Quantum Computing

QUANTUM COMPUTATION

Presented By:Aparajita Khan.

Roll No:20081023C.S.E

Registration No:2077 of 2008-09

Quantum Computation : What is it?

Quantum Computation

Computer Science

Physics

Mathematics

An entirely new domain of computation which that makes direct use of quantum mechanical phenomena to perform operations on data.

Its Roots :

Physics

Quantum

Mechanics

Classical/ Newtonia

n Mechanic

s

Super-positio

n

Entanglement Quantum

computation

Driving Principles : Quantum Superposition

Principle: elementary particle can be localized as if it were a point like particle; on the other hand it can exist everywhere just like a wave field .

Quantum entanglement: causes one member of entangled pair to take a definite value (e.g.,clockwise spin). ,other member of entangled pair at any subsequent time takes the appropriately correlated value (e.g., counterclockwise spin).

Classical and Quantum model of Computer

Classical Quantu

m

Bits exist in one of two

distinct states, a 0 or a 1

Qubits two possible states of

qubit,

And any linear combination (superposition) of them is also physically possible.

QUBIT : quantum analogue of the bit. physical state of a qubit is the superposition,

where α and β are complex numbers. According to quantum theory,measure of qubit is occurance of

such that,

Reason behind superiority of Quantum Computer

With 2 classical bits, 4possible states (00, 01, 10, 11). Correspondingly, a pair of qubits has four computational basis states

But single classical two-bit register can store these numbers only one at a time, while a pair of qubits can also exist in a superposition of these four basis states, each of which with its own complex coefficient.

All four possible states are simultaneously “stored” in a single two-qubit quantum register.

Amount of information that can be stored in a system of n unmeasured qubits grows exponentially in n.

Components of Quantum ComputationQubits

Quantum Gates

Quantum CircuitsQuantum Algorithms : If implemented gives exponential “speed up” from classical algorithms.• A Fact : a classical computer can be estimated at taking

10 million billion years to factor a 1000 digit number, where as a quantum computer would take around 20 minutes! Amazing, but true.

Shor's algorithm :conventional computers the best known factoring algorithm runs in While for factoring numbers on a quantum computer which runs in

Building a quantum computer

Qubits

Quantum Gates

Quantum Circuits

Quantum Dots • Implementation of

Qubit.• Single electron

trapped in cage of atoms.

• Laser beam focused.• Transition in state as

NOT function.

Computing Liquids• Sea of

molecules to store data.

• In magnetic field, spin of nucleus reflects data or state.

Application Areas :Quantum Communication : Information encoded as the polarization of

photons oscillation in one direction can be thought

of as 0 and in another as a 1.

Quantum Cryptography : Idea from Heisenberg uncertainty principle -  limit on the

accuracy of measurement of 2 properties simultaneously. Quantum Key Distribution : suggest a key by sending a

series of photons with random polarizations. Then send message by some conventional or quantum method.

If eavesdropper has intercepted and forwarded the information, the receiver and sender will be alerted as a higher percentage of errors will be present than expected. So resend.

Pitfalls : De-Coherence: Potential power of quantum computers depends on

the quantum parallelism brought about by the coherent state

As soon as it measurable properties interacts with the environment it will de-cohere and fall into one of the two classical states.

Future Prospects: secure cloud computation using quantum

computing magnetic resonance imaging, banking solutions,

quantum steganography. Extreme computational speed up.