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Nawaf M Albadia 427121532 Slide 2 Introduction. Quantum Physical Phenomena. Quantum Computing in more details. Quantum Algorithms. Quantum Cryptography. Quantum Communication. Conclusion. 2 Slide 3 Superposition Is the state of a qubit when 0 and 1 at the same time. Entanglement Is a quantum mechanical phenomenon in which the quantum states of two or more objects are linked together so that one object cannot be adequately described without full mention of its counterpart. Interference In physics, interference is the addition (superposition) of two or more waves that result in a new wave pattern. Polarization Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave 3 Slide 4 New model of computing based on quantum mechanics. Quantum circuits, quantum Turing machines. More powerful than conventional models. 4 Slide 5 5 Slide 6 The demand for computation power is raising, and classical computing has a limit?? Moores Low 6 Slide 7 What happens when we hit the physical limit of Moores Law? There are apparently two possibilities: Optical Computers Or Quantum Computers 7 Slide 8 8 Information is in the form of a digital bit, 0 or 1 Information is in the form of a qubit, 0, 1, and any value in between at the same time Quantum Computers 0 1 1 0 Also known as superposition Slide 9 Increased computing power Factoring a number with 400 digits Supercomputers = billions of years Quantum computers = within a year Security advances Keys exchanged in private using quantum key distribution (QKD) No eavesdropper can obtain private key 9 Slide 10 Security problems? 10 What if I have it and you dont? Slide 11 Quantum computing Some scientists claim that they will begin when Moores law ends, 2020 Others say it will be three decades or more Beyond quantum computing Nanomachines. DNA computing. 11 Slide 12 Factoring: given N=pq, find p and q. ( Shors algorithm ) Best algorithm n -number of digits. Many cryptosystems based on hardness of factoring. O(log N) 3 time quantum algorithm [Shor, 1994] Similar quantum algorithm solves discrete log. 12 Slide 13 In 1994, Peter Shor gave a quantum algorithm for factoring an N-digit number that takes time O(log N) 3 Best known classical algorithm takes So if you had a quantum computer, you could break RSA and other public-key cryptosystems Heart of Shors algorithm is a quantum Fourier transform that finds the period of an exponentially long periodic sequence Interesting Slide 14 Find if there exists i for which x i =1. Queries: input i, output x i. Classically, n queries. Quantum, O( n) queries [Grover, 1996]. Speeds up exhaustive search. 14 0100... x1x1 x2x2 xnxn x3x3 Slide 15 Key distribution: two parties want to create a secret shared key by using a channel that can be eavesdropped. Classically: secure if discrete log hard. Quantum: secure if quantum mechanics valid [Bennett, Brassard, 1984]. No extra assumptions needed. 15 Slide 16 16 Theorem: Impossible to obtain information about non-orthogonal states without disturbing them. In this protocol: Entanglement. No-cloning theorem. Non-locality & uncertainty principle. Indistinguishability of nonorthogonal states Slide 17 Alice randomly chooses a fraction of the final string and announces it. Bob counts the number of different bits. If too many different bits, reject (eavesdropper found). If Eve measured many qubits, she gets caught. 17 Slide 18 Dense coding: 1 quantum bit can encode 2 classical bits. Teleportation: quantum states can be transmitted by sending classical information. Quantum protocols that send exponentially less bits than classical. 18 Slide 19 Can Quantum mechanics solve NP-Complete problems? 19 Answer: No Slide 20 Quantum Computing is very promising. Quantum mechanics are hard to implement. Eavesdropping is almost impossible in case of key distribution. Quantum provide efficient environment for communication. Quantum cant solve NP-complete problems 20 Slide 21 21