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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