1. Quantum Computing
Dorca Lee

2. Classical Computing Computing is digital data processing
Data is expressed in terms of bits
A bit can take values 0 or 1
A number is represented by a string of bits (binary representation).
A bit is physically encoded by a system that can be in two distinguished states.

3. Classical Computing Data is processed by a circuit of gates
Examples of classical gates:
The NOT gate
The OR gate
Discrete, some are irreversible.

4. Quantum Computing
A major difference between classical and quantum systems: Superposition
Scale down the size of bits to systems that have quantum behavior, superposition in particular
Develop Algorithms that take advantage of quantum properties.

5. Quantum Computing
A quantum bit or qubit can be in states |0>, |1> or any superposition α|0>+β|1>.
Quantum Parallelism: a qubit can carry much more information than a classical bit.
Quantum gates correspond to unitary transformations. Continuous, Reversible .
Example of a quantum gate, Hadamard gate:
|0> → 1/√2(|0>+|1>) and |1>→1/√2(|0>−|1>)

6. A Simple Example of Quantum Parallelism: Deutsch Problem
f :arbitrary function from {0,1} to {0,1}, four such functions
f can be :
constant f(0) = f(1)
balanced f(0) = f(1)
can we know if f is constant or balanced with only one referral to f ?
using a classical computer: NO
using a quantum computer:YES

7. Fast Quantum Algorithms
Deutsch problem: speed is increased by a factor of 2.
In case of a function acting on N bits, speed can be increased by a factor of 2^N by developing the right algorithm
Schor’s factoring algorithm: less than 3 years to factor a 400 digit number compared to 10^10 years using classical computing.

8. Difficulties More room for errors than in classical computers
Phase errors
Small errors
No Cloning, quantum information cannot always be copied
Solved by developing error correction codes
Decoherence: loss of information because of the system (qubit) interaction with its environment.