1. Quantum Mechanics(14/2) Hongki Lee BIOPHOTONICS ENGINEERING LABORATORY School of Electrical and Electronic Engineering, Yonsei University Quantum Computing Hongki Lee

2. Quantum Mechanics(14/2) Hongki Lee Contents  Introduction and History  Data Representation  Quantum Computation  Conclusion

3. 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

4. Quantum Mechanics(14/2) Hongki Lee Introduction and History  History - 1982, Richard Feynman - 1985, David Deutsch - 1994, Peter Shor - 1997, Lov Grover

5. Quantum Mechanics(14/2) Hongki Lee Data Representation 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>. Excited State Ground State Nucleus Light pulse of frequency for time interval t Electron State |0>State |1>  Qubits

6. Quantum Mechanics(14/2) Hongki Lee Data Representation  Superposition A qubit in superposition is in both of the states |1> and |0 at the same time

7. Quantum Mechanics(14/2) Hongki Lee  Superposition If we attempt to retrieve the values represented within a superposition, the superposition randomly collapses to represent just one of the original values. Data Representation

8. 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

9. Quantum Mechanics(14/2) Hongki Lee 9 Important single-qubit gates X Z H Quantum Computation

10. Quantum Mechanics(14/2) Hongki Lee Quantum Computation  Quantum parallel computation -N physical qubits can encode 2 N binary numbers simultaneously -A quantum computer can process all 2 N 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

11. Quantum Mechanics(14/2) Hongki Lee -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 Conclusion