Quantum mechanics in electronics
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Quantum mechanics in electronics
- 1. QUANTUM MECHANICS IN ELECTRONICS Amit Kumar Mohapatra 14MSL005
- 2. The memory capacity of a chip approximately doubles every 18 months – clock speeds and transistor density are rising exponentially...what is their ultimate fate???? Real computers are physical systems Computer technology in the last fifty years- dramatic miniaturization Faster and smaller –
- 3. Moore’s law
- 4. Extrapolating Moore’s law • If Moore’s law is extrapolated, by the year 2020 the basic memory component of the chip would be of the size of an atom – what will be space, time and energy considerations at these scales (heat dissipation…)? • At such scales, the laws of quantum physics would come into play - the laws of quantum physics are very different from the laws of classical physics - everything would change!
- 5. Bra-Ket Notation Involves Vector Xn can be represented two ways Ket |n> z y x w v Bra <n| = |n>t ( )***** zyxwv * m is the complex conjugate of m.
- 7. Classical Circuits vs. Quantum Circuits Classical Circuits based upon bits, which are represented with on and off states. These states are usually alternatively represented by 1 and 0 respectively. The medium of transportation of a bit is a conductive material, usually a copper wire or something similar. The 1 or 0 is represented with 2 different levels of current through the wire.
- 8. Circuits Continued… Quantum circuits use electron “spin” to hold their information, instead of the conductor that a classical circuit uses. While a classical circuit uses transistors to perform logic, quantum circuits use “quantum gates” such as the Hadamard Gates.
- 10. Quantum Gates and Circuit Symbols
- 11. Hadamard Gates Hadamard Gates can perform logic and are usually used to initialize states and to add random information to a circuit. Hadamard Gates are represented mathematically by the Hadamard Matrix which is below. − = 11 11 2 1 H
- 12. Circuit Diagram of a Hadamard Gate Hx y When represented in a Quantum Circuit Diagram, a Hadamard Gate looks like this: Where the x is the input qubit and the y is the output qubit.
- 13. C-Not Gates C-not Gates are one of the basic 2-qubit gates in quantum computing. C-not is short for controlled not, which means that one qubit (target qubit) is flipped if the other qubit (control qubit) is |1>, otherwise the target qubit is left alone. The mathematical representation of a C-Not Gate is below. = 0100 1000 0010 0001 CNU
- 14. Circuit Diagram of a C-Not Gate x y x yx ⊕ When represented in a Quantum Circuit Diagram, a C-Not Gate looks like this: Where x is the control qubit and y is the target qubit.
- 15. Hi friends, how my talk is?