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{{main|Model of computation}}
A model of computation describes how the output of a mathematical function is computed given its input. The model describes how units of computations, memories, and communications are organized.<ref>{{cite book|last=Savage|first=John E.|author-link = John E. Savage|title=Models Of Computation: Exploring the Power of Computing|year=1998|publisher=Addison-Wesley|isbn= {{Format ISBN|978-0201895391}}}}</ref> The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology.
A wide variety of models are commonly used; some closely resemble the workings of (idealized) conventional computers, while others do not. Some commonly used models are [[register machine]]s, [[random-access machine]]s, [[Turing machine]]s, [[lambda calculus]], [[rewriting system]]s, [[digital circuit]]s, [[cellular automaton|cellular automata]], and [[Petri net]]s.
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{{main|analog computer}}
An analog computer is a type of computer that uses ''[[analog signal]]s'', which are continuous physical quantities, to model and solve problems. These signals can be [[Electrical network|electrical]], [[Mechanics|mechanical]], or [[Hydraulics|hydraulic]] in nature. Analog computers were widely used in scientific and industrial applications, and were often faster than digital computers at the time. However, they started to become obsolete in the 1950s and 1960s and are now mostly used in specific applications such as aircraft flight simulators and teaching control systems in universities.<ref name="Johnston">{{cite book | url=https://books.google.com/books?id=iPfU_powAgAC&q=%22through%20the%201980s%22&pg=PA90 | title=Holographic Visions: A History of New Science | publisher=OUP Oxford | author=Johnston, Sean F. | year=2006 |
===Electronic digital computers===
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===Reservoir computing===
{{main|Reservoir computing}}
Reservoir computing is a computational framework derived from recurrent neural network theory that involves mapping input signals into higher-dimensional computational spaces through the dynamics of a fixed, non-linear system called a reservoir. The reservoir, which can be virtual or physical, is made up of individual non-linear units that are connected in recurrent loops, allowing it to store information. Training is performed only at the readout stage, as the reservoir dynamics are fixed, and this framework allows for the use of naturally available systems, both classical and quantum mechanical, to reduce the effective computational cost. One key benefit of reservoir computing is that it allows for a simple and fast learning algorithm, as well as hardware implementation through [[Reservoir computing#Physical reservoir computers|physical reservoirs]].<ref>{{Cite journal|last1=Tanaka|first1=Gouhei|last2=Yamane|first2=Toshiyuki|last3=Héroux|first3=Jean Benoit|last4=Nakane|first4=Ryosho|last5=Kanazawa|first5=Naoki|last6=Takeda|first6=Seiji|last7=Numata|first7=Hidetoshi|last8=Nakano|first8=Daiju|last9=Hirose|first9=Akira|date=2019-07-01|title=Recent advances in physical reservoir computing: A review|journal=Neural Networks|language=en|volume=115|pages=100–123|doi=10.1016/j.neunet.2019.03.005|pmid=30981085 |issn=0893-6080|doi-access=free|arxiv=1808.04962}}</ref><ref>{{Cite journal|last1=Röhm|first1=André|last2=Lüdge|first2=Kathy|date=2018-08-03|title=Multiplexed networks: reservoir computing with virtual and real nodes|journal=Journal of Physics Communications|volume=2|issue=8|
===Tangible computing===
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[[File:SandScape.jpg|thumb|upright=0.7|[http://tangible.media.mit.edu/project/sandscape/ SandScape], a tangible computing device installed in the [[Children's Creativity Museum]] in San Francisco]]
