Quantum Computing
Dorca Lee
Classical Computing
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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.
Classical Computing
• Data is processed by a
circuit of gates
• Examples of classical
gates:
 The NOT gate
 The OR gate
• Discrete, some are
irreversible.
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.
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>)
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
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.
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.