Need for Fast Data . . . Need to Take . . . Computer Scientists . . . Towards Parallel Quantum Need for Teleportation Problem Computing: Standard Communication Is a . . . Analysis of the Problem Quantum Teleportation Conclusion Algorithm Is, in Some Home Page Title Page Reasonable Sense, Unique ◭◭ ◮◮ Oscar Galindo, Olga Kosheleva, and Vladik Kreinovich ◭ ◮ Page 1 of 37 University of Texas at El Paso, El Paso, Texas 79968, USA, ogalindomo@miners.utep.edu, olgak@utep.edu, vladik@utep.edu Go Back Full Screen Close Quit
Need for Fast Data . . . 1. Need for Fast Data Processing Need to Take . . . Computer Scientists . . . • Computational models can predict, with high proba- Need for Teleportation bility, where a tornado will turn in the next hour. Problem • However, even on high performance computers, the Communication Is a . . . computations take longer than an hour. Analysis of the Problem Conclusion • This defeats the whole purpose of prediction. Home Page • This lengthy computation time is caused by uncer- Title Page tainty: ◭◭ ◮◮ – if we had full information about the state of the ◭ ◮ atmosphere, – we could simply solve the corresponding system of Page 2 of 37 partial differential equations. Go Back • However, in practice, we have only partial information, Full Screen we have uncertainty. Close Quit
Need for Fast Data . . . 2. Need for Fast Data Processing (cont-d) Need to Take . . . Computer Scientists . . . • Thus, to make reasonable predictions, we need to: Need for Teleportation – generate many different solutions, corresponding to Problem several different situations – and Communication Is a . . . – make predictions based on the frequency of solu- Analysis of the Problem tions corresponding to different directions. Conclusion Home Page • This is a general phenomenon: Title Page – taking uncertainty into account drastically increases ◭◭ ◮◮ the computation time, ◭ ◮ – because, under uncertainty, we need to process sev- eral alternative scenarios instead of a single one. Page 3 of 37 Go Back Full Screen Close Quit
Need for Fast Data . . . 3. Faster Processing Means Smaller Memory And Need to Take . . . Computation Cells Computer Scientists . . . Need for Teleportation • One of the main limits on the computation speed is Problem that all velocities are limited by the speed of light. Communication Is a . . . • The light is fast – it travels at 300 000 km/sec. Analysis of the Problem Conclusion • However, for a current computer of size 30 cm, this Home Page means that Title Page – the fastest we can move information from one side of the computer to another is 1 nanosecond, ◭◭ ◮◮ – and even the simplest current computers have pro- ◭ ◮ cessing speed of several Gigahertz, Page 4 of 37 – which means that several computation cycles take Go Back place while the information is transmitted. Full Screen • We thus need smaller computers – i.e., smaller memory Close and computation cells. Quit
Need for Fast Data . . . 4. Need to Take Quantum Effects into Account Need to Take . . . Computer Scientists . . . • Already in the existing computers, a memory cell some- Need for Teleportation times consists of several dozen atoms. Problem • For such small objects, we need to take into account Communication Is a . . . the laws of quantum physics. Analysis of the Problem • The main difference from traditional physics is in our Conclusion ability to measure things. Home Page Title Page • Indeed, the only way to measure a physical quantity is to interact with the corresponding object; e.g.: ◭◭ ◮◮ – to measure a distance to a faraway object, ◭ ◮ – we can send a laser beam to this object and measure Page 5 of 37 the time that it takes for this beam to come back. Go Back • This is how we measure, e.g., the distance to the Moon. Full Screen • For macro-size objects, the corresponding probe can be Close very small, much smaller than the object itself. Quit
Need for Fast Data . . . 5. Quantum Effects (cont-d) Need to Take . . . Computer Scientists . . . • Thus, we can safely ignore the effect of this probe on Need for Teleportation our object. Problem • We conclude that after the measurement, the object Communication Is a . . . remains the same. Analysis of the Problem • We do not expect the distance to the Moon to change Conclusion Home Page just because we hit the Moon with a laser beam. Title Page • We can thus measure the Moon’s location, velocity, and other characteristics with very high accuracy. ◭◭ ◮◮ • We can also send a photon to a proton and measure its ◭ ◮ bouncing back. Page 6 of 37 • However, this photon is already of approximately the Go Back same size as the particle whose location we measure. Full Screen • As a result, every measurement changes the state of Close the particle. Quit
