Nawaf M Albadia 427121532

Contents Introduction. Quantum Physical Phenomena. Quantum Computing in more details. Quantum Algorithms. Quantum Cryptography. Quantum Communication. Conclusion.

Terminologies Superposition Entanglement 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

What’s quantum computing New model of computing based on quantum mechanics. Quantum circuits, quantum Turing machines. More powerful than conventional models.

Physical Experiment Here a light source emits a photon along a path towards a half-silvered mirror. This mirror splits the light, reflecting half vertically toward detector A and transmiting half toward detector B. A photon, however, is a single quantized packet of light and cannot be split, so it is detected with equal probability at either A or B. Intuition would say that the photon randomly leaves the mirror in either the vertical or horizontal direction. However, quantum mechanics predicts that the photon actually travels both paths simultaneously! This is more clearly demonstrated in figure b. In this experiment, the photon first encounters a half-silvered mirror, then a fully silvered mirror, and finally another half-silvered mirror before reaching a detector, where each half-silvered mirror introduces the probability of the photon traveling down one path or the other.  Once a photon strikes the mirror along either of the two paths after the first beam splitter, the arrangement is identical to that in figure a, and so one might hypothesize that the photon will reach either detector A or detector B with equal probability.  However, experiment shows that in reality this arrangement causes detector A to register 100% of the time, and never at detector B!  How can this be?

Why Quantum computing? The demand for computation power is raising, and classical computing has a limit?? Moore’s Low

Why Quantum computing? What happens when we hit the physical limit of Moore’s Law? There are apparently two possibilities: Optical Computers Or Quantum Computers

Classical VS Quantum Classical Computers Quantum Computers 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 Also known as superposition 1 1

What are the benefits? Increased computing power Security advances 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

What if I have it and you don’t? What are the Risks? Security problems? What if I have it and you don’t?

Timeline of implementation Quantum computing Some scientists claim that they will begin when Moore’s law ends, 2020 Others say it will be three decades or more Beyond quantum computing Nanomachines. DNA computing.

Quantum Algorithms Factoring: given N=pq, find p and q. (Shor’s 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.

Interesting Shor’s Algorithm In 1994, Peter Shor gave a quantum algorithm for factoring an N-digit number that takes time O(log N)3 Interesting Best known classical algorithm takes So if you had a quantum computer, you could break RSA and other public-key cryptosystems Heart of Shor’s algorithm is a “quantum Fourier transform” that finds the period of an exponentially long periodic sequence

Quantum Algorithms ... 1 x1 x2 x3 xn 1 x1 x2 x3 xn Find if there exists i for which xi=1. Queries: input i, output xi. Classically, n queries. Quantum, O(n) queries [Grover, 1996]. Speeds up exhaustive search.

Quantum cryptography 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.

Eavesdropping 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

Check for Eavesdropping 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.

Quantum Communication 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.

Are there any limits? Can Quantum mechanics solve NP-Complete problems? Answer: No

Conclusion 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 can’t solve NP-complete problems 

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