Download Quantum Computing

Quantum Computing
Hongki Lee
BIOPHOTONICS ENGINEERING LABORATORY
School of Electrical and Electronic Engineering, Yonsei University
Quantum Mechanics(14/2)
Hongki Lee
Contents
 Introduction and History
 Data Representation
 Quantum Computation
 Conclusion
Quantum Mechanics(14/2)
Hongki Lee
Introduction and History
 Quantum computing
- calculations based on the laws of quantum mechanics
 Quantum principles
- Quantum uncertainty
- Superposition
- Quantum entanglement
Quantum Mechanics(14/2)
Hongki Lee
Introduction and History
 History
- 1982, Richard Feynman
- 1985, David Deutsch
- 1994, Peter Shor
- 1997, Lov Grover
Quantum Mechanics(14/2)
Hongki Lee
Data Representation
 Qubits
A bit of data is represented by a single atom that is in one of two states
denoted by |0> and |1>. A single bit of this form is known as a qubit
A physical implementation of a qubit could use the two energy levels of an
atom. An excited state representing |1> and a ground state representing |0>.
Light pulse of
frequency  for
time interval t
Excited
State
Ground
State
Nucleus
Electron
State |0>
Quantum Mechanics(14/2)
State |1>
Hongki Lee
Data Representation
 Superposition
- A single qubit can be forced into a superposition of the two states denoted
by the addition of the state vectors:
| > = 𝛼1 | > + 𝛼2 |1 >
where 𝛼1 and 𝛼1 are complex numbers and |𝛼1 |2 + |𝛼2 |2 = 1
A qubit in superposition is in both of the states
|1> and |0 at the same time
Quantum Mechanics(14/2)
Hongki Lee
Data Representation
 Superposition
- Consider a 3 bit qubit register:
| > =
1
8
|000 >
1
8
|001 > + ⋯
1
8
|111
- An n qubit register 2𝑛 states
If we attempt to retrieve the values represented within a
superposition, the superposition randomly collapses to
represent just one of the original values.
Quantum Mechanics(14/2)
Hongki Lee
Data Representation
 Entanglement
- ability of quantum systems to exhibit correlations between states within a
superposition.
- Imagine two qubits, each in the state |0> + |1> (a superposition of the 0 and
1.) We can entangle the two qubits such that the measurement of one qubit
is always correlated to the measurement of the other qubit.
Result: If two entangled qubits are separated by any distance
and one of them is measured then the other, at the same instant,
enters a predictable state
Quantum Mechanics(14/2)
Hongki Lee
Quantum Computation
Important single-qubit gates
𝛼1 0 > + 𝛼2 1 >
X
𝛼1 0 > + 𝛼2 1 >
Z
𝛼1 0 > + 𝛼2 1 >
Quantum Mechanics(14/2)
H
𝛼1 1 > + 𝛼2 0 >
𝛼1 1 > − 𝛼2 0 >
𝛼1
|0 > +|1 >
2
+ 𝛼2
|0 > −|1 >
2
Hongki 9Lee
Quantum Computation
 Quantum parallel computation
- N physical qubits can encode 2N binary numbers simultaneously
- A quantum computer can process all 2N numbers in parallel on a single
machine with N physical qubits.
- Very hard to simulate a quantum computer on a classical computer.
- Efficiency : How many steps are required to compute a function
- Algorithms
Quantum Mechanics(14/2)
Hongki Lee
Conclusion
-
Quantum computing machines enable new algorithms that cannot be
realised in a classical world.
-
The algorithms can be powerful physical simulators.
-
The physics determines the algorithm.
-
Hardware
Quantum Mechanics(14/2)
Hongki Lee