Tangible computing refers to the use of physical objects as user interfaces for interacting with digital information. This approach aims to take advantage of the human ability to grasp and manipulate physical objects in order to facilitate collaboration, learning, and design. Characteristics of tangible user interfaces include the coupling of physical representations to underlying digital information and the embodiment of mechanisms for interactive control.<ref>{{cite book |doi=10.1145/1347390.1347392 |chapter=Tangible bits |title=Proceedings of the 2nd international conference on Tangible and embedded interaction - TEI '08 |year=2008 |last1=Ishii |first1=Hiroshi |
===Human computing===
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===Spintronics===
{{main|Spintronics}}
Spintronics is a field of study that involves the use of the intrinsic spin and magnetic moment of electrons in solid-state devices.<ref>{{Cite journal | last1 = Wolf | first1 = S. A. | last2 = Chtchelkanova | first2 = A. Y. | last3 = Treger | first3 = D. M. | title = Spintronics—A retrospective and perspective | doi = 10.1147/rd.501.0101 | journal = IBM Journal of Research and Development | volume = 50 | pages = 101–110 | year = 2006 }}</ref><ref>{{Cite web|url=http://video.google.com/videoplay?docid=2927943907685656536&q=LevyResearch&ei=dxd1SNCtOqj2rAKxzf1p|title=Physics Profile: "Stu Wolf: True D! Hollywood Story"|access-date=2022-12-30|archive-date=2011-04-18|archive-url=https://web.archive.org/web/20110418015231/http://video.google.com/videoplay?docid=2927943907685656536
===Atomtronics===
{{main|Atomtronics}}
Atomtronics is a form of computing that involves the use of ultra-cold atoms in coherent matter-wave circuits, which can have components similar to those found in electronic or optical systems.<ref>{{Cite journal |last1=Amico |first1=L. |last2=Boshier |first2=M. |last3=Birkl |first3=G. |last4=Minguzzi |first4=A.|author4-link=Anna Minguzzi |last5=Miniatura |first5=C. |last6=Kwek |first6=L.-C. |last7=Aghamalyan |first7=D. |last8=Ahufinger |first8=V. |last9=Anderson |first9=D. |last10=Andrei |first10=N. |last11=Arnold |first11=A. S. |last12=Baker |first12=M. |last13=Bell |first13=T. A. |last14=Bland |first14=T. |last15=Brantut |first15=J. P. |year=2021 |title=Roadmap on Atomtronics: State of the art and perspective |url=https://avs.scitation.org/doi/10.1116/5.0026178 |journal=AVS Quantum Science |language=en |volume=3 |issue=3 |
===Fluidics===
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{{main|Quantum computing}}
Quantum computing, perhaps the most well-known and developed unconventional computing method, is a type of computation that utilizes the principles of quantum mechanics, such as [[quantum superposition|superposition]] and entanglement, to perform calculations.<ref name="Hidary">{{cite book | last=Hidary | first=Jack | title=Quantum computing
=== Neuromorphic quantum computing ===
Neuromorphic Quantum Computing<ref>{{Cite journal |title=Neuromrophic Quantum Computing {{!}} Quromorphic Project {{!}} Fact Sheet {{!}} H2020 |url=https://cordis.europa.eu/project/id/828826 |access-date=2024-03-18 |website=CORDIS {{!}} European Commission |language=en |doi=10.3030/828826}}</ref><ref>{{Citation |last1=Pehle |first1=Christian |title=Neuromorphic quantum computing |date=2021-03-30 |arxiv=2005.01533 |last2=Wetterich |first2=Christof|journal=Physical Review E |volume=106 |issue=4 |page=045311 |doi=10.1103/PhysRevE.106.045311 |bibcode=2022PhRvE.106d5311P }}</ref> (abbreviated as 'n.quantum computing') is an unconventional type of computing that uses [[Neuromorphic engineering|neuromorphic computing]] to perform quantum operations. It was suggested that [[Quantum algorithm|quantum algorithms]], which are algorithms that run on a realistic model of [[Quantum computing|quantum computation]], can be computed equally efficiently with neuromorphic quantum computing.