QUANTUM MECHANICS IN

ELECTRONICS

Amit Kumar Mohapatra

14MSL005

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 –

Moore’s law

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!

Bra-Ket Notation InvolvesVector 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.

Quantum bit- qubit

Classical Circuits vs.

Quantum CircuitsClassical 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.

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.

01

10X

0

0

i

iY

10

01Z

Quantum Gates and Circuit Symbols

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

1H

Circuit Diagram of aHadamard 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.

C-Not GatesC-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

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.

Hi friends, how my talk is?