Optical computing: Difference between revisions

Revision as of 21:55, 30 December 2022

Revision as of 02:03, 25 February 2023

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The basic idea is to delay light (or any other signal) in order to perform useful computations.<ref name="oltean_hamiltonian">{{cite conference|last=Oltean|first=Mihai|title= A light-based device for solving the Hamiltonian path problem |conference=Unconventional Computing| pages= 217–227| publisher= Springer LNCS 4135|doi=10.1007/11839132_18|date=2006|arxiv=0708.1496}}</ref> Of interest would be to solve [[NP-completeness|NP-complete problem]]s as those are difficult problems for the conventional computers.

There are 2two basic properties of light that are actually used in this approach:

* The light can be delayed by passing it through an optical fiber of a certain length.

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The first problem attacked in this way was the [[Hamiltonian path problem]].<ref name="oltean_hamiltonian"/>

The simplest one is the [[subset sum problem]].<ref>{{cite journal|author=Mihai Oltean, Oana Muntean| title = Solving the subset-sum problem with a light-based device|journal= Natural Computing| volume= 8| issue= 2|pages =321–331| doi=10.1007/s11047-007-9059-3| date=2009 |arxiv=0708.1964| s2cid = 869226}}</ref> An optical device solving an instance with 4four numbers {''a1, a2, a3, a4''} is depicted below:

[[File:Optical device for solving the Subset sum problem.png|Optical device for solving the Subset sum problem]]

The light will enter in Start node. It will be divided into 2two (sub)rays of smaller intensity. These 2two rays will arrive into the second node at moments ''a1'' and 0. Each of them will be divided into 2two subrays which

will arrive in the 3rdthird node at moments 0, ''a1'', ''a2'' and ''a1 + a2''. These represents the all subsets of the set {''a1, a2''}. We expect fluctuations in the intensity of the signal at no more than 4four different moments. In the destination node we expect fluctuations at no more than 16 different moments (which are all the subsets of the given). If we have a fluctuation in the target moment ''B'', it means that we have a solution of the problem, otherwise there is no subset whose sum of elements equals ''B''. For the practical implementation we cannot have zero-length cables, thus all cables are increased with a small (fixed for all) value ''k'. In this case the solution is expected at moment ''B+n*kn×k''.

===Wavelength-based computing===

Wavelength-based computing<ref>{{cite conference|author=Sama Goliaei, Saeed Jalili|title= An Optical Wavelength-Based Solution to the 3-SAT Problem|conference=Optical SuperComputing Workshop|date=2009|doi=10.1007/978-3-642-10442-8_10| pages=77–85|bibcode=2009LNCS.5882...77G}}</ref> can be used to solve the [[Boolean satisfiability problem#3-satisfiability|3-SAT]] problem with ''n'' variables, ''m'' clauses and with no more than 3three variables per clause. Each wavelength, contained in a light ray, is considered as possible value-assignments to ''n'' variables. The optical device contains prisms and mirrors are used to discriminate proper wavelengths which satisfy the formula.<ref>{{Cite journal|last1=Bartlett|first1=Ben|last2=Dutt|first2=Avik|last3=Fan|first3=Shanhui|date=2021-12-20|title=Deterministic photonic quantum computation in a synthetic time dimension|url=https://www.osapublishing.org/optica/abstract.cfm?uri=optica-8-12-1515|journal=Optica|language=EN|volume=8|issue=12|pages=1515–1523|doi=10.1364/OPTICA.424258|arxiv=2101.07786|bibcode=2021Optic...8.1515B|issn=2334-2536}}</ref>

===Computing by xeroxing on transparencies===

<!-- remember that "xerox" *is* a trademark, and something of an americanism: the globally-understood equivalent is photocopier, to photocopy, a photocopy -->

This approach uses a Xerox machinephotocopier and transparent sheets for performing computations.<ref>{{cite conference|last=Head|first=Tom|title= Parallel Computing by Xeroxing on Transparencies|conference= Algorithmic Bioprocesses|date= 2009|pages=631–637|publisher=Springer|doi=10.1007/978-3-540-88869-7_31}}</ref> [[Boolean satisfiability problem#3-satisfiability|k-SAT problem]] with ''n'' variables, ''m'' clauses and at most ''k'' variables per clause has been solved in 3three steps:<ref>{{Citation |title=Computing by xeroxing on transparencies |url=https://www.youtube.com/watch?v=4DeXPB3RU8Y |language=en |access-date=2022-08-14}}</ref>

* Firstly all 2^ⁿ possible assignments of ''n'' variables have been generated by performing ''n'' xerox copiesphotocopies.

This approach uses a Xerox machine and transparent sheets for performing computations.<ref>{{cite conference|last=Head|first=Tom|title= Parallel Computing by Xeroxing on Transparencies|conference= Algorithmic Bioprocesses|date= 2009|pages=631–637|publisher=Springer|doi=10.1007/978-3-540-88869-7_31}}</ref> [[Boolean satisfiability problem#3-satisfiability|k-SAT problem]] with n variables, m clauses and at most k variables per clause has been solved in 3 steps:<ref>{{Citation |title=Computing by xeroxing on transparencies |url=https://www.youtube.com/watch?v=4DeXPB3RU8Y |language=en |access-date=2022-08-14}}</ref>

* Using at most 2k2''k'' copies of the truth table, each clause is evaluated at every row of the truth table simultaneously.

* The solution is obtained by making a single copy operation of the overlapped transparencies of all ''m'' clauses.

* Firstly all 2^n possible assignments of n variables have been generated by performing n xerox copies.

* Using at most 2k copies of the truth table, each clause is evaluated at every row of the truth table simultaneously.

* The solution is obtained by making a single copy operation of the overlapped transparencies of all m clauses.

===Masking optical beams===