<ref>{{Cite journal |last1=Carleo |first1=Giuseppe |last2=Troyer |first2=Matthias |date=2017-02-10 |title=Solving the quantum many-body problem with artificial neural networks |url=https://www.science.org/doi/10.1126/science.aag2302 |journal=Science |language=en |volume=355 |issue=6325 |pages=602–606 |doi=10.1126/science.aag2302 |pmid=28183973 |issn=0036-8075|arxiv=1606.02318 |bibcode=2017Sci...355..602C }}</ref><ref>{{Cite journal |last1=Torlai |first1=Giacomo |last2=Mazzola |first2=Guglielmo |last3=Carrasquilla |first3=Juan |last4=Troyer |first4=Matthias |last5=Melko |first5=Roger |last6=Carleo |first6=Giuseppe |date=2018-02-26 |title=Neural-network quantum state tomography |url=https://www.nature.com/articles/s41567-018-0048-5 |journal=[[Nature Physics]] |language=en |volume=14 |issue=5 |pages=447–450 |doi=10.1038/s41567-018-0048-5 |issn=1745-2481|arxiv=1703.05334 |bibcode=2018NatPh..14..447T }}</ref><ref>{{Cite journal |last1=Sharir |first1=Or |last2=Levine |first2=Yoav |last3=Wies |first3=Noam |last4=Carleo |first4=Giuseppe |last5=Shashua |first5=Amnon |date=2020-01-16 |title=Deep Autoregressive Models for the Efficient Variational Simulation of Many-Body Quantum Systems |url=https://link.aps.org/doi/10.1103/PhysRevLett.124.020503 |journal=Physical Review Letters |volume=124 |issue=2 |
Both traditional [[quantum computing]] and neuromorphic quantum computing are physics-based unconventional computing approaches to computations and don't follow the [[von Neumann architecture]]. They both construct a system (a circuit) that represents the physical problem at hand, and then leverage their respective physics properties of the system to seek the "minimum". Neuromorphic quantum computing and [[quantum computing]] share similar physical properties during computation<ref name="DiVentra2022" /><ref>{{Cite journal |last1=Wilkinson |first1=Samuel A. |last2=Hartmann |first2=Michael J. |date=2020-06-08 |title=Superconducting quantum many-body circuits for quantum simulation and computing
===Superconducting computing===
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{{main|Microelectromechanical systems|Nanoelectromechanical systems}}
Microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) are technologies that involve the use of microscopic devices with moving parts, ranging in size from micrometers to nanometers. These devices typically consist of a central processing unit (such as an integrated circuit) and several components that interact with their surroundings, such as sensors.<ref>{{cite book|title=Nanocomputers and Swarm Intelligence|vauthors=Waldner JB|publisher=[[ISTE Ltd|ISTE]] [[John Wiley & Sons]]|year=2008|isbn={{Format ISBN|9781848210097}}|place=London|
==Chemistry approaches==
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{{main|Molecular scale electronics|Chemical computing|Molecular logic gate}}
Molecular computing is an unconventional form of computing that utilizes chemical reactions to perform computations. Data is represented by variations in chemical concentrations,<ref name="ijirt.org">{{cite journal |url=http://www.ijirt.org/paperpublished/IJIRT101166_PAPER.pdf |title=Chemical Computing: The different way of computing|first1=Ambar |last1=Kumar|first2=Akash Kumar | last2 =Mahato| first3=Akashdeep |last3=Singh |journal=International Journal of Innovative Research in Technology |volume =1| issue =6 | issn= 2349-6002|date=2014 |
==Biochemistry approaches==
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===Neuroscience===
{{main|Neuromorphic computing|wetware computer}}
