Dam). This and further work on
reversible simulations as in Section 2 appears in quant-ph/970300
Are all reversible computations tidy?
It has long been known that to minimise the heat emitted by a deterministic
computer during it's operation it is necessary to make the computation act in a
logically reversible manner\cite{Lan61}. Such logically reversible operations
require a number of auxiliary bits to be stored, maintaining a history of the
computation, and which allows the initial state to be reconstructed by running
the computation in reverse. These auxiliary bits are wasteful of resources and
may require a dissipation of energy for them to be reused. A simple procedure
due to Bennett\cite{Ben73} allows these auxiliary bits to be "tidied", without
dissipating energy, on a classical computer. All reversible classical
computations can be made tidy in this way. However, this procedure depends upon
a classical operation ("cloning") that cannot be generalised to quantum
computers\cite{WZ82}. Quantum computations must be logically reversible, and
therefore produce auxiliary qbits during their operation. We show that there
are classes of quantum computation for which Bennett's procedure cannot be
implemented. For some of these computations there may exist another method for
which the computation may be "tidied". However, we also show there are quantum
computations for which there is no possible method for tidying the auxiliary
qbits. Not all reversible quantum computations can be made "tidy". This
represents a fundamental additional energy burden to quantum computations. This
paper extends results in \cite{Mar01}.Comment: 7 pages, 1 figure ep
Logics between classical reversible logic and quantum logic
Classical reversible logic and quantum computing share the common feature that all computations are reversible, each result of a computation can be brought back to the initial state without loss of information
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