|
| related topics |
| {time, systems, information} |
| {algorithm, log, probability} |
| {let, theorem, proof} |
| {error, code, errors} |
| {state, algorithm, problem} |
| {qubit, qubits, gate} |
| {information, entropy, channel} |
|
Reversibility and Adiabatic Computation: Trading Time and Space for
Energy
Ming Li, Paul Vitanyi
abstract: 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/9703022
- categories:
- quant-ph cs.CC cs.CE cs.DS
- comments:
- 30 pages, Latex. Lemma 2.3 should be replaced by the slightly better
``There is a winning strategy with $n+2$ pebbles and $m-1$ erasures for
pebble games $G$ with $T_G= m2^n$, for all $m \geq 1$'' 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/9703009
- doi:
- 10.1098/rspa.1996.0039
- arxiv_id:
- quant-ph/9703022
- journal_ref:
- Proc. Royal Society of London, Series A, 452(1996), 769-789
- created:
- 1997-03-13
Full article ▸
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