quantum mechanics(14/2) hongki lee biophotonics engineering laboratory school of electrical and...

Quantum Mechanics(14/2) Hongki Lee

BIOPHOTONICS ENGINEERING LABORATORYSchool of Electrical and Electronic Engineering, Yonsei University

Quantum Computing

Hongki Lee


Contents

Introduction and History

Data Representation

Quantum Computation

Conclusion



Quantum computing - calculations based on the laws of quantum mechanics

Quantum principles - Quantum uncertainty

- Superposition

- Quantum entanglement



History

- 1982, Richard Feynman - 1985, David Deutsch - 1994, Peter Shor - 1997, Lov Grover


Data Representation

A bit of data is represented by a single atom that is in one of two states de-noted 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>.

Ex-cited State

Ground

State

Nu-cleus

Light pulse of frequency

for time inter-val t

Elec-tronState |

0>State |1>

Qubits


Data Representation

Superposition- A single qubit can be forced into a superposition of the two states denoted by the addition of the state vectors:

where and are complex numbers and + = 1

A qubit in superposition is in both of the states

|1> and |0 at the same time


Superposition

- Consider a 3 bit qubit register:

- An n qubit register states

If we attempt to retrieve the values represented within a superpo-sition, the superposition randomly collapses to represent just

one of the original values.

Data Representation


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 Lee9

Important single-qubit gates

X

Z

H

Quantum Computation

𝛼1|0>+𝛼2|1>¿

𝛼1|0>+𝛼2|1>¿

𝛼1|0>+𝛼2|1>¿

𝛼1|1>+𝛼2|0>¿

𝛼1|1>−𝛼2|0>¿

𝛼1¿0>+¿1> ¿√2

+𝛼2 ¿0>−∨1> ¿√2

¿¿


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 computing machines enable new algorithms that cannot be real-ised in a classical world.

- The algorithms can be powerful physical simulators.

- The physics determines the algorithm.

- Hardware

Conclusion

quantum mechanics(14/2) hongki lee biophotonics engineering laboratory school of electrical and...

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