Introduction to quantum mechanics Quantum mechanics is a fundamental branch of theoretical physics with wide applications in experimental physics that replaces classical mechanics and classical electromagnetism at the atomic and subatomic levels.

Introduction to quantum mechanics:

Introduction to quantum mechanics Quantum mechanics is a more fundamental theory than Newtonian mechanics and classical electromagnetism. It provides accurate and precise descriptions for many phenomena that these "classical" theories simply cannot explain on the atomic and subatomic level.

What is a quantum computer? :

A quantum computer is a machine that performs calculations based on the laws of quantum mechanics, which is the behavior of particles at the sub-atomic level. What is a quantum computer?

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Moore’s Law: We hit the quantum level 2010~2020. Why bother with quantum computation ?

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Computer technology is making devices smaller and smaller… …reaching a point where classical physics is no longer a suitable model for the laws of physics.

Physics and Computation :

Physics and Computation Information is stored in a physical medium, and manipulated by physical processes. The laws of physics dictate the capabilities of any information processing device. Designs of “classical” computers are implicitly based in the classical framework for physics.

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… consider a modification of the experiment … 100% The simplest explanation is wrong! The simplest explanation for the modified setup would still predict a 50-50 distribution … full mirror The “weirdness "of quantum mechanics

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… consider a modification of the experiment … The simplest explanation for the modified setup would still predict a 50-50 distribution … full mirror Explanation of experiment 100%

Representation of Data:

Representation of Data Quantum computers, which have not been built yet, would be based on the strange principles of quantum mechanics, in which the smallest particles of light and matter can be in different places at the same time. In a quantum computer, one “cubit" - quantum bit - could be both 0 and 1 at the same time.

Representation of Data - Cubits:

Representation of Data - Cubits A physical implementation of a qubit could use the two energy levels of an atom. An excited state representing |1> and a ground state representing |0>. Excited State Ground State Nucleus Light pulse of frequency for time interval t Electron State |0> State |1>

Representation of Data Superposition:

Representation of Data Superposition A single qubit can be forced into a superposition of the two states denoted by the addition of the state vectors: | > = |0> + |1> Where and are complex numbers and | | + | | = 1 1 2 1 2 1 2 2 2

Representation of Data – Superposition:

Representation of Data – Superposition Light pulse of frequency for time interval t/2 State |0> State |0> + |1>

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What do we mean by “efficient”? The complexity of an algorithm measures how much of some resource (e.g. time, space, energy) the algorithm uses as a function of the input size. e.g. the best known algorithms for factoring an n bit number uses time in

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Application Efficient simulations of quantum systems. Factoring and Discrete Logarithms. Hidden subgroup problems. Amplitude amplification.

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Quantum Algorithms a,b G , a k = b , find k Integer Factorization (basis of RSA cryptography): Discrete logarithms (basis of DH crypto, including ECC): Given N= pq , find p and q.

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Quantum Information Security Quantum key establishment (available now/soon). Quantum money (require stable quantum memory). Quantum digital signatures (requires quantum computer). The security depends only on the laws of physics, and not on computational assumptions.

Implementation requirements:

Implementation requirements Cubit implementation itself. Control of unitary evolution. Initial state preparation (cubits). Measurement of the final state(s).

CONCLUSION:

CONCLUSION one of the tasks of classical computers since their inception as been to simulate electrical circuits to help design faster computers .

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