Faster, Faster, Faster: . . . Blame It on Einstein’s . . . Honey, I Shrunk the . . . Why Is Micro-World . . . Quantum Computing, At First Glance, This . . . Here We Come! Making Lemonade . . . Fast Search Vladik Kreinovich End of Privacy, End of . . . We Will Beat RSA . . . Department of Computer Science Home Page University of Texas at El Paso El Paso, TX 79968, USA Title Page vladik@utep.edu ◭◭ ◮◮ http://www.cs.utep.edu/vladik ◭ ◮ Page 1 of 25 Go Back Full Screen Close Quit
Faster, Faster, Faster: . . . Blame It on Einstein’s . . . 1. Faster, Faster, Faster: Why? Honey, I Shrunk the . . . • Computers are getting faster. Why Is Micro-World . . . At First Glance, This . . . • On the cheapest laptop, we can now solve problem that Making Lemonade . . . decades ago, required a supercomputer. Fast Search • For customers, this means faster downloads, more de- End of Privacy, End of . . . tailed video games. We Will Beat RSA . . . Home Page • But seriously, why do we need faster computers? Title Page ◭◭ ◮◮ ◭ ◮ Page 2 of 25 Go Back Full Screen Close Quit
Faster, Faster, Faster: . . . Blame It on Einstein’s . . . 2. Why Faster Honey, I Shrunk the . . . • Why do we need faster computers? Why Is Micro-World . . . At First Glance, This . . . • Because for many practical problems, the current speed Making Lemonade . . . is not enough. Fast Search • For example, we can usually predict tomorrow’s End of Privacy, End of . . . weather reasonably well. We Will Beat RSA . . . Home Page • The corresponding computations may take hours on a high performance computer. Title Page • However, the results are still available way before to- ◭◭ ◮◮ morrow. ◭ ◮ • In principle, similar algorithms can also predict where Page 3 of 25 a tornado will go in the next 10 minutes. Go Back • However, in this case, we cannot wait hours. Full Screen Close Quit
Faster, Faster, Faster: . . . Blame It on Einstein’s . . . 3. Blame It on Einstein’s Special Relativity Honey, I Shrunk the . . . • In the past, computer speed doubled every 1-2 years: Why Is Micro-World . . . Moore’s law. At First Glance, This . . . Making Lemonade . . . • But now, this speeding-up slowed down. Fast Search • Why? End of Privacy, End of . . . • One of the main reasons is special relativity. We Will Beat RSA . . . Home Page • According to special relativity, all velocities are bounded by the speed of light. Title Page • Light travels very fast, at 300,000 km/sec. ◭◭ ◮◮ • This means that to go through a laptop of usual size ◭ ◮ 30 cm, a signal needs at least 10 − 9 seconds. Page 4 of 25 • This may sound fast, but modern computers have sev- Go Back eral GHz speed. Full Screen • This means that several operations can be performed Close while we reach a computer cell. Quit
Faster, Faster, Faster: . . . Blame It on Einstein’s . . . 4. Honey, I Shrunk the Computer Honey, I Shrunk the . . . • So, the only way to make computers faster is to make Why Is Micro-World . . . them smaller in size. At First Glance, This . . . Making Lemonade . . . • This means decreasing the size of each memory and Fast Search processing cell. End of Privacy, End of . . . • Here comes a problem. We Will Beat RSA . . . Home Page • Already now, on fastest computers, a cell consists of several dozen molecules. Title Page • When we shrink it even further, it will consist of a few ◭◭ ◮◮ molecules. ◭ ◮ • As a result, we will have to take into account quantum Page 5 of 25 physics – physics of micro-objects like molecules. Go Back Full Screen Close Quit
Faster, Faster, Faster: . . . Blame It on Einstein’s . . . 5. Why Is Micro-World Different? Honey, I Shrunk the . . . • But why is micro-world different? Why Is Micro-World . . . At First Glance, This . . . • We can simply say that this is what physics experi- Making Lemonade . . . ments show. Fast Search • But in reality, there is a good reason for this difference. End of Privacy, End of . . . • How do we describe the state of a macro-object – e.g., We Will Beat RSA . . . Home Page of a car? Title Page • We can describe its location, its velocity, how much gas is left, etc. ◭◭ ◮◮ • In principle, all these values can be measured very ac- ◭ ◮ curately. Page 6 of 25 • A police officer shoots a beam of photons to the car, Go Back and she gets the car’s speed. Full Screen Close Quit