Need for Fast Data . . . 6. Quantum Effects (cont-d) Need to Take . . . Computer Scientists . . . • So, even if we get the particle’s location, its speed Need for Teleportation changes. Problem • If we afterwards measure its speed, it will be different Communication Is a . . . from the speed of the original particle. Analysis of the Problem Conclusion • Because of this, for a micro-object, we cannot uniquely Home Page determine its state. Title Page • We can only describe the probability of different mea- surement results. ◭◭ ◮◮ ◭ ◮ Page 7 of 37 Go Back Full Screen Close Quit
Need for Fast Data . . . 7. Computer Scientists Managed to Transform This Need to Take . . . Lemon into Lemonade Computer Scientists . . . Need for Teleportation • At first glance, this makes computations more compli- Problem cated. Communication Is a . . . • As we decrease the size of the cells, we get quantum Analysis of the Problem effects. Conclusion Home Page • So, the resulting states become only probabilistically predictable. Title Page • In other words, we have a lot of noise added to our ◭◭ ◮◮ computations, noise that makes computations difficult. ◭ ◮ • However, researchers managed to use quantum effects Page 8 of 37 to speed up computations. Go Back • This is done by re-arranging the corresponding com- Full Screen putation schemes. Close Quit
Need for Fast Data . . . 8. Lemon into Lemonade (cont-d) Need to Take . . . Computer Scientists . . . • In non-quantum computing, finding an element in an Need for Teleportation unsorted database with n entries may require time n . Problem • Indeed, we may need to look at each record. Communication Is a . . . Analysis of the Problem • In quantum computing, it is possible to find this ele- ment in much smaller time √ n . Conclusion Home Page • An even larger speed-up is achieved in the problem of Title Page factorizing large integers. ◭◭ ◮◮ • Traditional algorithms require time which is exponen- ◭ ◮ tial in terms of the number’s length. Page 9 of 37 • Thus, they are not feasible for large lengths. Go Back Full Screen Close Quit
Need for Fast Data . . . 9. Lemon into Lemonade (cont-d) Need to Take . . . Computer Scientists . . . • However, quantum computing can do it in polynomial Need for Teleportation time; this application is important, since: Problem – most current online encryption algorithms Communication Is a . . . – are based on the difficulty of factoring large inte- Analysis of the Problem gers. Conclusion Home Page • So once quantum computers become a reality, we will Title Page be able to read all the so-far encrypted messages. ◭◭ ◮◮ ◭ ◮ Page 10 of 37 Go Back Full Screen Close Quit
Need for Fast Data . . . 10. Need for Parallel Quantum Computing Need to Take . . . Computer Scientists . . . • While quantum computing is fast, its speeds are also Need for Teleportation limited. Problem • To further speed up computations, a natural idea is to Communication Is a . . . have several quantum computers working in parallel. Analysis of the Problem Conclusion • Then each of them solves a part of the problem. Home Page • This idea is similar to how we humans solve complex Title Page problems: ◭◭ ◮◮ – if a task is too difficult for one person to solve – be ◭ ◮ it building a big house or proving a theorem, – several people team up and together solve the task. Page 11 of 37 Go Back Full Screen Close Quit
Need for Fast Data . . . 11. Need for Teleportation Need to Take . . . Computer Scientists . . . • To successfully collaborate, quantum computers need Need for Teleportation to exchange intermediate states of their computations. Problem • Here lies a problem: for complex problems, we would Communication Is a . . . like to use computers in different geographic areas. Analysis of the Problem Conclusion • However, a quantum state gets changed when it is sent Home Page far away. Title Page • Researchers have come up with a way to avoid this sending, called teleportation . ◭◭ ◮◮ ◭ ◮ • There exists a scheme for teleportation. Page 12 of 37 Go Back Full Screen Close Quit
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