Neuromorphic computing involves using electronic circuits to mimic the neurobiological architectures found in the human nervous system, with the goal of creating artificial neural systems that are inspired by biological ones.<ref>{{Cite journal |last1=Ham |first1=Donhee |last2=Park |first2=Hongkun |last3=Hwang |first3=Sungwoo |last4=Kim |first4=Kinam |title=Neuromorphic electronics based on copying and pasting the brain |url=https://www.nature.com/articles/s41928-021-00646-1 |journal=Nature Electronics |year=2021 |language=en |volume=4 |issue=9 |pages=635–644 |doi=10.1038/s41928-021-00646-1 |s2cid=240580331 |issn=2520-1131}}</ref><ref>{{Cite journal |last1=van de Burgt |first1=Yoeri |last2=Lubberman |first2=Ewout |last3=Fuller |first3=Elliot J. |last4=Keene |first4=Scott T. |last5=Faria |first5=Grégorio C. |last6=Agarwal |first6=Sapan |last7=Marinella |first7=Matthew J. |last8=Alec Talin |first8=A. |last9=Salleo |first9=Alberto |date=April 2017 |title=A non-volatile organic electrochemical device as a low-voltage artificial synapse for neuromorphic computing |url=https://www.nature.com/articles/nmat4856 |journal=Nature Materials |language=en |volume=16 |issue=4 |pages=414–418 |doi=10.1038/nmat4856 |pmid=28218920 |bibcode=2017NatMa..16..414V |issn=1476-4660}}</ref> These systems can be implemented using a variety of hardware, such as memristors,<ref name="Maan 1–13">{{Cite journal|last1=Maan|first1=A. K.|last2=Jayadevi|first2=D. A.|last3=James|first3=A. P.|date=2016-01-01|title=A Survey of Memristive Threshold Logic Circuits|journal=IEEE Transactions on Neural Networks and Learning Systems|volume=PP|issue=99|pages=1734–1746|doi=10.1109/TNNLS.2016.2547842|pmid=27164608|issn=2162-237X|arxiv=1604.07121|bibcode=2016arXiv160407121M|s2cid=1798273}}</ref> spintronic memories, and transistors,<ref>{{Cite journal|title = Mott Memory and Neuromorphic Devices|journal = Proceedings of the IEEE|date = 2015-08-01|issn = 0018-9219|pages = 1289–1310|volume = 103|issue = 8|doi = 10.1109/JPROC.2015.2431914|first1 = You|last1 = Zhou|first2 = S.|last2 = Ramanathan|s2cid = 11347598|url=https://zenodo.org/record/895565}}</ref><ref name=":2">{{Cite conference |last1=Alzahrani |first1=Rami A. |last2=Parker |first2= Alice C. |date=2020-07-28 |title=Neuromorphic Circuits With Neural Modulation Enhancing the Information Content of Neural Signaling |conference=International Conference on Neuromorphic Systems 2020|language=EN|doi=10.1145/3407197.3407204|s2cid=220794387|doi-access=free}}</ref> and can be trained using a range of software-based approaches, including error backpropagation<ref>{{cite arXiv |last1=Eshraghian|first1=Jason K.|last2=Ward|first2=Max|last3=Neftci |first3=Emre|last4=Wang|first4=Xinxin|last5=Lenz|first5=Gregor|last6=Dwivedi|first6=Girish|last7=Bennamoun|first7=Mohammed|last8=Jeong|first8=Doo Seok|last9=Lu|first9=Wei D.|title=Training Spiking Neural Networks Using Lessons from Deep Learning |date=1 October 2021 |class=cs.NE |eprint=2109.12894 }}</ref> and canonical learning rules.<ref>{{Cite web |url=https://github.com/Hananel-Hazan/bindsnet | title=Hananel-Hazan/bindsnet: Simulation of spiking neural networks (SNNs) using PyTorch.| website=[[GitHub]]| date=31 March 2020}}</ref> The field of neuromorphic engineering seeks to understand how the design and structure of artificial neural systems affects their computation, representation of information, adaptability, and overall function, with the ultimate aim of creating systems that exhibit similar properties to those found in nature. Wetware computers, which are composed of living neurons, are a conceptual form of neuromorphic computing that has been explored in limited prototypes.<ref name=":1">{{cite web |author=Sincell, Mark |title=Future Tech |work=Discover |url=http://web.archive.org/web/20191120075215 |access-date=2024-03-01}}</ref> Electron microscopy has already been imaging high-resolution anatomical neural connection diagrams<ref>{{cite journal |last1=Devineni |first1=Anita |title=A complete map of the fruit-fly |journal=Nature |date=
===Cellular automata and amorphous computing===
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