Faster, Faster, Faster: . . . Blame It on Einstein’s . . . 6. Why Is Micro-World Different (cont-d) Honey, I Shrunk the . . . • We can (and do) shoot a laster beam to the Moon. Why Is Micro-World . . . At First Glance, This . . . • It bounces back and we can find the exact distance to Making Lemonade . . . the Moon. Fast Search • In both cases, the beam is much much smaller than the End of Privacy, End of . . . object; thus, the beam does not affect the object. We Will Beat RSA . . . • The car does not change its direction just because its Home Page speed is measured (unless a driver breaks :-) Title Page • The Moon does not change its trajectory because we ◭◭ ◮◮ shot a laser beam at it. ◭ ◮ • Thus, at any given moment of time, we can get an Page 7 of 25 exact description of the state. Go Back • Thus, we can accurately predict future behavior. Full Screen • For example, we can predict Lunar eclipses centuries ahead. Close Quit
Faster, Faster, Faster: . . . Blame It on Einstein’s . . . 7. Micro-World Is Different Honey, I Shrunk the . . . • It is different for micro-objects. Why Is Micro-World . . . At First Glance, This . . . • To find a location of an electron, we can also shoot a Making Lemonade . . . photon at it. Fast Search • But now the photon is about the same size as the elec- End of Privacy, End of . . . tron. We Will Beat RSA . . . Home Page • As a result, each measurement drastically changes the state of the object. Title Page • Once we measured the location, the velocity changes, ◭◭ ◮◮ and vice versa. ◭ ◮ • As a result, we cannot determine the exact state – and Page 8 of 25 thus, cannot make exact predictions. Go Back • At best, we can predict the probability of different fu- Full Screen ture states. Close Quit
Faster, Faster, Faster: . . . Blame It on Einstein’s . . . 8. At First Glance, This Is Bad for Computing Honey, I Shrunk the . . . • Computers are very precise machines. Why Is Micro-World . . . At First Glance, This . . . • Humans make mistakes, computers usually don’t. Making Lemonade . . . • A computer can perform billions of operations – and Fast Search still get a correct result. End of Privacy, End of . . . • If we repeat the computations twice, we get the exact We Will Beat RSA . . . Home Page same result. Title Page • But this assumes that everything works deterministi- cally. ◭◭ ◮◮ ◭ ◮ Page 9 of 25 Go Back Full Screen Close Quit
Faster, Faster, Faster: . . . Blame It on Einstein’s . . . 9. Bad for Computing? Honey, I Shrunk the . . . • If we decrease the size of computer cells to a few Why Is Micro-World . . . molecules, we need to account for quantum effects. At First Glance, This . . . Making Lemonade . . . • This means that the outcome becomes probabilistic. Fast Search • We run the same program twice, and get two different End of Privacy, End of . . . results – a disaster. We Will Beat RSA . . . Home Page • A disaster? Title Page ◭◭ ◮◮ ◭ ◮ Page 10 of 25 Go Back Full Screen Close Quit
Faster, Faster, Faster: . . . Blame It on Einstein’s . . . 10. Making Lemonade Out of Lemons Honey, I Shrunk the . . . • For a long time, quantum effects on computing were Why Is Micro-World . . . viewed as distracting noise. At First Glance, This . . . Making Lemonade . . . • Indeed, if we run the existing algorithms on a quantum- Fast Search size computer, the results will drown in noise. End of Privacy, End of . . . • What can we do? We Will Beat RSA . . . Home Page • The previous phrase has a hint: existing algorithms. Title Page • It turns out that we can modify algorithms so that: ◭◭ ◮◮ – not only we are affected by noise, ◭ ◮ – we can even further speed up computations! Page 11 of 25 Go Back Full Screen Close Quit
Faster, Faster, Faster: . . . Blame It on Einstein’s . . . 11. Fast Search Honey, I Shrunk the . . . • In action movies, an enemy is often hiding in one of Why Is Micro-World . . . the main rooms, we do not know in which one. At First Glance, This . . . Making Lemonade . . . • If there are n rooms, then the only way to find the bad Fast Search guy is to look into all the rooms until we find him. End of Privacy, End of . . . • In the worst case, we need to look into all the rooms – We Will Beat RSA . . . if we do not search all the rooms, we may miss him. Home Page • Similarly: Title Page – if we have an unsorted database with n records, ◭◭ ◮◮ – in the worst case, we need to look at all n records. ◭ ◮ • In quantum computing, Grover’s algorithm can find an Page 12 of 25 element in √ n steps. Go Back • How faster is it? Full Screen Close Quit
Recommend
More recommend
